diff --git a/.github/workflows/ci_optimizers.yml b/.github/workflows/ci_optimizers.yml
new file mode 100644
index 00000000..be7203df
--- /dev/null
+++ b/.github/workflows/ci_optimizers.yml
@@ -0,0 +1,39 @@
+# This workflow will install Python dependencies, run tests and lint with a variety of Python versions
+# For more information see: https://help.github.com/actions/language-and-framework-guides/using-python-with-github-actions
+
+name: Tequila-Test-Optimizers
+
+on:
+  push:
+    branches: [ master, devel ]
+  pull_request:
+    branches: [ master, devel ]
+
+jobs:
+
+  build:
+
+    runs-on: ubuntu-latest
+    strategy:
+      matrix:
+        python-version: [3.6, 3.7, 3.8]
+
+    steps:
+    - uses: actions/checkout@v2
+    - name: Set up Python ${{ matrix.python-version }}
+      uses: actions/setup-python@v1
+      with:
+        python-version: ${{ matrix.python-version }}
+    - name: Install quantum backends
+      run: |
+              pip install --upgrade cirq qiskit qulacs
+              
+    - name: Install and test GPyOpt interface (no qibo)
+      run: |  
+              python -m pip install --upgrade pip 
+              pip install --upgrade -r requirements.txt
+              pip install --upgrade -r requirements_gpyopt.txt
+              pip install -e .
+
+              pytest tests/test_gpyopt.py --slow
+
diff --git a/README.md b/README.md
index b89d0a81..41d53820 100644
--- a/README.md
+++ b/README.md
@@ -6,9 +6,9 @@ Tequila is an Extensible Quantum Information and Learning Architecture where the
 It operates on abstract data structures allowing the formulation, combination, automatic differentiation and optimization of generalized objectives.
 Tequila can execute the underlying quantum expectation values on state of the art simulators as well as on real quantum devices.
 
-[You can get an overview from this presentation](/docs/tequila.pdf)  
+[You can get an overview from this presentation](/docs/tequila.pdf) or from it's [video recording](https://www.youtube.com/watch?v=hUdf0P2fW2E)  
 
-[Get started with our Tutorials](/tutorials/)  
+[Get started with our Tutorials](https://github.com/aspuru-guzik-group/tequila-tutorials)  
 
 or checkout our [overview article](https://arxiv.org/abs/2011.03057)  
 
@@ -22,12 +22,23 @@ Currently supported
 
 Tequila detects backends automatically if they are installed on your systems.  
 All of them are available over standard pip installation like for example `pip install qulacs`.  
-For best performance tt is recommended to have `qulacs` installed.
+For best performance it is recommended to have `qulacs` installed.
 
 # QuantumChemistry:
-Tequila supports [Psi4](https://github.com/psi4/psi4).  
+Currently supported
+- [Psi4](https://github.com/psi4/psi4).  
 In a conda environment this can be installed with  
-`conda install psi4 -c psi4`
+```bash
+conda install psi4 -c psi4
+```
+Here is a small [tutorial](https://github.com/aspuru-guzik-group/tequila-tutorials/blob/main/Chemistry.ipynb) that illustrates the usage. 
+
+- [Madness](https://github.com/kottmanj/madness)  
+Currently you need to compile from a separate [fork](https://github.com/kottmanj/madness).  
+See the github page of this fork for installation instruction.  
+Note that the madness interface is currently only available on the `devel` branch of tequila (coming to master soon).  
+Here is a small [tutorial](https://github.com/aspuru-guzik-group/tequila-tutorials/blob/main/ChemistryMadnessInterface.ipynb) that illustrates the usage.  
+
 
 # Installation
 We recommend installing in editable mode with  
@@ -124,6 +135,10 @@ Quantum Computer-Aided design of Quantum Optics Hardware.
 [arxiv.org/abs/2006.03075](https://arxiv.org/abs/2006.03075)
 [example code](https://github.com/kottmanj/Photonic)  
 
+A. Anand, M. Degroote, A. Aspuru-Guzik.  
+Natural Evolutionary Strategies for Variational Quantum Computation.  
+[arxiv.org/abs/2012.00101](https://arxiv.org/abs/2012.00101)  
+
 Let us know, if you want your research project to be included in this list!
 
 # Dependencies
@@ -185,4 +200,5 @@ They can be installed for example over visual studio.
 Tequila runs on Macs OSX.  
 You might get in trouble with installing qulacs since it currently does not work with Apple's clang compiler.  
 You need to install latest GNU compile (at least gcc-7 and g++7) and set them as default before installing qulacs over pip.  
-
+## Qibo and GPyOpt
+Currently you can't use Qibo and GPyOpt within the same environment
diff --git a/requirements.txt b/requirements.txt
index 4c046f2c..2a665c29 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -6,7 +6,7 @@ jaxlib
 #autograd # use if jaxlib gives you trouble, make sure jax is uninstalled then
 setuptools 
 pytest
-openfermion
+openfermion <= 0.11*
 cmake # needed by qulacs, can be removed otherwise
 qulacs # default simulator, remove if the installation gives you trouble
 
@@ -16,3 +16,6 @@ qulacs # default simulator, remove if the installation gives you trouble
 #pyquil # you need to install the forest-sdk
 #qulacs-gpu
 #qibo <= 0.1.1
+
+#optional third party libraries
+#pyzx
diff --git a/src/tequila/__init__.py b/src/tequila/__init__.py
index e3b8caa9..30be3f8e 100644
--- a/src/tequila/__init__.py
+++ b/src/tequila/__init__.py
@@ -14,6 +14,8 @@
     INSTALLED_SAMPLERS, \
     INSTALLED_SIMULATORS, SUPPORTED_BACKENDS, INSTALLED_BACKENDS, show_available_simulators
 from tequila.wavefunction import QubitWaveFunction
+from tequila.circuit.qasm import export_open_qasm, import_open_qasm, import_open_qasm_from_file
+from tequila.circuit.pyzx import convert_to_pyzx, convert_from_pyzx
 import tequila.quantumchemistry as chemistry # shortcut
 from tequila.quantumchemistry import Molecule, MoleculeFromOpenFermion
 
diff --git a/src/tequila/circuit/_gates_impl.py b/src/tequila/circuit/_gates_impl.py
index 6230ee6d..257a230f 100644
--- a/src/tequila/circuit/_gates_impl.py
+++ b/src/tequila/circuit/_gates_impl.py
@@ -6,6 +6,7 @@
 from tequila.objective.objective import Variable, FixedVariable, assign_variable,Objective,VectorObjective
 from tequila.hamiltonian import PauliString, QubitHamiltonian, paulis
 from tequila.tools import list_assignment
+from numpy import pi
 
 from dataclasses import dataclass
 
@@ -30,11 +31,16 @@ def control(self):
 
     @property
     def qubits(self):
-        return self._qubits
+        # Set the active qubits
+        if self.control:
+            qubits = self.target + self.control
+        else:
+            qubits = self.target
+        return sorted(tuple(set(qubits)))
 
     @property
     def max_qubit(self):
-        return self._max_qubit
+        return self.compute_max_qubit()
 
     def extract_variables(self):
         return []
@@ -53,13 +59,6 @@ def __init__(self, name, target: UnionList, control: UnionList = None, generator
         self._target = tuple(list_assignment(target))
         self._control = tuple(list_assignment(control))
         self.finalize()
-        # Set the active qubits
-        if self.control:
-            self._qubits = self.target + self.control
-        else:
-            self._qubits = self.target
-        self._qubits = sorted(tuple(set(self._qubits)))
-        self._max_qubit = self.compute_max_qubit()
         self.generator = generator
 
     def copy(self):
@@ -96,6 +95,16 @@ def finalize(self):
             for c in self.target:
                 if c in self.control:
                     raise Exception("control and target are the same qubit: " + self.__str__())
+        if hasattr(self,"generator") and self.generator:
+            if set(list(self.generator.qubits)) != set(list(self.target)):
+                raise Exception("qubits of generator and targets don't agree -- mapping error?\n gate = {}".format(self.__str__()))
+        if hasattr(self, "generators"):
+            genq = []
+            for generator in self.generators:
+                genq += generator.qubits
+            if set(list(genq)) != set(list(self.target)):
+                raise Exception("qubits of generator and targets don't agree -- mapping error?\n gate = {}".format(self.__str__()))
+
 
     def __str__(self):
         result = str(self.name) + "(target=" + str(self.target)
@@ -131,14 +140,12 @@ def __eq__(self, other):
     def map_qubits(self, qubit_map: dict):
         mapped = copy.deepcopy(self)
         mapped._target = tuple([qubit_map[i] for i in self.target])
-        qubits = mapped._target
         if self.control is not None:
             mapped._control = tuple([qubit_map[i] for i in self.control])
-            qubits += mapped._control
-        mapped._qubits = sorted(tuple(set(qubits)))
-        mapped._max_qubit = mapped.compute_max_qubit()
-        if self.generator:
-            mapped.generator = self.generator.map_qubits(qubit_map)
+        if hasattr(self, "generator") and self.generator:
+            mapped.generator = self.generator.map_qubits(qubit_map=qubit_map)
+        if hasattr(self, "generators"):
+            mapped.generators = [i.map_qubits(qubit_map=qubit_map) for i in self.generators]
         mapped.finalize()
         return mapped
 
@@ -275,14 +282,35 @@ def __pow__(self, power, modulo=None):
 
 
 class PowerGateImpl(ParametrizedGateImpl):
+    """
+    Attributes
+    ---------
+    power
+        numeric type (fixed exponent) or hashable type (parametrized exponent)
+    parameter
+        power multiplied by pi
+        to be consitent with exp(-i a/2 G) representation [a: gate.parameter, G: gate.generator]
+    """
 
-    def __init__(self, name, target: list, power=None, control: list = None, generator: QubitHamiltonian = None):
-        super().__init__(name=name, parameter=power, target=target, control=control, generator=generator)
+    @property
+    def power(self):
+        return self._power
+
+    @power.setter
+    def power(self, other):
+        self._power = assign_variable(variable=other)
+
+    def __init__(self, name, target: list, power, control: list = None, generator: QubitHamiltonian = None):
+        super().__init__(name=name, parameter=power * pi, target=target, control=control, generator=generator)
+        self._power = assign_variable(variable=power)
 
     def dagger(self):
         result = copy.deepcopy(self)
+        result._parameter = assign_variable(-self.parameter)
+        result._power = assign_variable(-self.power)
         return result
 
+
 class GeneralizedRotationImpl(DifferentiableGateImpl):
     """
     A gate which behaves like a generalized rotation
@@ -428,8 +456,3 @@ def dagger(self):
             angles.append(-angle)
         result.angles = angles
         return result
-
-    def map_qubits(self, qubit_map: dict):
-        mapped = super().map_qubits(qubit_map=qubit_map)
-        mapped.generators = [generator.map_qubits(qubit_map=qubit_map) for generator in mapped.generators]
-        return mapped
diff --git a/src/tequila/circuit/compiler.py b/src/tequila/circuit/compiler.py
index f8295dae..634c90b0 100644
--- a/src/tequila/circuit/compiler.py
+++ b/src/tequila/circuit/compiler.py
@@ -1,6 +1,6 @@
 from tequila import TequilaException
 from tequila.circuit.circuit import QCircuit
-from tequila.circuit.gates import Rx, Ry, H, X, Rz, ExpPauli, CNOT, Phase, T, Z, Y
+from tequila.circuit.gates import Rx, Ry, H, X, Rz, ExpPauli, CNOT, Phase, T, Z, Y, S, CX
 from tequila.circuit._gates_impl import RotationGateImpl, PhaseGateImpl, QGateImpl, \
     ExponentialPauliGateImpl, TrotterizedGateImpl, PowerGateImpl
 from tequila.utils import to_float
@@ -54,7 +54,10 @@ def __init__(self,
                  controlled_rotation=False,
                  swap=False,
                  cc_max=False,
-                 gradient_mode=False
+                 gradient_mode=False,
+                 ry_gate=False,
+                 y_gate=False,
+                 ch_gate=False
                  ):
 
         """
@@ -93,6 +96,12 @@ def __init__(self,
             whether or not to break down swap gates into CNOT gates.
         cc_max:
             whether or not to break down all controlled gates with 2 or more controls.
+        ry_gate:
+            whether or not to break down all rotational y gates
+        y_gate:
+            whether or not to break down all y gates
+        ch_gate:
+            whether or not to break down all controlled-H gates
         """
         self.multitarget = multitarget
         self.multicontrol = multicontrol
@@ -111,6 +120,9 @@ def __init__(self,
         self.swap = swap
         self.cc_max = cc_max
         self.gradient_mode = gradient_mode
+        self.ry_gate = ry_gate
+        self.y_gate = y_gate
+        self.ch_gate = ch_gate
 
     def __call__(self, objective: typing.Union[Objective, QCircuit, ExpectationValueImpl], variables=None, *args,
                  **kwargs):
@@ -269,33 +281,35 @@ def compile_circuit(self, abstract_circuit: QCircuit, variables=None, *args, **k
             if self.multicontrol:
                 raise NotImplementedError("Multicontrol compilation does not work yet")
 
-            if self.hadamard_power:
-                cg = compile_h_power(gate=cg)
             if self.phase_to_z:
                 cg = compile_phase_to_z(gate=cg)
             if self.power:
                 cg = compile_power_gate(gate=cg)
             if self.phase:
                 cg = compile_phase(gate=cg)
+            if self.ch_gate:
+                cg = compile_ch(gate=cg)
+            if self.y_gate:
+                cg = compile_y(gate=cg)
+            if self.ry_gate:
+                cg = compile_ry(gate=cg, controlled_rotation=self.controlled_rotation)
             if controlled:
                 if self.cc_max:
-                    cg = compile_to_cc(gate=cg)
+                    cg = compile_to_single_control(gate=cg)
                 if self.controlled_exponential_pauli:
                     cg = compile_exponential_pauli_gate(gate=cg)
-                if self.hadamard_power:
-                    cg = compile_h_power(gate=cg)
                 if self.controlled_power:
-                    cg = compile_power_gate(gate=cg)
+                    cg = compile_controlled_power(gate=cg)
                 if self.controlled_phase:
                     cg = compile_controlled_phase(gate=cg)
+                    if self.phase:
+                        cg = compile_phase(gate=cg)
                 if self.toffoli:
                     cg = compile_toffoli(gate=cg)
                     if self.phase:
                         cg = compile_phase(gate=cg)
                 if self.controlled_rotation:
                     cg = compile_controlled_rotation(gate=cg)
-                if self.cc_max:
-                    cg = compile_to_cc(gate=cg)
 
             compiled_gates.append((idx, cg))
 
@@ -351,7 +365,7 @@ def wrapper(gate, **kwargs):
     return wrapper
 
 
-def change_basis(target, axis, daggered=False):
+def change_basis(target, axis=None, name=None, daggered=False):
     """
     helper function; returns circuit that performs change of basis.
     Parameters
@@ -368,6 +382,19 @@ def change_basis(target, axis, daggered=False):
     QCircuit that performs change of basis on target qubit onto desired axis
 
     """
+    if axis is None and name is None:
+        raise TequilaException('axis or name must be given.')
+
+    if name:
+        name = name.lower()
+        if name in ['h', 'hadamard'] and daggered:
+            return Ry(angle=numpy.pi / 4, target=target)
+        elif name in ['h', 'hadamard']:
+            return Ry(angle=-numpy.pi / 4, target=target)
+        else:
+            name_to_axis = {'rx': 0, 'ry': 1, 'rz': 2}
+            axis = name_to_axis.get(name, name)
+
     if isinstance(axis, str):
         axis = RotationGateImpl.string_to_axis[axis.lower()]
 
@@ -420,13 +447,21 @@ def compile_multitarget(gate, variables=None) -> QCircuit:
     return result
 
 
+# return index of control qubits in Gray Code order.
+def _pattern(n):
+    if n == 1:
+        return [0]
+    pn = _pattern(n - 1)
+
+    return pn + [n - 1] + pn
+
+
 @compiler
-def compile_controlled_rotation(gate: RotationGateImpl, angles: list = None) -> QCircuit:
+def compile_controlled_rotation(gate: RotationGateImpl) -> QCircuit:
     """
     Recompilation of a controlled-rotation gate
     Basis change into Rz then recompilation of controled Rz, then change basis back
     :param gate: The rotational gate
-    :param angles: new angles to set, given as a list of two. If None the angle in the gate is used (default)
     :return: set of gates wrapped in QCircuit class
     """
 
@@ -436,20 +471,22 @@ def compile_controlled_rotation(gate: RotationGateImpl, angles: list = None) ->
     if not isinstance(gate, RotationGateImpl):
         return QCircuit.wrap_gate(gate)
 
-    if angles is None:
-        angles = [gate.parameter / 2, -gate.parameter / 2]
-
     if len(gate.target) > 1:
-        return compile_controlled_rotation(gate=compile_multitarget(gate=gate), angles=angles)
+        return compile_controlled_rotation(gate=compile_multitarget(gate=gate))
 
     target = gate.target
     control = gate.control
+    k = len(control)
+    cind = _pattern(k) + [k - 1]
+
     result = QCircuit()
     result += change_basis(target=target, axis=gate._axis)
-    result += RotationGateImpl(axis="z", target=target, angle=angles[0])
-    result += QGateImpl(name="X", target=target, control=control)
-    result += RotationGateImpl(axis="Z", target=target, angle=angles[1])
-    result += QGateImpl(name="X", target=target, control=control)
+    coeff = - 1 / pow(2, k)
+    for i, ci in enumerate(cind):
+        coeff *= -1
+
+        result += Rz(target=target, angle=coeff * gate.parameter)
+        result += CNOT(control[ci], target)
     result += change_basis(target=target, axis=gate._axis, daggered=True)
 
     result.n_qubits = result.max_qubit() + 1
@@ -457,9 +494,9 @@ def compile_controlled_rotation(gate: RotationGateImpl, angles: list = None) ->
 
 
 @compiler
-def compile_to_cc(gate) -> QCircuit:
+def compile_to_single_control(gate) -> QCircuit:
     """
-    break down a gate into a sequence with no more than double-controlled gates.
+    break down a gate into a sequence with no more than single-controlled gates.
     Parameters
     ----------
     gate:
@@ -474,7 +511,7 @@ def compile_to_cc(gate) -> QCircuit:
     cl = len(gate.control)
     target = gate.target
     control = gate.control
-    if cl <= 2:
+    if cl <= 1:
         return QCircuit.wrap_gate(gate)
     name = gate.name
     back = QCircuit()
@@ -484,13 +521,14 @@ def compile_to_cc(gate) -> QCircuit:
         else:
             power = 1.0
         new = PowerGateImpl(name=name, power=power, target=target, control=control)
-        back += compile_power_gate(gate=new, cut=True)
+        partial = compile_power_gate(gate=new)
+        back += compile_to_single_control(gate=partial)
     elif isinstance(gate, RotationGateImpl):
         partial = compile_controlled_rotation(gate=gate)
-        back += compile_to_cc(gate=partial)
+        back += compile_to_single_control(gate=partial)
     elif isinstance(gate, PhaseGateImpl):
         partial = compile_controlled_phase(gate=gate)
-        back += compile_to_cc(gate=partial)
+        back += compile_to_single_control(gate=partial)
     else:
         print(gate)
         raise TequilaException('frankly, what the fuck is this gate?')
@@ -538,7 +576,7 @@ def compile_toffoli(gate) -> QCircuit:
 
 
 @compiler
-def compile_power_gate(gate, cut=False) -> QCircuit:
+def compile_power_gate(gate) -> QCircuit:
     """
     break down power gates into the rotation gates.
     Parameters
@@ -552,83 +590,16 @@ def compile_power_gate(gate, cut=False) -> QCircuit:
     """
     if not isinstance(gate, PowerGateImpl):
         return QCircuit.wrap_gate(gate)
-    if gate.name.lower() in ['h', 'hadamard']:
-        return QCircuit.wrap_gate(gate=gate)
     if not gate.is_controlled():
         return compile_power_base(gate=gate)
 
-    return power_recursor(gate=gate, cut=cut)
-
-
-@compiler
-def power_recursor(gate, cut=False) -> QCircuit:
-    """
-    recursive function for decomposing parametrized, possibly controlled, power gates.
-    Parameters
-    ----------
-    gate:
-        the gate.
-    cut: bool:
-        whether or not to stop recursion at 2 controls maximum.
-        Default: False.
-    Returns
-    -------
-        A QCircuit; the result of compilation.
-    """
-
-    result = QCircuit()
-    cl = 0
-    if gate.is_controlled():
-        cl = len(gate.control)
-    if cl == 0:
-        return compile_power_base(gate=gate)
-    elif cl == 1:
-        return get_axbxc_decomp(gate=gate)
-
-    elif cl == 2 and not cut:
-        v = type(gate)(name=gate.name, power=gate.parameter / 2, target=gate.target, control=gate.control[1])
-        result += get_axbxc_decomp(v)
-        result += CNOT(gate.control[0], gate.control[1])
-        vdag = type(gate)(name=gate.name, power=gate.parameter / 2, target=gate.target,
-                          control=gate.control[1]).dagger()
-        result += get_axbxc_decomp(vdag)
-        result += CNOT(gate.control[0], gate.control[1])
-        again = type(gate)(name=gate.name, power=gate.parameter / 2, target=gate.target, control=gate.control[0])
-        result += get_axbxc_decomp(again)
-
-    elif cl == 2 and cut:
-        if gate.name in ['CCx', 'CCNOT', 'CCX', 'X']:
-            return QCircuit.wrap_gate(gate)
-        else:
-            v = type(gate)(name=gate.name, power=gate.parameter / 2, target=gate.target, control=gate.control[1])
-            result += get_axbxc_decomp(v)
-            result += CNOT(gate.control[0], gate.control[1])
-            vdag = type(gate)(name=gate.name, power=gate.parameter / 2, target=gate.target,
-                              control=gate.control[1]).dagger()
-            result += get_axbxc_decomp(vdag)
-            result += CNOT(gate.control[0], gate.control[1])
-            again = type(gate)(name=gate.name, power=gate.parameter / 2, target=gate.target, control=gate.control[0])
-            result += get_axbxc_decomp(again)
-
-    else:
-        v = type(gate)(name=gate.name, power=gate.parameter / 2, target=gate.target, control=gate.control[-1])
-        result += get_axbxc_decomp(v)
-        result += CNOT(target=gate.control[cl - 1], control=gate.control[0:cl - 1])
-        vdag = type(gate)(name=gate.name, power=gate.parameter / 2, target=gate.target,
-                          control=gate.control[-1]).dagger()
-        result += get_axbxc_decomp(vdag)
-        result += CNOT(target=gate.control[cl - 1], control=gate.control[0:cl - 1])
-        rebuild = type(gate)(name=gate.name, power=gate.parameter / 2, target=gate.target,
-                             control=gate.control[:cl - 1])
-        result += power_recursor(gate=rebuild, cut=cut)
-
-    return result
+    return compile_controlled_power(gate=gate)
 
 
 @compiler
 def compile_power_base(gate):
     """
-    Base case of power_recursor: convert a 1-qubit parametrized power gate into rotation gates.
+    Base case of compile_power_gate: convert a 1-qubit parametrized power gate into rotation gates.
     Parameters
     ----------
     gate:
@@ -640,10 +611,20 @@ def compile_power_base(gate):
     """
     if not isinstance(gate, PowerGateImpl):
         return QCircuit.wrap_gate(gate)
-    power = gate.parameter
-    if gate.name in ['H', 'h', 'Hadamard', 'hadamard']:
-        return compile_h_power(gate=gate)
-    if gate.name == 'X':
+
+    if gate.is_controlled():
+        return QCircuit.wrap_gate(gate)
+
+    power = gate.power
+    if gate.name.lower() in ['h', 'hadamard']:
+        ### off by global phase of Exp[ pi power /2]
+        theta = power * numpy.pi
+
+        result = QCircuit()
+        result += Ry(angle=-numpy.pi / 4, target=gate.target)
+        result += Rz(angle=theta, target=gate.target)
+        result += Ry(angle=numpy.pi / 4, target=gate.target)
+    elif gate.name == 'X':
         ### off by global phase of Exp[ pi power /2]
         '''
         if we wanted to do it formally we would use the following
@@ -676,362 +657,36 @@ def compile_power_base(gate):
 
 
 @compiler
-def get_axbxc_decomp(gate):
-    """
-    Break down single controlled parametrized power gates into CNOT and rotations.
-    Parameters
-    ----------
-    gate:
-        the gate.
-
-    Returns
-    -------
-    QCircuit; the result of compilation.
-    """
-
-    if not isinstance(gate, PowerGateImpl) or gate.name not in ['X', 'Y', 'Z']:
-        return QCircuit.wrap_gate(gate)
-    power = gate.parameter
-    target = gate.target
-    result = QCircuit()
-    if gate.name == 'X':
-        a = -numpy.pi / 2
-        b = numpy.pi / 2
-        theta = power * numpy.pi
-
-        '''
-        result+=Phase(numpy.pi*power/2,gate.control)
-        result+=Rz(-(a-b)/2,target)
-        result+=CNOT(gate.control,target)
-        #result+=Rz(-(a+b)/2,target)
-        result+=Ry(-theta/2,target)
-        result+=CNOT(gate.control,target)
-        result+=Ry(theta/2,target)
-        result+=Rz(a,target=target)
-        '''
-
-        '''
-        result+=Rz((a-b)/2,target)
-        result+=CNOT(gate.control,target)
-        #result+=Rz(-(a+b)/2,target)
-        result+=Ry(-theta/2,target)
-        result+=CNOT(gate.control,target)
-        result+=Ry(theta/2,target)
-        result+=Rz(a,target)
-        result += Phase(numpy.pi * power / 2, gate.control)
-        '''
-        result += Rx(angle=theta, target=target, control=gate.control)
-        result += Phase(numpy.pi * power / 2, gate.control)
-
-    elif gate.name == 'Y':
-        ### off by global phase of Exp[ pi power /2]
-
-        theta = power * numpy.pi
-
-        '''
-        result+=Phase(numpy.pi*power/2,gate.control)
-        result+=CNOT(gate.control,target)
-        result+=Ry(-theta/2,target)
-        result+=CNOT(gate.control,target)
-        result+=Ry(theta/2,target)
-        '''
-        a = 0
-        b = 0
-        # result+=Rz((a-b)/2,target)
-        result += CNOT(gate.control, target)
-        # result+=Rz(-(a+b)/2,target)
-        result += Ry(-theta / 2, target)
-        result += CNOT(gate.control, target)
-        result += Ry(theta / 2, target)
-        # result+=Rz(a,target)
-        result += Phase(numpy.pi * power / 2, gate.control)
-
-
-
-    elif gate.name == 'Z':
-        a = 0
-        b = power * numpy.pi
-        theta = 0
-
-        result += Rz(b / 2, target)
-        result += CNOT(gate.control, target)
-        result += Rz(-b / 2, target)
-        result += CNOT(gate.control, target)
-        # result+=Rz(a,target)
-        result += Phase(numpy.pi * power / 2, gate.control)
-
-        '''
-        result+=Rz(b/2,target)
-        result+=CNOT(gate.control,target)
-        result+=Rz(-b/2,target)
-        result+=CNOT(gate.control,target)
-        '''
-    return result
-
-
-@compiler
-def compile_h_power(gate) -> QCircuit:
+def compile_controlled_power(gate: PowerGateImpl) -> QCircuit:
     """
-    compile hadamard to some power.
-    Parameters
-    ----------
-    gate:
-        the gate.
-
-    Returns
-    -------
-    QCircuit, the result of compilation.
+    Recompilation of a controlled-power gate
+    Basis change into Z then recompilation of controled Z, then change basis back
+    :param gate: The power gate
+    :return: set of gates wrapped in QCircuit class
     """
-    if not isinstance(gate, PowerGateImpl) or gate.name not in ['H', 'h', 'hadamard']:
-        return QCircuit.wrap_gate(gate)
-
     if not gate.is_controlled():
-        return hadamard_base(gate=gate)
-    return hadamard_recursor(gate=gate)
-
-
-@compiler
-def hadamard_base(gate) -> QCircuit:
-    """
-    base case for hadamard compilation; returns powers of hadamard as sequence of single qubit rotations.
-    Parameters
-    ----------
-    gate:
-        the gate.
-
-    Returns
-    -------
-        A QCircuit; the result of compilation.
-    """
-    if not isinstance(gate, PowerGateImpl) or gate.name not in ['H', 'h', 'hadamard']:
         return QCircuit.wrap_gate(gate)
-    power = gate.parameter
-    a = power.wrap(a_calc)
-    b = power.wrap(b_calc)
-    theta = power.wrap(theta_calc)
-
-    result = QCircuit()
 
-    result += Rz(angle=b, target=gate.target)
-    result += Ry(angle=theta, target=gate.target)
-    result += Rz(angle=a, target=gate.target)
-
-    return result
-
-
-@compiler
-def hadamard_axbxc(gate) -> QCircuit:
-    """
-    Decompose 1 control parametrized hadamard into single qubit rotation and CNOT.
-    Parameters
-    ----------
-    gate:
-        the gate
-
-    Returns
-    -------
-    QCircuit, the result of compilation.
-    """
-    if not isinstance(gate, PowerGateImpl) or gate.name not in ['H', 'h', 'hadamard']:
+    if not isinstance(gate, PowerGateImpl):
         return QCircuit.wrap_gate(gate)
-    power = gate.parameter
-    target = gate.target
-    a = power.wrap(a_calc)
-    b = power.wrap(b_calc)
-    theta = power.wrap(theta_calc)
-    phase = power * jnp.pi / 2
-
-    result = QCircuit()
 
-    result += Rz((a - b) / 2, target)
-    result += CNOT(gate.control, target)
-    result += Rz(-(a + b) / 2, target)
-    result += Ry(-theta / 2, target)
-    result += CNOT(gate.control, target)
-    result += Ry(theta / 2, target)
-    result += Rz(a, target)
-    result += Phase(numpy.pi * power / 2, gate.control)
-
-    return result
-
-
-@compiler
-def hadamard_recursor(gate) -> QCircuit:
-    """
-    recursive function for decomposing parametrized hadamard, potentially with controls.
-    Parameters
-    ----------
-    gate:
-        the gate.
-
-    Returns
-    -------
-    QCircuit, the result of compilation.
+    if len(gate.target) > 1:
+        return compile_controlled_power(gate=compile_multitarget(gate=gate))
 
-    """
+    power = gate.power
+    target = gate.target
+    control = gate.control
 
-    if not isinstance(gate, PowerGateImpl) or gate.name not in ['H', 'h', 'hadamard']:
-        return QCircuit.wrap_gate(gate)
     result = QCircuit()
-    cl = 0
-    if gate.is_controlled():
-        cl = len(gate.control)
-    if cl == 0:
-        return hadamard_base(gate)
-    if cl == 1:
-        return hadamard_axbxc(gate)
-
-    if cl == 2:
-        v = type(gate)(name=gate.name, power=gate.parameter / 2, target=gate.target, control=gate.control[1])
-        result += hadamard_axbxc(v)
-        result += CNOT(gate.control[0], gate.control[1])
-        vdag = type(gate)(name=gate.name, power=gate.parameter / 2, target=gate.target,
-                          control=gate.control[1]).dagger()
-        result += hadamard_axbxc(vdag)
-        result += CNOT(gate.control[0], gate.control[1])
-        again = type(gate)(name=gate.name, power=gate.parameter / 2, target=gate.target, control=gate.control[0])
-        result += hadamard_axbxc(again)
+    result += Phase(target=control[0], control=control[1:], phi=power * pi / 2)
+    result += change_basis(target=target, name=gate.name)
+    result += Rz(target=target, control=control, angle=power * pi)
+    result += change_basis(target=target, name=gate.name, daggered=True)
 
-    else:
-        v = type(gate)(name=gate.name, power=gate.parameter / 2, target=gate.target, control=gate.control[-1])
-        result += hadamard_axbxc(v)
-        result += CNOT(target=gate.control[cl - 1], control=gate.control[0:cl - 1])
-        vdag = type(gate)(name=gate.name, power=gate.parameter / 2, target=gate.target,
-                          control=gate.control[-1]).dagger()
-        result += hadamard_axbxc(vdag)
-        result += CNOT(target=gate.control[cl - 1], control=gate.control[0:cl - 1])
-        rebuild = type(gate)(name=gate.name, power=gate.parameter / 2, target=gate.target,
-                             control=gate.control[:cl - 1])
-        result += hadamard_recursor(rebuild)
+    result.n_qubits = result.max_qubit() + 1
     return result
 
 
-def exp(x):
-    """
-    helper for hadamard decomp.
-    """
-    return jnp.exp(1j * pi * x)
-
-
-def root_exp(x):
-    """
-    helper for hadamard decomp.
-    """
-    return jnp.sqrt(exp(x))
-
-
-def neg_half_exp(x):
-    """
-    helper for hadamard decomp.
-    """
-    return jnp.exp(-1j * pi * x / 2)
-
-
-def exp_min_1(x):
-    """
-    helper for hadamard decomp.
-    """
-    return exp(x) - 1
-
-
-def top_a(x):
-    """
-    helper for hadamard decomp.
-    """
-    return root_exp(x) * exp_min_1(x) * neg_half_exp(x)
-
-
-def under_right(x):
-    """
-    helper for hadamard decomp.
-    """
-    return 3 + 2 * jnp.sqrt(2) + exp(x)
-
-
-def bottom(x):
-    """
-    helper for hadamard decomp.
-    """
-    return jnp.sqrt(exp_min_1(x) * under_right(x))
-
-
-def my_cosecant(x):
-    """
-    helper for hadamard decomp.
-    """
-    return 1 / jnp.sin(pi * x / 2)
-
-
-def back_log_in(x):
-    """
-    helper for hadamard decomp.
-    """
-    return -1 + 2 * (my_cosecant(x) ** 2)
-
-
-def first_log_a(x):
-    """
-    helper for hadamard decomp.
-    """
-    return 4 * jnp.log(top_a(x) / bottom(x))
-
-
-def second_log_a(x):
-    """
-    helper for hadamard decomp.
-    """
-    return jnp.log(back_log_in(x))
-
-
-def a_calc(x):
-    """
-    helper for hadamard decomp.
-    """
-    return jnp.real((-(0.5) * 1j * (2 * jnp.arcsinh(1) + first_log_a(x) + second_log_a(x))))
-
-
-def top_right_in(x):
-    """
-    helper for hadamard decomp.
-    """
-    return ((3 + jnp.cos(pi * x)) * (jnp.sin(pi * x / 2) ** 2)) ** (1 / 4)
-
-
-def top_b(x):
-    """
-    helper for hadamard decomp.
-    """
-    return -(2 ** (3 / 4)) * root_exp(x) * top_right_in(x)
-
-
-def log_b(x):
-    """
-    helper for hadamard decomp.
-    """
-    return 2 * jnp.log(top_b(x) / bottom(x))
-
-
-def b_calc(x):
-    """
-    helper for hadamard decomp.
-    """
-    return jnp.real((-1j * (jnp.arcsinh(1) + log_b(x))))
-
-
-def in_the_arc(x):
-    """
-    helper for hadamard decomp.
-    """
-    return -2 / (jnp.sqrt(3 + jnp.cos(pi * x)))
-
-
-def theta_calc(x):
-    """
-    helper for hadamard decomp.
-    """
-    return jnp.real(2 * jnp.arccos(1 / in_the_arc(x)))
-
-
 @compiler
 def compile_phase(gate) -> QCircuit:
     """
@@ -1052,18 +707,15 @@ def compile_phase(gate) -> QCircuit:
     if len(gate.control) == 0:
         return Rz(angle=phase, target=gate.target)
 
-    if len(gate.control) == 1:
-        result += Rz(angle=phase / 2, target=gate.control, control=None)
-        result += Rz(angle=phase, target=gate.target, control=gate.control)
-        return result
-    else:
-        return compile_controlled_phase(gate)
+    result = compile_controlled_phase(gate)
+    result = compile_phase(result)
+    return result
 
 
 @compiler
-def compile_phase_to_z(gate) -> QCircuit:
+def compile_controlled_phase(gate) -> QCircuit:
     """
-    Compile phase gate to parametrized Z gate.
+    Compile multi-controlled phase gates to 1q - phase gate and multi-controlled Rz gates.
     Parameters
     ----------
     gate:
@@ -1072,18 +724,25 @@ def compile_phase_to_z(gate) -> QCircuit:
     Returns
     -------
     QCircuit, the result of compilation.
-
     """
     if not isinstance(gate, PhaseGateImpl):
         return QCircuit.wrap_gate(gate)
+
+    if len(gate.control) == 0:
+        return QCircuit.wrap_gate(gate)
+
     phase = gate.parameter
-    return Z(power=phase / pi, target=gate.target, control=gate.control)
+
+    result = QCircuit()
+    result += Phase(target=gate.control[0], control=gate.control[1:], phi=phase / 2)
+    result += Rz(target=gate.target, control=gate.control, angle=phase)
+    return compile_controlled_phase(result)
 
 
 @compiler
-def compile_controlled_phase(gate) -> QCircuit:
+def compile_phase_to_z(gate) -> QCircuit:
     """
-    Compile multi-controlled phase gates.
+    Compile phase gate to parametrized Z gate.
     Parameters
     ----------
     gate:
@@ -1092,31 +751,12 @@ def compile_controlled_phase(gate) -> QCircuit:
     Returns
     -------
     QCircuit, the result of compilation.
+
     """
     if not isinstance(gate, PhaseGateImpl):
         return QCircuit.wrap_gate(gate)
-    if len(gate.control) == 0:
-        return QCircuit.wrap_gate(gate)
-    count = len(gate.control)
-    result = QCircuit()
     phase = gate.parameter
-
-    if count == 1:
-        result += H(target=gate.target)
-        result += CNOT(gate.control, gate.target)
-        result += H(target=gate.target)
-        result += Phase(gate.parameter + numpy.pi, target=gate.target)
-    elif count == 2:
-        result += Rz(angle=phase / (2 ** 2), target=gate.control[0])
-        result += Rz(angle=phase / (2 ** (1)), target=gate.control[1], control=gate.control[0])
-        result += Rz(angle=phase, target=gate.target, control=gate.control)
-
-    elif count >= 3:
-        result += Rz(angle=phase / (2 ** count), target=gate.control[0])
-        for i in range(1, count):
-            result += Rz(angle=phase / (2 ** (count - i)), target=gate.control[i], control=gate.control[0:i])
-        result += Rz(angle=phase, target=gate.target, control=gate.control)
-    return result
+    return Z(power=phase / pi, target=gate.target, control=gate.control)
 
 
 @compiler
@@ -1135,15 +775,16 @@ def compile_swap(gate) -> QCircuit:
     if gate.name.lower() == "swap":
         if len(gate.target) != 2:
             raise TequilaCompilerException("SWAP gates needs two targets")
-        if hasattr(gate, "power") and gate.parameter != 1:
-            raise TequilaCompilerException("SWAP gate with power can not be compiled into CNOTS")
+        power = 1
+        if hasattr(gate, "power"):
+            power = gate.power
 
         c = []
         if gate.control is not None:
             c = gate.control
-        return X(target=gate.target[0], control=[gate.target[1]] + list(c)) \
-               + X(target=gate.target[1], control=[gate.target[0]] + list(c)) \
-               + X(target=gate.target[0], control=[gate.target[1]] + list(c))
+        return X(target=gate.target[0], control=[gate.target[1]]) \
+               + X(target=gate.target[1], control=[gate.target[0]] + list(c), power=power) \
+               + X(target=gate.target[0], control=[gate.target[1]])
 
     else:
         return QCircuit.wrap_gate(gate)
@@ -1223,11 +864,11 @@ def do_compile_trotterized_gate(generator, steps, factor, randomize, control):
         if randomize:
             numpy.random.shuffle(paulistrings)
         for ps in paulistrings:
-            if len(ps._data) == 0:
-                print("ignoring constant term in trotterized gate")
-                continue
             coeff = to_float(ps.coeff)
-            circuit += ExpPauli(paulistring=ps.naked(), angle=factor * coeff, control=control)
+            if len(ps._data) == 0 and len(control) > 0:
+                circuit += Phase(target=control[0], control=control[1:], phi=-factor * coeff / 2)
+            else:
+                circuit += ExpPauli(paulistring=ps.naked(), angle=factor * coeff, control=control)
 
     return circuit
 
@@ -1296,3 +937,76 @@ def compile_trotterized_gate(gate, compile_exponential_pauli: bool = False):
         return compile_exponential_pauli_gate(result)
     else:
         return result
+
+
+@compiler
+def compile_ry(gate: RotationGateImpl, controlled_rotation: bool = False) -> QCircuit:
+    """
+    Compile Ry gates into Rx and Rz.
+    Parameters
+    ----------
+    gate:
+        the gate.
+    controlled_rotation:
+        determines if the decomposition of the controlled-Ry gate will be performed in compile_controlled_rotation,
+        if not, decomposition will be performed here
+
+    Returns
+    -------
+    QCircuit, the result of compilation.
+    """
+    if gate.name.lower() == "ry":
+
+        if not (gate.is_controlled() and controlled_rotation):
+
+            return Rz(target=gate.target, control=None, angle=-numpy.pi / 2) \
+                   + Rx(target=gate.target, control=gate.control, angle=gate.parameter) \
+                   + Rz(target=gate.target, control=None, angle=numpy.pi / 2)
+
+    return QCircuit.wrap_gate(gate)
+
+
+@compiler
+def compile_y(gate) -> QCircuit:
+    """
+    Compile Y gates into X and Rz.
+    Parameters
+    ----------
+    gate:
+        the gate.
+
+    Returns
+    -------
+    QCircuit, the result of compilation.
+    """
+    if gate.name.lower() == "y":
+
+        return Rz(target=gate.target, control=None, angle=-numpy.pi / 2) \
+               + X(target=gate.target, control=gate.control, power=gate.parameter if gate.is_parametrized() else None) \
+               + Rz(target=gate.target, control=None, angle=numpy.pi / 2)
+
+    else:
+        return QCircuit.wrap_gate(gate)
+
+
+@compiler
+def compile_ch(gate: QGateImpl) -> QCircuit:
+    """
+    Compile CH gates into its equivalent:
+        CH = Ry(0.25pi) CZ Ry(-0.25pi)
+    Parameters
+    ----------
+    gate:
+        the gate.
+
+    Returns
+    -------
+    QCircuit, the result of compilation.
+    """
+    if gate.name.lower() == "h" and gate.is_controlled():
+
+        return Ry(target=gate.target, control=None, angle=-numpy.pi / 4) \
+               + Z(target=gate.target, control=gate.control, power=gate.parameter if gate.is_parametrized() else None) \
+               + Ry(target=gate.target, control=None, angle=numpy.pi / 4)
+    else:
+        return QCircuit.wrap_gate(gate)
\ No newline at end of file
diff --git a/src/tequila/circuit/gates.py b/src/tequila/circuit/gates.py
index 510e97d5..0f40c191 100644
--- a/src/tequila/circuit/gates.py
+++ b/src/tequila/circuit/gates.py
@@ -688,6 +688,177 @@ def CRz(control: int, target: int, angle: float) -> QCircuit:
     return Rz(target=target, control=control, angle=angle)
 
 
+def U(theta, phi, lambd, target: typing.Union[list, int], control: typing.Union[list, int] = None) -> QCircuit:
+    """
+    Notes
+    ----------
+    Convenient gate, one of the abstract gates defined by OpenQASM.
+
+    .. math::
+        U(\\theta, \\phi, \\lambda) = R_z(\\phi)R_x(-\\pi/2)R_z(\\theta)R_x(\\pi/2)R_z(\\lambda)
+        U(\\theta, \\phi, \\lambda) = \\begin{pmatrix}
+                                            e^{-i \\frac{\\phi}{2}} & 0 \\\\
+                                            0 & e^{i \\frac{\\phi}{2}}
+                                        \\end{pmatrix}
+                                        \\begin{pmatrix}
+                                            \\cos{-\\frac{\\pi}{4}} & -i \\sin{-\\frac{\\pi}{4}} \\\\
+                                            -i \\sin{-\\frac{\\pi}{4}} & \\cos{-\\frac{\\pi}{4}}
+                                        \\end{pmatrix}
+                                        \\begin{pmatrix}
+                                            e^{-i \\frac{\\theta}{2}} & 0 \\\\
+                                            0 & e^{i \\frac{\\theta}{2}}
+                                        \\end{pmatrix}
+                                        \\begin{pmatrix}
+                                            \\cos{\\frac{\\pi}{4}} & -i \\sin{\\frac{\\pi}{4}} \\\\
+                                            -i \\sin{\\frac{\\pi}{4}} & \\cos{\\frac{\\pi}{4}}
+                                        \\end{pmatrix}
+                                        \\begin{pmatrix}
+                                            e^{-i \\frac{\\lambda}{2}} & 0 \\\\
+                                            0 & e^{i \\frac{\\lambda}{2}}
+                                        \\end{pmatrix}
+
+        U(\\theta, \\phi, \\lambda) = \\begin{pmatrix}
+                                        \\cos{\\frac{\\theta}{2}} &
+                                        -e^{i \\lambda} \\sin{\\frac{\\theta}{2}} \\\\
+                                        e^{i \\phi} \\sin{\\frac{\\theta}{2}} &
+                                        e^{i (\\phi+\\lambda)} \\cos{\\frac{\\theta}{2}}
+                                      \\end{pmatrix}
+
+    Parameters
+    ----------
+    theta
+        first parameter angle
+    phi
+        second parameter angle
+    lamnd
+        third parameter angle
+    target
+        int or list of int
+    control
+        int or list of int
+
+    Returns
+    -------
+    QCircuit object
+    """
+
+    theta = assign_variable(theta)
+    phi = assign_variable(phi)
+    lambd = assign_variable(lambd)
+    pi_half = assign_variable(np.pi / 2)
+
+    return Rz(angle=lambd, target=target, control=control) + \
+           Rx(angle=pi_half, target=target, control=control) + \
+           Rz(angle=theta, target=target, control=control) + \
+           Rx(angle=-pi_half, target=target, control=control) + \
+           Rz(angle=phi, target=target, control=control)
+
+
+def u1(lambd, target: typing.Union[list, int], control: typing.Union[list, int] = None) -> QCircuit:
+    """
+    Notes
+    ----------
+    Convenient gate, one of the abstract gates defined by Quantum Experience Standard Header.
+    Changes the phase of a carrier without applying any pulses.
+
+    .. math::
+        from OpenQASM 2.0 specification:
+            u1(\\lambda) \\sim U(0, 0, \\lambda) = R_z(\\lambda) = e^{-i\\frac{\\lambda}{2} \\sigma_{z}}
+        also is equal to:
+            u1(\\lambda) = \\begin{pmatrix} 1 & 0 \\\\ 0 & e^{i\\lambda} \\end{pmatrix}
+        which is the Tequila Phase gate:
+            u1(\\lambda) = Phase(\\lambda)
+
+    Parameters
+    ----------
+    lambd
+        parameter angle
+    target
+        int or list of int
+    control
+        int or list of int
+
+    Returns
+    -------
+    QCircuit object
+    """
+
+    return Phase(phi=lambd, target=target, control=control)
+
+
+def u2(phi, lambd, target: typing.Union[list, int], control: typing.Union[list, int] = None) -> QCircuit:
+    """
+    Notes
+    ----------
+    Convenient gate, one of the abstract gates defined by Quantum Experience Standard Header.
+    Uses a single \\pi/2-pulse.
+
+    .. math::
+        u2(\\phi, \\lambda) = U(\\pi/2, \\phi, \\lambda) = R_z(\\phi + \\pi/2)R_x(\\pi/2)R_z(\\lambda - \\pi/2)
+
+        u2(\\phi, \\lambda) = \\frac{1}{\\sqrt{2}}
+                              \\begin{pmatrix}
+                                    1          & -e^{i\\lambda} \\\\
+                                    e^{i\\phi} & e^{i(\\phi+\\lambda)}
+                              \\end{pmatrix}
+
+    Parameters
+    ----------
+    phi
+        first parameter angle
+    lambd
+        second parameter angle
+    target
+        int or list of int
+    control
+        int or list of int
+
+    Returns
+    -------
+    QCircuit object
+    """
+
+    return U(theta=np.pi/2, phi=phi, lambd=lambd, target=target, control=control)
+
+
+def u3(theta, phi, lambd, target: typing.Union[list, int], control: typing.Union[list, int] = None) -> QCircuit:
+    """
+    Notes
+    ----------
+    Convenient gate, one of the abstract gates defined by Quantum Experience Standard Header
+    The most general single-qubit gate.
+    Uses a pair of \\pi/2-pulses.
+
+    .. math::
+        u3(\\theta, \\phi, \\lambda) = U(\\theta, \\phi, \\lambda)
+                                     = \\begin{pmatrix}
+                                            \\cos{\\frac{\\5theta}{2}} &
+                                            -e^{i \\lambda} \\sin{\\frac{\\theta}{2}} \\\\
+                                            e^{i \\phi} \\sin{\\frac{\\theta}{2}} &
+                                            e^{i (\\phi+\\lambda)} \\cos{\\frac{\\theta}{2}}
+                                       \\end{pmatrix}
+
+    Parameters
+    ----------
+    theta
+        first parameter angle
+    phi
+        second parameter angle
+    lambd
+        third parameter angle
+    target
+        int or list of int
+    control
+        int or list of int
+
+    Returns
+    -------
+    QCircuit object
+    """
+
+    return U(theta=theta, phi=phi, lambd=lambd, target=target, control=control)
+
+
 if __name__ == "__main__":
     G = CRx(1, 0, 2.0)
 
diff --git a/src/tequila/circuit/pyzx.py b/src/tequila/circuit/pyzx.py
new file mode 100644
index 00000000..d99adf07
--- /dev/null
+++ b/src/tequila/circuit/pyzx.py
@@ -0,0 +1,52 @@
+"""
+Add to tequila the ability to make ZX-Calculus
+
+Using the pyzx library: https://github.com/Quantomatic/pyzx
+"""
+
+HAS_PYZX = True
+try:
+    import pyzx
+    HAS_PYZX = True
+except ImportError:
+    HAS_PYZX = False
+
+from tequila import TequilaException
+from tequila import export_open_qasm, import_open_qasm
+from tequila.circuit import QCircuit
+
+
+def convert_to_pyzx(circuit: QCircuit, variables=None):
+    """
+    Allow convert from Tequila circuit to pyzx circuit
+
+    Args:
+        circuit: in Tequila format to be exported to pyzx
+        variables: optional dictionary with values for variables
+
+    Returns:
+        pyzx.circuit.Circuit: pyzx circuit
+    """
+    if HAS_PYZX:
+        return pyzx.circuit.Circuit.from_qasm(export_open_qasm(circuit=circuit, variables=variables, version="2.0", zx_calculus=True))
+    else:
+        raise TequilaException("Pyzx package not installed.")
+
+
+def convert_from_pyzx(circuit) -> QCircuit:
+    """
+    Allow convert from pyzx circuit to Tequila circuit
+
+    Args:
+        circuit: in pyzx format (pyzx.circuit.Circuit) to be exported to Tequila circuit
+
+    Returns:
+        QCircuit: Tequila circuit
+    """
+    if HAS_PYZX:
+        if isinstance(circuit, pyzx.circuit.Circuit):
+            return import_open_qasm(circuit.to_qasm(), version="2.0")
+        else:
+            raise TequilaException("Circuit provided must be of type pyzx.circuit.Circuit")
+    else:
+        raise TequilaException("Pyzx package not installed.")
\ No newline at end of file
diff --git a/src/tequila/circuit/qasm.py b/src/tequila/circuit/qasm.py
new file mode 100644
index 00000000..27f41727
--- /dev/null
+++ b/src/tequila/circuit/qasm.py
@@ -0,0 +1,418 @@
+"""
+Export QCircuits as qasm code
+
+OPENQASM version 2.0 specification from:
+A. W. Cross, L. S. Bishop, J. A. Smolin, and J. M. Gambetta, e-print arXiv:1707.03429v2 [quant-ph] (2017).
+https://arxiv.org/pdf/1707.03429v2.pdf
+"""
+from tequila import TequilaException
+from tequila.circuit import QCircuit
+from tequila.circuit.compiler import Compiler
+from tequila.circuit.gates import *
+from numpy import pi
+from typing import Dict
+
+
+def export_open_qasm(circuit: QCircuit, variables=None, version: str = "2.0", filename: str = None, zx_calculus: bool = False) -> str:
+    """
+    Allow export to different versions of OpenQASM
+
+    Args:
+        circuit: to be exported to OpenQASM
+        variables: optional dictionary with values for variables
+        version: of the OpenQASM specification, optional
+        filename: optional file name to save the generated OpenQASM code
+        zx_calculus: indicate if y-gates must be transformed to xz equivalents
+
+    Returns:
+        str: OpenQASM string
+    """
+
+    if version == "2.0":
+        result = convert_to_open_qasm_2(circuit=circuit, variables=variables, zx_calculus=zx_calculus)
+    else:
+        return "Unsupported OpenQASM version : " + version
+    # TODO: export to version 3
+
+    if filename is not None:
+        with open(filename, "w") as file:
+            file.write(result)
+            file.close()
+
+    return result
+
+
+def import_open_qasm(qasm_code: str, version: str = "2.0", rigorous: bool = True) -> QCircuit:
+    """
+    Allow import from different versions of OpenQASM
+
+    Args:
+        qasm_code: string with the OpenQASM code
+        version: of the OpenQASM specification, optional
+        rigorous: indicates whether the QASM code should be read rigorously
+
+    Returns:
+        QCircuit: equivalent to the OpenQASM code received
+    """
+
+    if version == "2.0":
+        result = parse_from_open_qasm_2(qasm_code=qasm_code, rigorous=rigorous)
+    else:
+        return "Unsupported OpenQASM version : " + version
+    # TODO: export to version 3
+
+    return result
+
+
+def import_open_qasm_from_file(filename: str, version: str = "2.0", rigorous: bool = True) -> QCircuit:
+    """
+    Allow import from different versions of OpenQASM from a file
+
+    Args:
+        filename: string with the file name with the OpenQASM code
+        variables: optional dictionary with values for variables
+        version: of the OpenQASM specification, optional
+        rigorous: indicates whether the QASM code should be read rigorously
+
+    Returns:
+        QCircuit: equivalent to the OpenQASM code received
+    """
+
+    with open(filename, "r") as file:
+        qasm_code = file.read()
+        file.close()
+
+    return import_open_qasm(qasm_code, version=version, rigorous=rigorous)
+
+
+def convert_to_open_qasm_2(circuit: QCircuit, variables=None, zx_calculus: bool = False) -> str:
+    """
+    Allow export to OpenQASM version 2.0
+
+    Args:
+        circuit: to be exported to OpenQASM
+        variables: optional dictionary with values for variables
+        zx_calculus: indicate if y-gates must be transformed to xz equivalents
+
+    Returns:
+        str: OpenQASM string
+    """
+
+    if variables is None and not (len(circuit.extract_variables()) == 0):
+        raise TequilaException(
+            "You called export_open_qasm for a parametrized type but forgot to pass down the variables: {}".format(
+                circuit.extract_variables()))
+
+    compiler = Compiler(multitarget=True,
+                        multicontrol=False,
+                        trotterized=True,
+                        generalized_rotation=True,
+                        exponential_pauli=True,
+                        controlled_exponential_pauli=True,
+                        hadamard_power=True,
+                        controlled_power=True,
+                        power=True,
+                        toffoli=True,
+                        controlled_phase=True,
+                        phase=True,
+                        phase_to_z=True,
+                        controlled_rotation=True,
+                        swap=True,
+                        cc_max=True,
+                        gradient_mode=False,
+                        ry_gate=zx_calculus,
+                        y_gate=zx_calculus,
+                        ch_gate=zx_calculus)
+
+    compiled = compiler(circuit, variables=None)
+
+    result = "OPENQASM 2.0;\ninclude \"qelib1.inc\";\n"
+
+    qubits_names: Dict[int, str] = {}
+    for q in compiled.qubits:
+        name = "q[" + str(q) + "]"
+        qubits_names[q] = name
+
+    result += "qreg q[" + str(compiled.n_qubits) + "];\n"
+    result += "creg c[" + str(compiled.n_qubits) + "];\n"
+
+    for g in compiled.gates:
+
+        control_str = ''
+        if g.is_controlled():
+
+            if len(g.control) > 2:
+                raise TequilaException(
+                    "Multi-controls beyond 2 not yet supported for OpenQASM 2.0. Gate was:\n{}".format(g))
+
+            controls = list(map(lambda c: qubits_names[c], g.control))
+            control_str = ','.join(controls) + ','
+
+        gate_name = name_and_params(g, variables)
+        for t in g.target:
+            result += gate_name
+            result += control_str
+            result += qubits_names[t]
+            result += ";\n"
+
+    return result
+
+
+def name_and_params(g, variables):
+    """
+    Determines the quantum gate name and its parameters if applicable
+
+    Args:
+        g: gate to get its name
+        variables: dictionary with values for variables
+
+    Returns:
+        str: name (and parameter) to the gate specified
+    """
+
+    res = ""
+
+    for c in range(len(g.control)):
+        res += "c"
+
+    res += g.name.lower()
+
+    if hasattr(g, "parameter") and g.parameter is not None:
+        res += "(" + str(g.parameter(variables)) + ")"
+
+    res += " "
+
+    return res
+
+
+def parse_from_open_qasm_2(qasm_code: str, rigorous: bool = True) -> QCircuit:
+
+    lines = qasm_code.splitlines()
+    clean_code = []
+    # ignore comments
+    for line in lines:
+        if line.find("//") != -1:
+            clean_line = line[0:line.find("//")].strip()
+        else:
+            clean_line = line.strip()
+        if clean_line:
+            clean_code.append(clean_line)
+
+    if clean_code[0].startswith("OPENQASM"):
+        clean_code.pop(0)
+    elif rigorous:
+        raise TequilaException("File must start with the 'OPENQASM' directive")
+
+    if clean_code[0].startswith('include "qelib1.inc";'):
+        clean_code.pop(0)
+    elif rigorous:
+        raise TequilaException("File must import standard library (qelib1.inc)")
+
+    code_circuit = "\n".join(clean_code)
+    # separate the custom command definitions from the normal commands
+    custom_gates_map: Dict[str, QCircuit] = {}
+    while True:
+        i = code_circuit.find("gate ")
+        if i == -1:
+            break
+        j = code_circuit.find("}", i)
+        custom_name, custom_circuit = parse_custom_gate(code_circuit[i:j + 1], custom_gates_map=custom_gates_map)
+        custom_gates_map[custom_name] = custom_circuit
+        code_circuit = code_circuit[:i] + code_circuit[j + 1:]
+
+    # parse regular commands
+    commands = [s.strip() for s in code_circuit.split(";") if s.strip()]
+    qregisters: Dict[str, int] = {}
+
+    circuit = QCircuit()
+    for c in commands:
+        partial_circuit = parse_command(command=c, custom_gates_map=custom_gates_map, qregisters=qregisters)
+        if partial_circuit is not None:
+            circuit += partial_circuit
+
+    return circuit
+
+
+def parse_custom_gate(gate_custom: str, custom_gates_map: Dict[str, QCircuit]) -> (str, QCircuit):
+    """
+    Parse custom gates code
+
+    Args:
+        gate_custom: code with custom gates
+    """
+    gate_custom = gate_custom[5:]
+    spec, body = gate_custom.split("{", 1)
+
+    if "(" in spec:
+        i = spec.find("(")
+        j = spec.find(")")
+        if spec[i + 1:j].strip():
+            raise TequilaException("Parameters for custom gates not supported: {}".format(spec))
+        spec = spec[:i] + spec[j + 1:]
+
+    spec = spec.strip()
+
+    if " " in spec:
+        name, qargs = spec.split(" ", 1)
+        name = name.strip()
+        qargs = qargs.strip()
+    else:
+        raise TequilaException("Custom gate specification doesn't have any arguments: {}".format(spec))
+
+    custom_qregisters: Dict[str, int] = {}
+    for qarg in qargs.split(','):
+        custom_qregisters[qarg] = len(custom_qregisters)
+
+    body = body[:-1].strip()
+    commands = [s.strip() for s in body.split(";") if s.strip()]
+
+    custom_circuit = QCircuit()
+    for c in commands:
+        partial_circuit = parse_command(command=c, custom_gates_map=custom_gates_map, qregisters=custom_qregisters)
+        if partial_circuit is not None:
+            custom_circuit += partial_circuit
+
+    return name, custom_circuit
+
+
+def parse_command(command: str, custom_gates_map: Dict[str, QCircuit], qregisters: Dict[str, int]) -> QCircuit:
+    """
+    Parse qasm code command
+
+    Args:
+        command: open qasm code to be parsed
+        custom_gates_map: map with custom gates
+    """
+
+    name, rest = command.split(" ", 1)
+
+    if name in ("barrier", "creg", "measure", "id"):
+        return None
+    if name in ("opaque", "if"):
+        raise TequilaException("Unsupported operation {}".format(command))
+
+    args = [s.strip() for s in rest.split(",") if s.strip()]
+
+    if name == "qreg":
+        regname, sizep = args[0].split("[", 1)
+        size = int(sizep[:-1])
+        for i in range(size):
+            qregisters[regname + "[" + str(i) + "]"] = len(qregisters)
+        return None
+
+    for arg in args:
+        if not (arg in qregisters or arg in [key.split("[",1)[0] for key in qregisters.keys()]):
+            raise TequilaException("Invalid register {}".format(arg))
+
+    if name in custom_gates_map:
+        custom_circuit = custom_gates_map[name]
+        qregisters_values = []
+        for a in args:
+            qregisters_values.append(get_qregister(a, qregisters))
+        return apply_custom_gate(custom_circuit=custom_circuit, qregisters_values=qregisters_values)
+
+    if name in ("x", "y", "z", "h", "cx", "cy", "cz", "ch"):
+        return QCircuit.wrap_gate(QGateImpl(name=(name[1] if name[0] == 'c' else name).upper(),
+                                            control=get_qregister(args[0], qregisters) if name[0] == 'c' else None,
+                                            target=get_qregister(args[1 if name[0] == 'c' else 0], qregisters)))
+    if name in ("ccx", "ccy", "ccz"):
+        return QCircuit.wrap_gate(QGateImpl(name=name.upper()[2],
+                                            control=[get_qregister(args[0], qregisters), get_qregister(args[1], qregisters)],
+                                            target=get_qregister(args[2], qregisters)))
+    if name.startswith("rx(") or name.startswith("ry(") or name.startswith("rz(") or \
+        name.startswith("crx(") or name.startswith("cry(") or name.startswith("crz("):
+        return QCircuit.wrap_gate(RotationGateImpl(axis=name[2 if name[0] == 'c' else 1],
+                                                   angle=get_angle(name)[0],
+                                                   control=get_qregister(args[0], qregisters) if name[0] == 'c' else None,
+                                                   target=get_qregister(args[1 if name[0] == 'c' else 0], qregisters)))
+    if name.startswith("U("):
+        angles = get_angle(name)
+        return U(theta=angles[0], phi=angles[1], lambd=angles[2],
+                 control=None,
+                 target=get_qregister(args[0], qregisters))
+    if name.startswith("u1("):
+        angles = get_angle(name)
+        return u1(lambd=angles[0],
+                  control=None,
+                  target=get_qregister(args[0], qregisters))
+    if name.startswith("u2("):
+        angles = get_angle(name)
+        return u2(phi=angles[0], lambd=angles[1],
+                  control=None,
+                  target=get_qregister(args[0], qregisters))
+    if name.startswith("u3("):
+        angles = get_angle(name)
+        return u3(theta=angles[0], phi=angles[1], lambd=angles[2],
+                  control=None,
+                  target=get_qregister(args[0], qregisters))
+    if name.startswith("cu1("):
+        angles = get_angle(name)
+        return u1(lambd=angles[0],
+                  control=get_qregister(args[0], qregisters),
+                  target=get_qregister(args[1], qregisters))
+    if name.startswith("cu2("):
+        angles = get_angle(name)
+        return u2(phi=angles[0], lambd=angles[1],
+                  control=get_qregister(args[0], qregisters),
+                  target=get_qregister(args[1], qregisters))
+    if name.startswith("cu3("):
+        angles = get_angle(name)
+        return u3(theta=angles[0], phi=angles[1], lambd=angles[2],
+                  control=get_qregister(args[0], qregisters),
+                  target=get_qregister(args[1], qregisters))
+    if name in ("s", "t", "sdg", "tdg"):
+        g = Phase(np.pi / (2 if name.startswith("s") else 4),
+                     control=None,
+                     target=get_qregister(args[0], qregisters))
+        if name.find("dg") != -1:
+            g = g.dagger()
+        return g
+
+
+def apply_custom_gate(custom_circuit: QCircuit, qregisters_values: list) -> QCircuit:
+    applied_custom_circuit = QCircuit()
+    for gate in custom_circuit.gates:
+        g = gate.copy()
+        g._target = tuple([qregisters_values[i] for i in gate._target])
+        g._control = tuple([qregisters_values[i] for i in gate._control]) if gate.is_controlled() else gate._control
+        applied_custom_circuit += g
+    return applied_custom_circuit
+
+
+def get_qregister(qreg: str, qregisters: Dict[str, int]) -> typing.Union[list, int]:
+    if qreg == qreg.split("[", 1)[0]:
+        qreg_tequila = [qregisters[key] for key in qregisters.keys() if qreg == key.split("[", 1)[0]]
+    else:
+        qreg_tequila = qregisters[qreg]
+    return qreg_tequila
+
+def get_angle(name: str) -> list:
+    i = name.find('(')
+    j = name.find(')')
+    if j == -1:
+        raise TequilaException("Invalid specification {}".format(name))
+    angles_str = name[i+1:j].split(',')
+    angles = []
+    for angle in angles_str:
+        try:
+            phase = float(angle)
+        except ValueError:
+            if angle.find('pi') == -1:
+                raise TequilaException("Invalid specification {}".format(name))
+            angle = angle.replace('pi', '')
+            try:
+                if angle.find('*') != -1:
+                    angle = angle.replace('*', '')
+                    phase = float(angle) * pi
+                elif angle.find('/') != -1:
+                    angle = angle.replace('/', '')
+                    phase = pi / float(angle)
+                elif len(angle) == 0:
+                    phase = pi
+                else:
+                    phase = float(angle)
+            except ValueError:
+                raise TequilaException("Invalid specification {}".format(name))
+        angles.append(phase)
+    return angles
+
diff --git a/src/tequila/optimizers/__init__.py b/src/tequila/optimizers/__init__.py
index 90113d27..0cd37949 100644
--- a/src/tequila/optimizers/__init__.py
+++ b/src/tequila/optimizers/__init__.py
@@ -80,7 +80,7 @@ def show_available_optimizers(module=None):
 def minimize(method: str,
              objective,
              variables: list=None,
-             initial_values: dict=None,
+             initial_values: typing.Union[dict,numbers.Number]=None,
              maxiter: int=None,
              *args,
              **kwargs):
diff --git a/src/tequila/quantumchemistry/madness_interface.py b/src/tequila/quantumchemistry/madness_interface.py
index d4ab4c5e..f9fae9d6 100644
--- a/src/tequila/quantumchemistry/madness_interface.py
+++ b/src/tequila/quantumchemistry/madness_interface.py
@@ -8,6 +8,10 @@
 
 from dataclasses import dataclass
 
+class TequilaMadnessException(TequilaException):
+    def __str__(self):
+        return "Error in madness backend:" + self.message
+
 
 class QuantumChemistryMadness(QuantumChemistryBase):
     @dataclass
@@ -98,7 +102,7 @@ def __init__(self, parameters: ParametersQC,
             status += "found {}_htensor.npy={}\n".format(name, h != "failed")
             status += "found {}_gtensor.npy={}\n".format(name, h != "failed")
             if h == "failed" or g == "failed":
-                raise TequilaException("Could not initialize the madness interface\n"
+                raise TequilaMadnessException("Could not initialize the madness interface\n"
                                        "Status report is\n"
                                        "{status}\n"
                                        "either provide {name}_gtensor.npy and {name}_htensor.npy files\n"
@@ -130,7 +134,7 @@ def __init__(self, parameters: ParametersQC,
             kwargs["nuclear_repulsion"] = nuclear_repulsion
 
         if pairinfo is None:
-            raise TequilaException("Pairinfo from madness calculation not found\nPlease provide pnoinfo.txt")
+            raise TequilaMadnessException("Pairinfo from madness calculation not found\nPlease provide pnoinfo.txt")
 
         n_orbitals = h.shape[0]
         assert h.shape[1] == n_orbitals
@@ -155,7 +159,7 @@ def __init__(self, parameters: ParametersQC,
                 if active_orbitals is None or i in active_orbitals:
                     orbitals.append(self.OrbitalData(idx_total=i, idx=len(orbitals), pno_pair=p, occ=occinfo[i]))
         else:
-            raise TequilaException("No pairinfo given")
+            raise TequilaMadnessException("No pairinfo given")
         self.orbitals = tuple(orbitals)
 
         # print warning if read data does not match expectations
@@ -275,9 +279,11 @@ def make_pno_upccgsd_ansatz(self, include_singles: bool = True, generalized=Fals
 
     def write_madness_input(self, n_pno, n_virt=0, frozen_core=False, filename="input", *args, **kwargs):
         if n_pno is None:
-            raise TequilaException("Can't write madness input without n_pnos")
+            raise TequilaMadnessException("Can't write madness input without n_pnos")
         data = {}
-        data["dft"] = {"xc": "hf", "k": 7, "econv": 1.e-4, "dconv": 3.e-4, "ncf": "( none , 1.0 )"}
+        if self.parameters.multiplicity != 1:
+            raise TequilaMadnessException("Currently only closed shell supported for MRA-PNO-MP2, you demanded multiplicity={} for the surrogate".format(self.parameters.multiplicity))
+        data["dft"] = {"charge":self.parameters.charge, "xc": "hf", "k": 7, "econv": 1.e-4, "dconv": 3.e-4, "ncf": "( none , 1.0 )"}
         data["pno"] = {"maxrank": n_pno, "f12": "false", "thresh": 1.e-4}
         if not frozen_core:
             data["pno"]["freeze"] = 0
diff --git a/src/tequila/quantumchemistry/qc_base.py b/src/tequila/quantumchemistry/qc_base.py
index 8d503ee6..4f8965c9 100644
--- a/src/tequila/quantumchemistry/qc_base.py
+++ b/src/tequila/quantumchemistry/qc_base.py
@@ -39,6 +39,15 @@ def __init__(self, angle, generator, p0, assume_real=True, control=None):
         self.p0 = p0
         self.assume_real = assume_real
 
+    def map_qubits(self, qubit_map: dict):
+        mapped_generator = self.generator.map_qubits(qubit_map=qubit_map)
+        mapped_p0 = self.p0.map_qubits(qubit_map=qubit_map)
+        mapped_control = self.control
+        if mapped_control is not None:
+            mapped_control=tuple([qubit_map[i] for i in self.control])
+        return FermionicGateImpl(angle=self.parameter, generator=mapped_generator, p0=mapped_p0, assume_real=self.assume_real, control=mapped_control)
+
+
     def compile(self):
         return gates.Trotterized(angles=[self.parameter], generators=[self.generator], steps=1)
 
diff --git a/src/tequila/simulators/simulator_api.py b/src/tequila/simulators/simulator_api.py
index 9a63c437..e5ca1088 100755
--- a/src/tequila/simulators/simulator_api.py
+++ b/src/tequila/simulators/simulator_api.py
@@ -342,7 +342,7 @@ def compile_circuit(abstract_circuit: 'QCircuit',
         else:
             return abstract_circuit
 
-    return CircType(abstract_circuit=abstract_circuit, variables=variables, noise=noise, device=device)
+    return CircType(abstract_circuit=abstract_circuit, variables=variables, noise=noise, device=device, *args, **kwargs)
 
 
 def simulate(objective: typing.Union['Objective', 'QCircuit'],
diff --git a/src/tequila/simulators/simulator_base.py b/src/tequila/simulators/simulator_base.py
index b47e74fe..524b60c1 100755
--- a/src/tequila/simulators/simulator_base.py
+++ b/src/tequila/simulators/simulator_base.py
@@ -1,4 +1,4 @@
-from tequila.utils import TequilaException, to_float
+from tequila.utils import TequilaException, to_float, TequilaWarning
 from tequila.circuit.circuit import QCircuit
 from tequila.utils.keymap import KeyMapSubregisterToRegister
 from tequila.utils.misc import to_float
@@ -8,7 +8,7 @@
 from tequila.objective.objective import Variable, format_variable_dictionary
 from tequila.circuit import compiler
 
-import numbers, typing, numpy, copy
+import numbers, typing, numpy, copy, warnings
 
 from dataclasses import dataclass
 
@@ -154,7 +154,8 @@ def __init__(self, abstract_circuit: QCircuit, variables, noise=None, device=Non
         kwargs
         """
 
-        self._input_args = {"abstract_circuit":abstract_circuit, "variables":variables, "noise":noise, "qubit_map":qubit_map, "optimize_circuits":optimize_circuit, "device":device, **kwargs}
+        self._input_args = {"abstract_circuit": abstract_circuit, "variables": variables, "noise": noise,
+                            "qubit_map": qubit_map, "optimize_circuits": optimize_circuit, "device": device, **kwargs}
 
         self.no_translation = False
         self._variables = tuple(abstract_circuit.extract_variables())
@@ -171,6 +172,15 @@ def __init__(self, abstract_circuit: QCircuit, variables, noise=None, device=Non
 
         if qubit_map is None:
             qubit_map = {q: i for i, q in enumerate(abstract_circuit.qubits)}
+        else:
+            warnings.warn("reveived custom qubit_map = {}\n"
+                        "This is not fully integrated and might result in unexpected behaviour!"
+                          .format(qubit_map), TequilaWarning)
+
+            if len(qubit_map) > abstract_circuit.max_qubit()+1:
+                raise TequilaException("Custom qubit_map has too many qubits {} vs {}".format(len(qubit_map), abstract_circuit.max_qubit()+1))
+            if max(qubit_map.keys()) > abstract_circuit.max_qubit():
+                raise TequilaException("Custom qubit_map tries to assign qubit {} but we only have {}".format(max(qubit_map.keys()), abstract_circuit.max_qubit()))
 
         # qubit map is initialized to have BackendQubits as values (they carry number and instance attributes)
         self.qubit_map = self.make_qubit_map(qubit_map)
@@ -179,9 +189,7 @@ def __init__(self, abstract_circuit: QCircuit, variables, noise=None, device=Non
         compiled = c(abstract_circuit)
         self.abstract_circuit = compiled
 
-
         self.noise = noise
-
         self.check_device(device)
         self.device = self.retrieve_device(device)
 
@@ -191,8 +199,6 @@ def __init__(self, abstract_circuit: QCircuit, variables, noise=None, device=Non
         if optimize_circuit and noise is None:
             self.circuit = self.optimize_circuit(circuit=self.circuit)
 
-
-
     def __call__(self,
                  variables: typing.Dict[Variable, numbers.Real] = None,
                  samples: int = None,
@@ -278,7 +284,7 @@ def check_device(self, device):
         TequilaException
         """
         if device is not None:
-            TequilaException('Devices not enabled for {}'.format(str(type(self))))
+            raise TequilaException('Devices not enabled for {}'.format(str(type(self))))
 
     def retrieve_device(self, device):
         """
@@ -299,19 +305,19 @@ def retrieve_device(self, device):
         if device is None:
             return device
         else:
-            TequilaException('Devices not enabled for {}'.format(str(type(self))))
+            raise TequilaException('Devices not enabled for {}'.format(str(type(self))))
 
     def add_parametrized_gate(self, gate, circuit, *args, **kwargs):
-        TequilaException("Backend Handler needs to be overwritten for supported simulators")
+        raise TequilaException("Backend Handler needs to be overwritten for supported simulators")
 
     def add_basic_gate(self, gate, circuit, *args, **kwargs):
-        TequilaException("Backend Handler needs to be overwritten for supported simulators")
+        raise TequilaException("Backend Handler needs to be overwritten for supported simulators")
 
     def add_measurement(self, circuit, target_qubits, *args, **kwargs):
-        TequilaException("Backend Handler needs to be overwritten for supported simulators")
+        raise TequilaException("Backend Handler needs to be overwritten for supported simulators")
 
     def initialize_circuit(self, *args, **kwargs):
-        TequilaException("Backend Handler needs to be overwritten for supported simulators")
+        raise TequilaException("Backend Handler needs to be overwritten for supported simulators")
 
     def update_variables(self, variables):
         """
@@ -349,7 +355,8 @@ def simulate(self, variables, initial_state=0, *args, **kwargs) -> QubitWaveFunc
             initial_state = list(initial_state.keys())[0].integer
 
         all_qubits = [i for i in range(self.abstract_circuit.n_qubits)]
-        active_qubits = self.abstract_circuit.qubits
+        active_qubits = self.qubit_map.keys()
+
         # maps from reduced register to full register
         keymap = KeyMapSubregisterToRegister(subregister=active_qubits, register=all_qubits)
 
@@ -410,7 +417,7 @@ def sample_all_z_hamiltonian(self, samples: int, hamiltonian, variables, *args,
         """
         # make measurement instruction (measure all qubits in the Hamiltonian that are also in the circuit)
         abstract_qubits_H = hamiltonian.qubits
-        assert len(abstract_qubits_H) != 0 # this case should be filtered out before
+        assert len(abstract_qubits_H) != 0  # this case should be filtered out before
         # assert that the Hamiltonian was mapped before
         if not all(q in self.qubit_map.keys() for q in abstract_qubits_H):
             raise TequilaException(
@@ -519,7 +526,7 @@ def do_sample(self, samples, circuit, noise, abstract_qubits=None, *args, **kwar
             the result of sampling.
 
         """
-        TequilaException("Backend Handler needs to be overwritten for supported simulators")
+        raise TequilaException("Backend Handler needs to be overwritten for supported simulators")
 
     def do_simulate(self, variables, initial_state, *args, **kwargs) -> QubitWaveFunction:
         """
@@ -540,10 +547,10 @@ def do_simulate(self, variables, initial_state, *args, **kwargs) -> QubitWaveFun
             the result of simulating the circuit.
 
         """
-        TequilaException("Backend Handler needs to be overwritten for supported simulators")
+        raise TequilaException("Backend Handler needs to be overwritten for supported simulators")
 
     def convert_measurements(self, backend_result) -> QubitWaveFunction:
-        TequilaException("Backend Handler needs to be overwritten for supported simulators")
+        raise TequilaException("Backend Handler needs to be overwritten for supported simulators")
 
     def initialize_qubit(self, number: int):
         """
@@ -734,7 +741,7 @@ def __init__(self, E, variables, noise, device, *args, **kwargs):
             device for compilation of circuit
         """
         self.abstract_expectationvalue = E
-        self._input_args = {"variables":variables, "device":device, "noise":noise, **kwargs}
+        self._input_args = {"variables": variables, "device": device, "noise": noise, **kwargs}
         self._U = self.initialize_unitary(E.U, variables=variables, noise=noise, device=device, **kwargs)
         self._reduced_hamiltonians = self.reduce_hamiltonians(self.abstract_expectationvalue.H)
         self._H = self.initialize_hamiltonian(self._reduced_hamiltonians)
diff --git a/src/tequila/simulators/simulator_cirq.py b/src/tequila/simulators/simulator_cirq.py
index dfcfe04a..50828b29 100755
--- a/src/tequila/simulators/simulator_cirq.py
+++ b/src/tequila/simulators/simulator_cirq.py
@@ -254,14 +254,17 @@ def add_parametrized_gate(self, gate, circuit, *args, **kwargs):
         None
         """
         op, mapping = self.op_lookup[gate.name]
-        if isinstance(gate.parameter, float):
-            par = gate.parameter
+        parameter = gate.parameter
+        if hasattr(gate, 'power'):
+            parameter = gate.power
+        if isinstance(parameter, float):
+            par = parameter
         else:
             try:
-                par = self.tq_to_sympy[gate.parameter]
+                par = self.tq_to_sympy[parameter]
             except:
-                par = sympy.Symbol('{}_{}'.format(self._name_variable_objective(gate.parameter), str(self.counter)))
-                self.tq_to_sympy[gate.parameter] = par
+                par = sympy.Symbol('{}_{}'.format(self._name_variable_objective(parameter), str(self.counter)))
+                self.tq_to_sympy[parameter] = par
                 self.counter += 1
         cirq_gate = op(**mapping(par)).on(*[self.qubit(t) for t in gate.target])
         if gate.is_controlled():
diff --git a/src/tequila/simulators/simulator_qiskit.py b/src/tequila/simulators/simulator_qiskit.py
index be34b6bf..7eccf1e4 100755
--- a/src/tequila/simulators/simulator_qiskit.py
+++ b/src/tequila/simulators/simulator_qiskit.py
@@ -126,7 +126,7 @@ class BackendCircuitQiskit(BackendCircuit):
         "controlled_phase": False,
         "toffoli": False,
         "phase_to_z": False,
-        "cc_max": False
+        "cc_max": True
     }
 
     numbering = BitNumbering.LSB
@@ -402,8 +402,7 @@ def add_parametrized_gate(self, gate, circuit, *args, **kwargs):
             if len(gate.control) > 2:
                 pass
                 # raise TequilaQiskitException("multi-controls beyond 2 not yet supported for the qiskit backend. Gate was:\n{}".format(gate) )
-            ops[1](circuit)(par, q_controls=[self.qubit(c) for c in gate.control],
-                            q_target=self.qubit(gate.target[0]), q_ancillae=None, mode='noancilla')
+            ops[1](circuit)(par, self.qubit(gate.control[0]), self.qubit(gate.target[0]))
         else:
             ops[0](circuit)(par, self.qubit(gate.target[0]))
 
diff --git a/src/tequila/tools/qng.py b/src/tequila/tools/qng.py
index 4fddd430..9fc42bc1 100644
--- a/src/tequila/tools/qng.py
+++ b/src/tequila/tools/qng.py
@@ -5,7 +5,7 @@
 from tequila.simulators.simulator_api import compile_objective
 from tequila.circuit.gradient import __grad_inner
 from tequila.autograd_imports import jax
-from tequila.circuit.compiler import compile_controlled_rotation, compile_h_power, compile_power_gate, \
+from tequila.circuit.compiler import compile_controlled_rotation, compile_power_gate, \
     compile_trotterized_gate, compile_controlled_phase, compile_multitarget
 import typing
 import numpy
@@ -456,7 +456,6 @@ def get_qng_combos(objective, func=stokes_block,
     objective.contract()
     compiled = compile_multitarget(gate=objective)
     compiled = compile_trotterized_gate(gate=compiled)
-    compiled = compile_h_power(gate=compiled)
     compiled = compile_power_gate(gate=compiled)
     compiled = compile_controlled_phase(gate=compiled)
     compiled = compile_controlled_rotation(gate=compiled)
diff --git a/src/tequila/wavefunction/qubit_wavefunction.py b/src/tequila/wavefunction/qubit_wavefunction.py
index 120d4bb1..01f9c475 100644
--- a/src/tequila/wavefunction/qubit_wavefunction.py
+++ b/src/tequila/wavefunction/qubit_wavefunction.py
@@ -27,7 +27,11 @@ def apply_keymap(self, keymap, initial_state: BitString = None):
         self.n_qubits = keymap.n_qubits
         mapped_state = dict()
         for k, v in self.state.items():
-            mapped_state[keymap(input_state=k, initial_state=initial_state)] = v
+            mapped_key=keymap(input_state=k, initial_state=initial_state)
+            if mapped_key in mapped_state:
+                mapped_state[mapped_key] += v
+            else:
+                mapped_state[mapped_key] = v
 
         self.state = mapped_state
         return self
diff --git a/tests/test_chemistry_madness.py b/tests/test_chemistry_madness.py
index 904e6cf9..cf26f42b 100644
--- a/tests/test_chemistry_madness.py
+++ b/tests/test_chemistry_madness.py
@@ -28,7 +28,7 @@ def test_madness_he_data():
     print(result.energy)
     assert (numpy.isclose(-2.87761809, result.energy, atol=1.e-5))
 
-@pytest.mark.skipif(executable is None, reason="pno_integrals not found")
+@pytest.mark.skipif(executable is None, reason="madness was not found")
 def test_madness_full_he():
     # relies on madness being compiled and MAD_ROOT_DIR exported
     # or pno_integrals in the path
@@ -43,7 +43,22 @@ def test_madness_full_he():
     result = tq.minimize(method="bfgs", objective=E, initial_values=0.0, silent=True)
     assert (numpy.isclose(-2.87761809, result.energy, atol=1.e-5))
 
-@pytest.mark.skipif(executable is None, reason="pno_integrals not found")
+@pytest.mark.skipif(executable is None, reason="madness was not found")
+def test_madness_full_li_plus():
+    # relies on madness being compiled and MAD_ROOT_DIR exported
+    # or pno_integrals in the path
+    geomstring="Li 0.0 0.0 0.0"
+    molecule = tq.Molecule(name="li+", geometry=geomstring, n_pno=1, charge=1)
+    H = molecule.make_hamiltonian()
+    UHF = molecule.prepare_reference()
+    EHF = tq.simulate(tq.ExpectationValue(H=H, U=UHF))
+    assert(numpy.isclose(-7.236247e+00, EHF, atol=1.e-5))
+    U = molecule.make_upccgsd_ansatz()
+    E = tq.ExpectationValue(H=H, U=U)
+    result = tq.minimize(method="bfgs", objective=E, initial_values=0.0, silent=True)
+    assert (numpy.isclose(-7.251177798, result.energy, atol=1.e-5))
+
+@pytest.mark.skipif(executable is None, reason="madness was not found")
 def test_madness_full_be():
     # relies on madness being compiled and MAD_ROOT_DIR exported
     # or pno_integrals in the path
diff --git a/tests/test_circuits.py b/tests/test_circuits.py
index 24f3b40d..667e5218 100644
--- a/tests/test_circuits.py
+++ b/tests/test_circuits.py
@@ -1,10 +1,12 @@
-from tequila.circuit.gates import X, Y, Z, Rx, Ry, Rz, H, CNOT, QCircuit, RotationGate, Phase, ExpPauli, Trotterized
+from tequila.circuit.gates import X, Y, Z, Rx, Ry, Rz, H, CNOT, QCircuit, RotationGate, Phase, ExpPauli, Trotterized, \
+                                  U, u1, u2, u3, S, T
 from tequila.wavefunction.qubit_wavefunction import QubitWaveFunction
 from tequila.circuit._gates_impl import RotationGateImpl
 from tequila.objective.objective import Variable
 from tequila.simulators.simulator_api import simulate
 from tequila import assign_variable, paulis
 import numpy, sympy
+import pytest
 
 
 def test_qubit_map():
@@ -166,3 +168,103 @@ def test_circuit_from_moments():
     moms = c.moments
     c2 = QCircuit.from_moments(moms)
     assert c == c2
+
+
+@pytest.mark.parametrize(
+    "gate, angle",
+    [
+        (Z(target=0, control=None), numpy.pi),              # Z = u1(pi)
+        (Z(target=0, control=1), numpy.pi),
+        (S(target=0, control=None), numpy.pi/2),            # S = u1(pi/2)
+        (S(target=0, control=1), numpy.pi/2),
+        (S(target=0, control=None).dagger(), -numpy.pi/2),  # Sdg = u1(-pi/2)
+        (S(target=0, control=1).dagger(), -numpy.pi/2),
+        (T(target=0, control=None), numpy.pi/4),            # T = u1(pi/4)
+        (T(target=0, control=1), numpy.pi/4),
+        (T(target=0, control=None).dagger(), -numpy.pi/4),  # Tdg = u1(-pi/4)
+        (T(target=0, control=1).dagger(), -numpy.pi/4)
+    ]
+)
+def test_unitary_gate_u1(gate, angle):
+    """
+    Test some equivalences for u1 gate
+    """
+    c_u1 = u1(lambd=angle, target=gate.gates[0].target,
+              control=None if len(gate.gates[0].control) == 0 else gate.gates[0].control)
+
+    if len(gate.gates[0].control) > 0:
+        c_u1 = X(target=gate.gates[0].control) + c_u1
+        gate = X(target=gate.gates[0].control) + gate
+
+    wfn1 = simulate(c_u1, backend="symbolic")
+    wfn2 = simulate(gate, backend="symbolic")
+
+    assert (numpy.isclose(wfn1.inner(wfn2), 1.0))
+
+
+@pytest.mark.parametrize(
+    "ctrl, phi, lambd",
+    [
+        (None, numpy.pi / 13, numpy.pi / 7),
+        (1, numpy.pi / 13, numpy.pi / 7),
+        (None, 0, 0),
+        (1, 0, 0),
+        (None, numpy.pi, numpy.pi),
+        (1, numpy.pi, numpy.pi),
+        (None, 0, numpy.pi),
+        (1, numpy.pi, 0),
+    ]
+)
+def test_unitary_gate_u2(ctrl, phi, lambd):
+    """
+    Test some equivalences for u2 gate
+    Since u2(\\phi, \\lambda) = Rz(\\phi)Ry(\\pi/2)Rz(\\lambda)
+    """
+    c_u2 = u2(phi=phi, lambd=lambd, target=0, control=ctrl)
+    c_equiv = Rz(target=0, control=ctrl, angle=lambd) + \
+              Ry(target=0, control=ctrl, angle=numpy.pi / 2) + \
+              Rz(target=0, control=ctrl, angle=phi)
+
+    if ctrl is not None:
+        c_u2 = X(target=ctrl) + c_u2
+        c_equiv = X(target=ctrl) + c_equiv
+
+    wfn1 = simulate(c_u2, backend="symbolic")
+    wfn2 = simulate(c_equiv, backend="symbolic")
+
+    assert (numpy.isclose(wfn1.inner(wfn2), 1.0))
+
+
+@pytest.mark.parametrize(
+    "gate, theta, phi, lambd",
+    [
+        (Rx(target=0, control=None, angle=numpy.pi/5), numpy.pi/5, -numpy.pi/2, numpy.pi/2),  # Rx(angle) = u3(angle, -pi/2, pi/2)
+        (Rx(target=0, control=1, angle=numpy.pi/6), numpy.pi/6, -numpy.pi/2, numpy.pi/2),
+        (Rx(target=0, control=None, angle=numpy.pi/7), numpy.pi/7, -numpy.pi/2, numpy.pi/2),
+        (Rx(target=0, control=1, angle=numpy.pi/8), numpy.pi/8, -numpy.pi/2, numpy.pi/2),
+        (Ry(target=0, control=1, angle=numpy.pi/4), numpy.pi/4, 0, 0),                        # Ry(angle) = u3(angle, 0, 0)
+        (Ry(target=0, control=1, angle=numpy.pi/5), numpy.pi/5, 0, 0),
+        (Ry(target=0, control=1, angle=numpy.pi/3), numpy.pi/3, 0, 0),
+        (Ry(target=0, control=1, angle=numpy.pi/2), numpy.pi/2, 0, 0),
+        (Rz(target=0, control=None, angle=numpy.pi), 0, 0, numpy.pi),                         # Rz(angle) = U(0, 0, angle)
+        (Rz(target=0, control=1, angle=numpy.pi/6), 0, 0, numpy.pi/6),
+        (Rz(target=0, control=None, angle=numpy.pi/7), 0, 0, numpy.pi/7),
+        (Rz(target=0, control=1, angle=numpy.pi/8), 0, 0, numpy.pi/8)
+    ]
+)
+def test_unitary_gate_u_u3(gate, theta, phi, lambd):
+    """
+    Test some equivalences for u3 gate (also U gate, because U = u3)
+    """
+    c_u3 = u3(theta=theta, phi=phi, lambd=lambd, target=gate.gates[0].target,
+              control=None if len(gate.gates[0].control) == 0 else gate.gates[0].control)
+
+    if len(gate.gates[0].control) > 0:
+        c_u3 = X(target=gate.gates[0].control) + c_u3
+        gate = X(target=gate.gates[0].control) + gate
+
+    wfn1 = simulate(c_u3, backend="symbolic")
+    wfn2 = simulate(gate, backend="symbolic")
+
+    assert (numpy.isclose(wfn1.inner(wfn2), 1.0))
+
diff --git a/tests/test_pyzx.py b/tests/test_pyzx.py
new file mode 100644
index 00000000..887b7ed3
--- /dev/null
+++ b/tests/test_pyzx.py
@@ -0,0 +1,178 @@
+from tequila.circuit.pyzx import convert_to_pyzx, convert_from_pyzx
+from tequila.circuit.gates import *
+from tequila.simulators.simulator_api import simulate
+from tequila import TequilaException
+import numpy
+import pytest
+HAS_PYZX = True
+try:
+    import pyzx
+    HAS_PYZX = True
+except ImportError:
+    HAS_PYZX = False
+
+
+@pytest.mark.skipif(not HAS_PYZX,
+                    reason="Pyzx package not installed, test_convert_to_from_pyzx_simple not executed")
+@pytest.mark.parametrize(
+    "tequila_circuit",
+    [
+        (X(target=3) + Y(target=2) + Z(target=1)),
+        (Rx(target=1, control=0, angle=5.67) + Ry(target=2, angle=0.98) + Rz(target=3, angle=1.67)),
+        (H(target=1) + H(target=1, control=0) + X(target=1) + Y(target=0) + Z(target=2) +
+         CX(target=3, control=0) + CY(target=4, control=2) + CZ(target=5, control=1) +
+         CNOT(target=3, control=0) + SWAP(first=0, second=3) +
+         S(target=1, control=0) + T(target=1, control=2))
+    ]
+)
+def test_convert_to_from_pyzx_simple(tequila_circuit):
+
+    pyzx_circuit = convert_to_pyzx(tequila_circuit)
+    converted_circuit = convert_from_pyzx(pyzx_circuit)
+
+    wfn1 = simulate(tequila_circuit, backend="symbolic")
+    wfn2 = simulate(converted_circuit, backend="symbolic")
+
+    assert (numpy.isclose(wfn1.inner(wfn2), 1.0))
+
+
+@pytest.mark.skipif(not HAS_PYZX,
+                    reason="Pyzx package not installed, test_convert_to_from_pyzx not executed")
+@pytest.mark.parametrize(
+    "variabs",
+    [
+        ([2.8, 5.6, 7.6, 1.8, 4.98, 2.35, 3.12, 6.79, 0.12]),
+        ([1.5, 3.7, 9.2, 3.1, 7.62, 1.98, 8.56, 2.97, 1.34]),
+        ([0, 0, 0, 0, 0, 0, 0, 0, 0]),
+        ([numpy.pi/12, numpy.pi, numpy.pi/3, numpy.pi/6, numpy.pi*0.95, numpy.pi/2, numpy.pi*2.3, numpy.pi/7, 0.56])
+
+    ]
+)
+def test_convert_to_from_pyzx(variabs):
+
+    variables = {"ang1": variabs[0],
+                 "ang2": variabs[1],
+                 "ang3": variabs[2],
+                 "ang4": variabs[3],
+                 "ang5": variabs[4],
+                 "ang6": variabs[5],
+                 "ang7": variabs[6],
+                 "ang8": variabs[7],
+                 "ang9": variabs[8]}
+
+    tequila_circuit = H(target=[0, 1], control=2) + \
+                      X(target=1) + \
+                      Y(target=0) + \
+                      Z(target=2) + \
+                      CX(target=3, control=0) + \
+                      CY(target=4, control=2) + \
+                      CZ(target=5, control=1) + \
+                      CNOT(target=3, control=0) + \
+                      SWAP(first=0, second=3) + \
+                      Rx(target=1, angle="ang1") + \
+                      Ry(target=0, angle="ang2") + \
+                      Rz(target=2, angle="ang3") + \
+                      CRx(target=5, control=8, angle="ang4") + \
+                      CRy(target=6, control=9, angle="ang5") + \
+                      CRz(target=7, control=0, angle="ang6") + \
+                      Phase(control=0, target=1, phi="ang7") + \
+                      S(target=1, control=0) + \
+                      T(target=1, control=2) + \
+                      Rp(paulistring="Y(1)", angle="ang8") + \
+                      ExpPauli(paulistring="Z(1)X(2)", control=0, angle="ang9") + \
+                      Toffoli(target=2, first=4, second=3)
+
+    pyzx_circuit = convert_to_pyzx(tequila_circuit, variables=variables)
+    converted_circuit = convert_from_pyzx(pyzx_circuit)
+
+    wfn1 = simulate(tequila_circuit, backend="symbolic", variables=variables)
+    wfn2 = simulate(converted_circuit, backend="symbolic")
+
+    assert (numpy.isclose(wfn1.inner(wfn2), 1.0))
+
+
+@pytest.mark.skipif(not HAS_PYZX,
+                    reason="Pyzx package not installed, test_convert_to_from_pyzx_trotterized_gate not executed")
+@pytest.mark.parametrize(
+    "string1,string2,angles,steps",
+    [
+        ("1.0 X(1)Z(2) - 0.5 Z(3)X(4)", None,                          [numpy.pi/12],   1),
+        ("1.0 X(1)Z(2) + 0.5 Z(3)X(4)", "1.0 Y(1)X(2) - 0.9 X(2)Z(3)", [5.6, numpy.pi], 1),
+        ("1.5 Z(2)Z(4) + 0.8 Y(3)X(4)", None,                          [numpy.pi],      1)
+    ]
+)
+def test_convert_to_from_pyzx_trotterized_gate(string1, string2, angles, steps):
+
+    variables = {"ang1": angles[0]} if string2 is None else {"ang1": angles[0], "ang2": angles[1]}
+
+    g1 = QubitHamiltonian.from_string(string1)
+    g2 = None if string2 is None else QubitHamiltonian.from_string(string2)
+    tequila_circuit = Trotterized(generators=[g1] if string2 is None else [g1, g2],
+                                  angles=["ang1"] if string2 is None else ["ang1", "ang2"],
+                                  steps=steps)
+
+    pyzx_circuit = convert_to_pyzx(tequila_circuit, variables=variables)
+    converted_circuit = convert_from_pyzx(pyzx_circuit)
+
+    wfn1 = simulate(tequila_circuit, backend="symbolic", variables=variables)
+    wfn2 = simulate(converted_circuit, backend="symbolic")
+
+    assert (numpy.isclose(wfn1.inner(wfn2), 1.0))
+
+
+@pytest.mark.skipif(not HAS_PYZX,
+                    reason="Pyzx package not installed, test_convert_from_pyzx_exception not executed")
+def test_convert_from_pyzx_exception():
+
+    pyzx_circuit = pyzx.circuit.Circuit(qubit_amount=1)
+    tequila_circuit = QCircuit()
+
+    with pytest.raises(expected_exception=TequilaException,
+                       match="Circuit provided must be of type pyzx.circuit.Circuit"):
+        convert_from_pyzx(tequila_circuit)
+
+    assert (isinstance(convert_from_pyzx(pyzx_circuit), QCircuit))
+
+
+@pytest.mark.skipif(not HAS_PYZX,
+                    reason="Pyzx package not installed, test_convert_to_from_pyzx_optimizing_circuit not executed")
+@pytest.mark.parametrize(
+    "tequila_circuit,t_reduce",
+    [
+        (X(target=3) + Y(target=2) + Z(target=1), True),
+        (Rx(target=1, control=0, angle=5.67) + Ry(target=2, angle=0.98) + Rz(target=3, angle=1.67), False),
+        (H(target=1) + H(target=1, control=0) + X(target=1) + Y(target=0) + Z(target=2) +
+         CX(target=3, control=0) + CY(target=4, control=2) + CZ(target=5, control=1) +
+         CNOT(target=3, control=0) + SWAP(first=0, second=3) +
+         S(target=1, control=0) + T(target=1, control=2), True)
+    ]
+)
+def test_convert_to_from_pyzx_optimizing_circuit(tequila_circuit, t_reduce):
+
+    pyzx_circuit = convert_to_pyzx(tequila_circuit)
+
+    pyzx_graph = pyzx_circuit.to_graph()
+
+    if t_reduce:
+        pyzx.teleport_reduce(pyzx_graph)
+        pyzx_circuit_opt = pyzx.Circuit.from_graph(pyzx_graph)
+    else:
+        pyzx.full_reduce(pyzx_graph)
+        pyzx_graph.normalize()
+        pyzx_circuit_opt = pyzx.extract_circuit(pyzx_graph.copy())
+
+    # compare_tensors returns True if pyzx_circuit and pyzx_circuit_opt
+    # implement the same circuit (up to global phase)
+    assert (pyzx.compare_tensors(pyzx_circuit, pyzx_circuit_opt))
+
+    # verify_equality return True if full_reduce() is able to reduce the
+    # composition of the circuits to the identity
+    assert (pyzx_circuit.verify_equality(pyzx_circuit_opt))
+
+    converted_circuit = convert_from_pyzx(pyzx_circuit_opt)
+
+    wfn1 = simulate(tequila_circuit, backend="symbolic")
+    wfn2 = simulate(converted_circuit, backend="symbolic")
+
+    assert (numpy.isclose(wfn1.inner(wfn2), 1.0))
+
diff --git a/tests/test_qasm.py b/tests/test_qasm.py
new file mode 100644
index 00000000..b39454bd
--- /dev/null
+++ b/tests/test_qasm.py
@@ -0,0 +1,234 @@
+from tequila.circuit.qasm import export_open_qasm, import_open_qasm, import_open_qasm_from_file
+from tequila.circuit.gates import *
+from tequila.simulators.simulator_api import simulate
+import numpy
+import os
+import pytest
+
+
+@pytest.mark.parametrize(
+    "zx_calculus",
+    [
+        False,
+        True,
+    ]
+)
+def test_export_import_qasm_simple(zx_calculus):
+    tequila_circuit = H(target=1) + \
+                      X(target=1) + \
+                      Y(target=0) + \
+                      Z(target=2) + \
+                      CX(target=3, control=0) + \
+                      CY(target=4, control=2) + \
+                      CZ(target=5, control=1) + \
+                      CNOT(target=3, control=0) + \
+                      SWAP(first=0, second=3) + \
+                      S(target=1, control=0) + \
+                      T(target=1, control=2)
+
+    qasm_code_simple = export_open_qasm(tequila_circuit, zx_calculus=zx_calculus)
+    imported_circuit = import_open_qasm(qasm_code=qasm_code_simple)
+
+    wfn1 = simulate(tequila_circuit, backend="symbolic")
+    wfn2 = simulate(imported_circuit, backend="symbolic")
+
+    assert (numpy.isclose(wfn1.inner(wfn2), 1.0))
+
+
+@pytest.mark.parametrize(
+    "zx_calculus,variabs",
+    [
+        (False, [2.8, 5.6, 7.6, 1.8, 4.98, 2.35, 3.12, 6.79]),
+        (True,  [1.5, 3.7, 9.2, 3.1, 7.62, 1.98, 8.56, 2.97]),
+        (False, [0, 0, 0, 0, 0, 0, 0, 0]),
+        (True,  [0, 0, 0, 0, 0, 0, 0, 0]),
+        (False, [numpy.pi/12, numpy.pi, numpy.pi/3, numpy.pi/6, numpy.pi*0.95, numpy.pi/2, numpy.pi*2.3, numpy.pi/7]),
+        (True,  [numpy.pi/12, numpy.pi, numpy.pi/3, numpy.pi/6, numpy.pi*0.95, numpy.pi/2, numpy.pi*2.3, numpy.pi/7])
+    ]
+)
+def test_export_import_qasm(zx_calculus, variabs):
+
+    variables = {"ang1": variabs[0],
+                 "ang2": variabs[1],
+                 "ang3": variabs[2],
+                 "ang4": variabs[3],
+                 "ang5": variabs[4],
+                 "ang6": variabs[5],
+                 "ang7": variabs[6],
+                 "ang8": variabs[7]}
+
+    tequila_circuit = H(target=[0, 1]) + \
+                      H(target=0, control=1) + \
+                      X(target=1) + \
+                      Y(target=0) + \
+                      Z(target=2) + \
+                      CX(target=3, control=0) + \
+                      CY(target=4, control=2) + \
+                      CZ(target=5, control=1) + \
+                      CNOT(target=3, control=0) + \
+                      SWAP(first=0, second=3) + \
+                      Rx(target=1, angle="ang1") + \
+                      Ry(target=0, angle="ang2") + \
+                      Rz(target=2, angle="ang3") + \
+                      CRx(target=5, control=8, angle="ang4") + \
+                      CRy(target=6, control=9, angle="ang5") + \
+                      CRz(target=7, control=0, angle="ang6") + \
+                      Phase(control=0, target=1, phi="ang1") + \
+                      S(target=1, control=0) + \
+                      T(target=1, control=2) + \
+                      Rp(paulistring="Y(1)", angle="ang7") + \
+                      ExpPauli(paulistring="Z(1)X(2)", control=0, angle="ang8") + \
+                      Toffoli(target=2, first=4, second=3)
+
+    qasm_code = export_open_qasm(tequila_circuit, variables=variables, zx_calculus=zx_calculus)
+    imported_circuit = import_open_qasm(qasm_code=qasm_code)
+
+    wfn1 = simulate(tequila_circuit, backend="symbolic", variables=variables)
+    wfn2 = simulate(imported_circuit, backend="symbolic")
+
+    assert (numpy.isclose(wfn1.inner(wfn2), 1.0))
+
+
+@pytest.mark.parametrize(
+    "zx_calculus,target1,control1,target2,control2",
+    [
+        (False, 1,            None, 0,      1),
+        (True,  1,            None, 0,      1),
+        (False, [0, 1],       None, 0,      1),
+        (True,  [0, 1],       None, 0,      1),
+        (False, [0, 1, 2, 3], 4,    2,      1),
+        (True,  [0, 1, 2, 3], 4,    2,      1),
+        (False, [1, 2],       4,    [0, 3], 1),
+        (True,  [1, 2],       4,    [0, 3], 1)
+    ]
+)
+def test_export_import_qasm_h_ch_gate(zx_calculus, target1, control1, target2, control2):
+
+    tequila_circuit = H(target=target1, control=control1) + H(target=target2, control=control2)
+
+    qasm_code = export_open_qasm(tequila_circuit, zx_calculus=zx_calculus)
+    imported_circuit = import_open_qasm(qasm_code=qasm_code)
+
+    wfn1 = simulate(tequila_circuit, backend="symbolic")
+    wfn2 = simulate(imported_circuit, backend="symbolic")
+
+    assert (numpy.isclose(wfn1.inner(wfn2), 1.0))
+
+
+@pytest.mark.parametrize(
+    "zx_calculus,string1,string2,angles,steps",
+    [
+        (False, "1.0 X(1)Z(2) - 0.5 Z(3)X(4)", None,                          [numpy.pi/12],   1),
+        (True,  "1.0 X(1)Z(2) - 0.5 Z(3)X(4)", None,                          [numpy.pi/12],   1),
+        (False, "1.0 X(1)Z(2) + 0.5 Z(3)X(4)", "1.0 Y(1)X(2) - 0.9 X(2)Z(3)", [5.6, numpy.pi], 1),
+        (True,  "1.0 X(1)Z(2) + 0.5 Z(3)X(4)", "1.0 Y(1)X(2) - 0.9 X(2)Z(3)", [5.6, numpy.pi], 1),
+        (False, "1.5 Z(2)Z(4) + 0.8 Y(3)X(4)", None,                          [numpy.pi],      1),
+        (True,  "1.5 Z(2)Z(4) + 0.8 Y(3)X(4)", None,                          [numpy.pi],      2)
+    ]
+)
+def test_export_import_qasm_trotterized_gate(zx_calculus, string1, string2, angles, steps):
+
+    variables = {"ang1": angles[0]} if string2 is None else {"ang1": angles[0], "ang2": angles[1]}
+
+    g1 = QubitHamiltonian.from_string(string1)
+    g2 = None if string2 is None else QubitHamiltonian.from_string(string2)
+    tequila_circuit = Trotterized(generators=[g1] if string2 is None else [g1, g2],
+                                  angles=["ang1"] if string2 is None else ["ang1", "ang2"],
+                                  steps=steps)
+
+    qasm_code = export_open_qasm(tequila_circuit, variables=variables, zx_calculus=zx_calculus)
+    imported_circuit = import_open_qasm(qasm_code=qasm_code)
+
+    wfn1 = simulate(tequila_circuit, backend="symbolic", variables=variables)
+    wfn2 = simulate(imported_circuit, backend="symbolic")
+
+    assert (numpy.isclose(wfn1.inner(wfn2), 1.0))
+
+
+@pytest.mark.parametrize(
+    "zx_calculus,variabs",
+    [
+        (False, [2.8, 5.6, 7.6, 1.8, 4.98]),
+        (True,  [9.6, 4.1, 6.3, 2.5, 5.62]),
+        (False, [numpy.pi*3, numpy.pi, numpy.pi/3, numpy.pi, numpy.pi*0.95]),
+        (True,  [numpy.pi*2, numpy.pi, numpy.pi/4, numpy.pi, numpy.pi*0.68])
+    ]
+)
+def test_export_import_qasm_file(zx_calculus, variabs):
+
+    variables = {"ang1": variabs[0],
+                 "ang2": variabs[1],
+                 "ang3": variabs[2],
+                 "ang4": variabs[3],
+                 "ang5": variabs[4]}
+
+    tequila_circuit = H(target=[0, 1]) + \
+                      Y(target=0) + \
+                      Z(target=2) + \
+                      CY(target=4, control=2) + \
+                      SWAP(first=0, second=3) + \
+                      Ry(target=0, angle="ang1") + \
+                      Rz(target=2, angle="ang2") + \
+                      CRx(target=5, control=8, angle="ang3") + \
+                      CRy(target=6, control=9, angle="ang4") + \
+                      S(target=1, control=0) + \
+                      T(target=1, control=2) + \
+                      ExpPauli(paulistring="Y(1)Z(3)", control=0, angle="ang5") + \
+                      Toffoli(target=2, first=4, second=3)
+
+    file_name = "test_file_qasm.txt"
+
+    qasm_code = export_open_qasm(tequila_circuit, variables=variables, zx_calculus=zx_calculus,
+                                 filename=file_name)
+    imported_circuit = import_open_qasm(qasm_code=qasm_code)
+    imported_circuit_from_file = import_open_qasm_from_file(filename=file_name)
+
+    wfn1 = simulate(tequila_circuit, backend="symbolic", variables=variables)
+    wfn2 = simulate(imported_circuit, backend="symbolic")
+    wfn3 = simulate(imported_circuit_from_file, backend="symbolic")
+
+    # remove file
+    if os.path.exists(file_name):
+        os.remove(file_name)
+
+    assert (numpy.isclose(wfn1.inner(wfn2), 1.0))
+    assert (numpy.isclose(wfn1.inner(wfn3), 1.0))
+    assert (numpy.isclose(wfn2.inner(wfn3), 1.0))
+
+
+def test_import_qasm_with_custom_gates():
+
+    openqasmcode = "OPENQASM 2.0;\n" \
+                   "include \"qelib1.inc\";\n" \
+                   "gate mycustom a,b,c\n" \
+                   "{\n" \
+                   "cx c,b;\n" \
+                   "cx c,a;\n" \
+                   "}\n" \
+                   "qreg q1[3];\n" \
+                   "qreg q2[4];\n" \
+                   "creg c[3];\n" \
+                   "y q1[1];\n" \
+                   "z q2[2];\n" \
+                   "mycustom q1[0],q2[0],q1[2];\n" \
+                   "h q2[1];\n" \
+                   "mycustom q2[3],q1[1],q2[2];\n" \
+                   "y q2[1];\n"
+
+    imported_circuit = import_open_qasm(qasm_code=openqasmcode)
+
+    # openqasm   -> tequila qbits
+    # qreg q1[3] -> 0, 1, 2
+    # qreg q2[4] -> 3, 4, 5, 6
+
+    tequila_circuit = Y(target=1) + Z(target=5) + \
+                      CX(target=3, control=2) + CX(target=3, control=0) + \
+                      H(target=4) + \
+                      CX(target=1, control=5) + CX(target=6, control=5) + \
+                      Y(target=4)
+
+    wfn1 = simulate(tequila_circuit, backend="symbolic")
+    wfn2 = simulate(imported_circuit, backend="symbolic")
+
+    assert (numpy.isclose(wfn1.inner(wfn2), 1.0))
+
diff --git a/tests/test_recompilation_routines.py b/tests/test_recompilation_routines.py
index 8d43ca46..a7ca4da1 100644
--- a/tests/test_recompilation_routines.py
+++ b/tests/test_recompilation_routines.py
@@ -1,6 +1,7 @@
 import tequila.simulators.simulator_api
 from tequila.circuit import gates
-from tequila.circuit.compiler import compile_controlled_rotation, change_basis, compile_phase, compile_swap
+from tequila.circuit.compiler import compile_controlled_rotation, change_basis, compile_phase, compile_swap, \
+                                     compile_ry, compile_y, compile_ch
 from numpy.random import uniform, randint
 from numpy import pi, isclose
 from tequila.hamiltonian import paulis
@@ -90,4 +91,70 @@ def test_compile_swap():
     equivalent_swap = gates.X(target=0, control=3) + gates.X(target=3, control=0) + gates.X(target=0, control=3)
 
     assert (equivalent_circuit == equivalent_swap)
-    
+
+
+@pytest.mark.parametrize(
+    "target,control,angle",
+    [
+        (2, 4, 3.14),
+        (1, 0, numpy.pi / 7),
+        (1, None, numpy.pi / 5),
+        (5, None, 1.093)
+    ]
+)
+def test_compile_ry(target, control, angle):
+
+    circuit = gates.Ry(target=target, control=control, angle=angle)
+    equivalent_circuit = compile_ry(circuit)
+
+    equivalent_ry = gates.Rz(target=target, control=None, angle=-numpy.pi / 2) + \
+                    gates.Rx(target=target, control=control, angle=angle) + \
+                    gates.Rz(target=target, control=None, angle=numpy.pi / 2)
+
+    assert (equivalent_circuit == equivalent_ry)
+
+
+@pytest.mark.parametrize(
+    "target,control,power",
+    [
+        (2, 4, 1.5),
+        (4, 0, 1.0),
+        (0, 5, 2.9),
+        (1, None, 4.2),
+        (5, None, 3.9)
+    ]
+)
+def test_compile_y(target, control, power):
+
+    circuit = gates.Y(target=target, control=control, power=power)
+    equivalent_circuit_y = compile_y(circuit)
+
+    equivalent_y = gates.Rz(target=target, control=None, angle=-numpy.pi / 2) + \
+                   gates.X(target=target, control=control, power=power) + \
+                   gates.Rz(target=target, control=None, angle=numpy.pi / 2)
+
+    assert (equivalent_circuit_y == equivalent_y)
+
+
+@pytest.mark.parametrize(
+    "target,control,power",
+    [
+        (2, 4, 1.5),
+        (4, 2, 1.0),
+        (0, 5, 2.9),
+        (1, None, 4.2),
+        (5, None, 3.9)
+    ]
+)
+def test_compile_ch(target, control, power):
+
+    circuit = gates.H(target=target, control=control, power=power)
+    equivalent_circuit = compile_ch(circuit)
+
+    equivalent_ch = gates.Ry(target=target, control=None, angle=-numpy.pi / 4) + \
+                    gates.Z(target=target, control=control, power=power) + \
+                    gates.Ry(target=target, control=None, angle=numpy.pi / 4)
+
+    if control is not None:
+        assert (equivalent_circuit == equivalent_ch)
+
diff --git a/tests/test_simulator_backends.py b/tests/test_simulator_backends.py
index aac0850f..a47ab918 100644
--- a/tests/test_simulator_backends.py
+++ b/tests/test_simulator_backends.py
@@ -56,6 +56,16 @@ def test_interface(backend):
 INSTALLED_SIMULATORS = tequila.simulators.simulator_api.INSTALLED_SIMULATORS.keys()
 INSTALLED_SAMPLERS = tequila.simulators.simulator_api.INSTALLED_SAMPLERS.keys()
 
+@pytest.mark.parametrize("backend", INSTALLED_SAMPLERS)
+def test_sampling_accumulation(backend):
+    # minimal test that was added after a bug was discovered
+    # just needs to asssure that it runs through and no errors are thrown within the process
+    U = tq.gates.Ry(angle=numpy.pi/2, target=0) + tq.gates.CNOT(1,3)
+    H = tq.paulis.Qm(1)
+    E = tq.ExpectationValue(H=H, U=U)
+    result = tq.simulate(E, backend=backend, samples=100)
+    assert result == 0.0
+
 
 @pytest.mark.parametrize("backend", INSTALLED_SAMPLERS)
 def test_sampling_circuits(backend):
diff --git a/tutorials/BasicUsage.ipynb b/tutorials/BasicUsage.ipynb
deleted file mode 100644
index fc35a281..00000000
--- a/tutorials/BasicUsage.ipynb
+++ /dev/null
@@ -1,969 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Tequila Basic Usage"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Create and Simulate Quantum Circuits\n",
-    "\n",
-    "Tequila operators on abstract data types which can be translated and executed on various backends.  \n",
-    "In this part of the tutorial we show how to initialize and execute those.\n",
-    "\n",
-    "First import tequila and check which backends are installed on your system.  \n",
-    "If supported backends are not installed you can for most of them just install them with\n",
-    "`pip install --upgrade name`  in your command line  \n",
-    "If you have old versions of supported backends installed that might get you in trouble.   \n",
-    "You can upgrade them with the same command."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "backend         | wfn        | sampling   | noise      | installed \n",
-      "--------------------------------------------------------------------\n",
-      "qulacs_gpu      | False      | False      | False      | False     \n",
-      "qulacs          | True       | True       | True       | True      \n",
-      "qibo            | False      | False      | False      | False     \n",
-      "qiskit          | True       | True       | True       | True      \n",
-      "cirq            | True       | True       | True       | True      \n",
-      "pyquil          | True       | True       | True       | True      \n",
-      "symbolic        | True       | False      | False      | True      \n"
-     ]
-    }
-   ],
-   "source": [
-    "import tequila as tq\n",
-    "tq.show_available_simulators()\n",
-    "from numpy import pi\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Create Simple Circuits"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Lets create some simple unparametrized circutis.  \n",
-    "With unparametrized we mean here, that possible angles in the circuits are fixed.  \n",
-    "You can create tequila circuits and gates over the `tq.gates` module.  \n",
-    "Gates and circuits can be glued together with the `+` operation.  \n",
-    "\n",
-    "Gates can receive the keyword arguments `target` and `control` which defines qubit(s) on which the gates act"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "circuit = tq.gates.H(target=0) + tq.gates.CNOT(target=1,control=0)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Circuits can be printed out in list-type form or can be drawn by the backends.  \n",
-    "The result of tq.draw will depend which backends you have installed.  \n",
-    "If you want to draw with a specific backend, just pass the `backend` keyword, e.g. tq.draw(circuit,`backend='cirq'`)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "circuit: \n",
-      "H(target=(0,))\n",
-      "X(target=(1,), control=(0,))\n",
-      "\n"
-     ]
-    }
-   ],
-   "source": [
-    "print(circuit)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "0: ───H───@───\n",
-      "          │\n",
-      "1: ───────X───\n"
-     ]
-    }
-   ],
-   "source": [
-    "tq.draw(circuit)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Lets do the same with a list of qubits and see what happens"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "0: ───H───@───\n",
-      "          │\n",
-      "1: ───H───X───\n"
-     ]
-    }
-   ],
-   "source": [
-    "circuit = tq.gates.H(target=[0,1]) + tq.gates.X(target=1, control=0)\n",
-    "tq.draw(circuit)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Some gates have to be parametrized by `angle` and some can be parametrized by `power`.  \n",
-    "Note that if you use cirq to draw circuits, it will display those in different units. This does not affect the simulation.\n",
-    "\n",
-    "Tequila uses the standard convention for qubit rotations:\n",
-    "$$\n",
-    "R_i(\\theta) = e^{-i\\frac{\\theta}{2} \\sigma_i}, \\qquad i \\in \\left\\{ X, Y, Z \\right\\}\n",
-    "$$\n",
-    "\n",
-    "which is carried over for multi-qubit rotations\n",
-    "$$\n",
-    "R_P(\\theta) = e^{-i\\frac{\\theta}{2} P}\n",
-    "$$\n",
-    "where $P$ is a paulistring like e.g. $X(0)Y(1)$"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "0: ───H──────────@────────────────@───H───────────\n",
-      "                 │                │\n",
-      "1: ───Rx(0.5π)───X───Rz(0.318π)───X───Rx(-0.5π)───\n"
-     ]
-    }
-   ],
-   "source": [
-    "# Some further examples\n",
-    "circuit0 = tq.gates.Ry(angle=1.0, target=0) + tq.gates.X(target=1, control=0)\n",
-    "circuit1 = tq.gates.Y(power=0.5, target=0) + tq.gates.Ry(angle=1.0, target=1, control=0)\n",
-    "circuit2 = tq.gates.Rp(angle=1.0, paulistring=\"Y(0)\") + tq.gates.X(target=1, control=0) # acts the same as circuit0\n",
-    "circuit3 = tq.gates.Rp(angle=1.0, paulistring=\"X(0)Y(1)\")\n",
-    "\n",
-    "generator = tq.paulis.Y(0)\n",
-    "circuit4 = tq.gates.Trotterized(generators=[generator], angles=[1.0], steps=1) # acts the same as circuit0\n",
-    "generator = tq.paulis.X(0)*tq.paulis.Y(1)\n",
-    "circuit5 = tq.gates.Trotterized(generators=[generator], angles=[1.0], steps=1) # acts the same as circuit3\n",
-    "\n",
-    "tq.draw(circuit3)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Simulate and Sample Simple Circuits"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Lets simulate our last created circuit.  \n",
-    "This can be done by the `tq.simulate` function.   \n",
-    "The return type is a `QubitWaveFunction`"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "+0.5000|00> +0.5000|10> +0.5000|01> +0.5000|11> \n"
-     ]
-    }
-   ],
-   "source": [
-    "wfn = tq.simulate(circuit)\n",
-    "print(wfn)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "You can control on which backend the simulation is executed with the `backend=name` keyword where name is one of the backends that are installed on your system (see first cell)  "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "+0.5000|00> +0.5000|10> +0.5000|01> +0.5000|11> \n"
-     ]
-    }
-   ],
-   "source": [
-    "# simulate on 'qulacs' backend (which is the default)\n",
-    "# Note that this cell will crash if qulacs is not installed\n",
-    "# just switch the name with something that is installed on your system (check the first cell)\n",
-    "wfn = tq.simulate(circuit, backend='qulacs')\n",
-    "print(wfn)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "If you don't want to simulate a full wavefunction but rather simulate individual samples from it you can pass down the `samples=integer` keyword"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "+4.0000|11> +2.0000|10> +4.0000|00> \n"
-     ]
-    }
-   ],
-   "source": [
-    "measurements = tq.simulate(circuit, samples=10)\n",
-    "print(measurements)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "You can access the individual measurements either by integers in binary notation or by binary strings"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "4\n",
-      "4\n",
-      "2\n",
-      "2\n"
-     ]
-    }
-   ],
-   "source": [
-    "print(measurements(0))\n",
-    "print(measurements(\"00\"))\n",
-    "print(measurements(2))\n",
-    "print(measurements(\"10\"))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Individual measurement instructions can be added over the `read_out_qubits` keyword"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "+1.0000|0> +5.0000|1> "
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "compiled_circuit = tq.compile(circuit, samples=10, backend=\"qulacs\")\n",
-    "\n",
-    "compiled_circuit(samples=10, read_out_qubits=[0])"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Create Parametrized Circuits\n",
-    "\n",
-    "Now we will explore how to create parametrized circuits.  \n",
-    "This works analogue to the simple circuits before, just that `angle` and `power` can be set to hashable types.  \n",
-    "You can either initialize the variable directly or you can create a tequila variable object and use that.  \n",
-    "The latter is only important if you intend to pass down a manipulated variable (like for example $a^2$ instead of just $a$)\n",
-    "\n",
-    "Lets start with something simple: A parametrized rotation on a single qubit.  \n",
-    "We will call the variable $a$.  \n",
-    "If the circuit gets simulated the value of the variable has to be specified.  \n",
-    "This is done by passing down a dictionary holding the names and values of all variables."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# initialize the parametrized circuit\n",
-    "circuit = tq.gates.Ry(angle=\"a\", target=0)\n",
-    "pi = tq.numpy.pi\n",
-    "# set the value we want to simulate\n",
-    "variables = {\"a\" : pi**2}\n",
-    "wfn = tq.simulate(circuit, variables=variables)\n",
-    "print(wfn)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "You can see if a circuit is parametrized by calling `extract_variables` from the circuit.  \n",
-    "Note that if you use the cirq backend to draw the circuit"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "print(\"circuit has variables: \", circuit.extract_variables())"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Now the same thing a little more sophisticated.  \n",
-    "We will parametrized the gate by $a^2$ and also we want the $a$ to be in units of $\\pi$ "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "a = tq.Variable(\"a\")\n",
-    "\n",
-    "circuit = tq.gates.Ry(angle=(a*pi)**2, target=0)\n",
-    "\n",
-    "# set the value we want to simulate\n",
-    "variables = {\"a\" : 1.0}\n",
-    "wfn = tq.simulate(circuit, variables=variables)\n",
-    "print(wfn)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Now the same again with a stronger transformation on the variables:  \n",
-    "In general, if you want to apply transformations on Variables (and later on Objectives) this can be done with   \n",
-    "`variable.apply(your_function)`.  \n",
-    "Here we will take the exponential function of numpy. Note that it is adviced to take those functions from `tq.numpy` since this will be the `jax` numpy used for automaticl differentiation.  \n",
-    "By doing so consistently you will avoid potential problems with gradients later."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "a = tq.Variable(\"a\")\n",
-    "\n",
-    "circuit = tq.gates.Ry(angle=((a*pi)**2).apply(tq.numpy.exp), target=0)\n",
-    "\n",
-    "# set the value we want to simulate\n",
-    "variables = {\"a\" : 1.0}\n",
-    "wfn = tq.simulate(circuit, variables=variables)\n",
-    "print(wfn)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Lets do the same thing once more, but this time with a customized transformation (which will do the same as in the last cell)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# define your own transformation\n",
-    "def my_trafo(x):\n",
-    "    return tq.numpy.exp(x**2)\n",
-    "\n",
-    "a = tq.Variable(\"a\")\n",
-    "\n",
-    "# we will put the variable manipulation here for more overview\n",
-    "a = a*pi # a is now in a*pi\n",
-    "a = a.apply(my_trafo) # a is now exp((a*pi)**2)\n",
-    "\n",
-    "circuit = tq.gates.Ry(angle=a, target=0)\n",
-    "\n",
-    "# set the value we want to simulate\n",
-    "variables = {\"a\" : 1.0}\n",
-    "wfn = tq.simulate(circuit, variables=variables)\n",
-    "print(wfn)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Note that you don't have to use strings as variable names.  \n",
-    "You can use any hashable type except numeric types since those will be interpeted as fixed numbers.\n",
-    "Here is one example using a combination of strings and tuples"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "circuit = tq.gates.Ry(angle=(1,\"a\", \"its a stupid example\"), target=0)\n",
-    "print(circuit.extract_variables())\n",
-    "circuit = tq.gates.Ry(angle=(1,2,3), target=0)\n",
-    "print(circuit.extract_variables())"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Create and Simulate Objectives/Expectationvalues"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Within tequila you can define qubit operators which can either be used to generate gates and circuits over `tq.gates.Rp`, `tq.gates.Trotterized` or `tq.gates.GeneralizedRotation` or as Hamiltonians defining the measurements on the quantum experiments. \n",
-    "\n",
-    "`QCircuit` and `QubitHamiltonian` objects can be combined to expectation values which can be combined and transformed to become more general `Objectives` (in tequila an expectation value is already objective in its simplest form).\n",
-    "\n",
-    "We will start by demonstrating this with a simple one qubit example.  \n",
-    "We will take the one qubit rotation gate from previous sections and use a simple pauli operator as hamiltonian.\n",
-    "So our expectation value will be:  \n",
-    "\n",
-    "$$\n",
-    "E = \\langle\\Psi(a)\\rvert H \\lvert\\Psi(a) \\rangle = \\langle0\\rvert U^\\dagger\\left(a\\right) H  U\\left(a\\right) \\lvert 0\\rangle = \\langle H \\rangle_{ U\\left(a\\right)}\n",
-    "$$  \n",
-    "  \n",
-    "where $H = \\sigma_x = X $ and $ U\\left(a\\right) = Ry(a)$"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# the circuit\n",
-    "U = tq.gates.Ry(angle=\"a\", target=0)\n",
-    "# the Hamiltonian\n",
-    "H = tq.paulis.X(0)\n",
-    "# the Objective (a single expectation value)\n",
-    "E = tq.ExpectationValue(H=H, U=U)\n",
-    "print(\"Hamiltonian \", H)\n",
-    "print(E)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# better not use it for large objectives\n",
-    "tq.draw(E)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Lets simulate the objective for some choices of our variable.  \n",
-    "Note that the simulate function is the same as before for the circuits, you can use the `backend` and `sample` key in the same way.  \n",
-    "\n",
-    "Since the objective is defined with parametrized quantum circuits, the values of the variables have to be passed down in the same way as before.  \n",
-    "\n",
-    "Note that not all expectationvalues in the objective need to be parametrized and that the parameters don't need to be the same.  "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "variables = {\"a\": 1.0}\n",
-    "value = tq.simulate(E, variables=variables)\n",
-    "print(\"Objective({}) = {}\".format(variables[\"a\"], value))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Here are some more intuitive examples of Hamiltonians.  \n",
-    "Note that those operators are not automatically hermitian.  \n",
-    "You can use the `split` function to get the hermitian and/or antihermitian part  \n",
-    "Check also the `FAQ` notebook for some more information."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# Pauli Operators can be initialilzed and added/multipled \n",
-    "H = tq.paulis.X(qubit=[0,1,2,3]) + tq.paulis.Y(2) + tq.paulis.Z(qubit=[0,1])*tq.paulis.X(2)\n",
-    "print(H, \" is hermitian = \", H.is_hermitian())\n",
-    "\n",
-    "H = tq.paulis.Z(0)*tq.paulis.Y(0) + tq.paulis.X(0)\n",
-    "print(H, \" is hermitian = \", H.is_hermitian())\n",
-    "\n",
-    "hermitian_part, anti_hermitian_part = H.split()\n",
-    "print(\"hermitian part      = \", hermitian_part)\n",
-    "print(\"anti-hermitian part = \", anti_hermitian_part)\n",
-    "\n",
-    "H = tq.paulis.Projector(\"|00>\")\n",
-    "print(H, \" is hermitian = \", H.is_hermitian())\n",
-    "\n",
-    "H = tq.paulis.Projector(\"1.0*|00> + 1.0*|11>\")\n",
-    "print(H, \" is hermitian = \", H.is_hermitian())\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Lets proceed with our previous simple example of a single qubit rotation and a single X as Hamiltonian.\n",
-    "\n",
-    "If you intent to evaluate the objective with lots of different choices of the variables it is useful to compile it.  A compiled objective is tied to a specific backend and can be used like a function taking a dictionary of variables.\n",
-    "\n",
-    "The compile function takes also the `backend` and `sample` keyword. If no backend is chosen tequila will pick automatically from the installed ones. If you intent to sample your objective instead of fully simulate it you can give a dummy integer of samples to `compile`. This will help tequila pick the best available backend but will not fix the number of samples for future evaluations.\n",
-    "\n",
-    "Compiling first will make your code faster since then the abstract circuits do not need to be re-translated to the backend every time."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "compiled_objective = tq.compile(E)\n",
-    "\n",
-    "# the compiled objective can now be used like a function\n",
-    "for value in [0.0, 0.5, 1.0]:\n",
-    "    evaluated = compiled_objective(variables={\"a\": value})\n",
-    "    print(\"objective({}) = {}\".format(value, evaluated))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Lets simulate our compiled objetive and plot the results"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def compile_and_evaluate(objective, steps=25, samples=None, start=0, stop=2*pi):\n",
-    "    from matplotlib import pyplot as plt\n",
-    "    plt.figure()\n",
-    "    \n",
-    "    compiled_objective = tq.compile(objective, samples=samples)\n",
-    "    values = [start + (stop-start)*step/steps for step in range(steps)]\n",
-    "    evaluated = [compiled_objective(variables={\"a\": value}, samples=samples) for value in values]\n",
-    "\n",
-    "    plt.plot(values, evaluated)\n",
-    "    plt.show()\n",
-    "    return values, evaluated\n",
-    "\n",
-    "compile_and_evaluate(E);"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Lets do the same again with a more complicated objective.  \n",
-    "Lets take the square of our original expectation value and shift it by 1\n",
-    "\n",
-    "$$\n",
-    "L = E^2 + 1\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# this is the new objective\n",
-    "L = E**2 + 1\n",
-    "\n",
-    "compile_and_evaluate(L);"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "And the same, but shifted by $e^{-a^2}$, so the shift is not constant and will only affect $L$ for small values of $a$.\n",
-    "\n",
-    "$$\n",
-    "L = E^2 + e^{-a^2}\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# For completeness we initialize the variable again here\n",
-    "a = tq.Variable(\"a\")\n",
-    "# to be sure that the variable is the same as the one from the objective we could also do\n",
-    "# a = objective.extract_variables()[0]\n",
-    "\n",
-    "# this is the new objective\n",
-    "L = E**2 + (-a**2).apply(tq.numpy.exp)\n",
-    "\n",
-    "compile_and_evaluate(L);"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Now we also transform the expectation value in a more complicated way. It works the same way as it works for variables\n",
-    "\n",
-    "$$\n",
-    "L = exp(-E^2) + exp(-a^2)E\n",
-    "$$\n",
-    "\n",
-    "Note that the original expectation value now enters two times into the objective.  \n",
-    "But tequila will only evaluate it once per run."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# For completeness we initialize the variable again here\n",
-    "a = tq.Variable(\"a\")\n",
-    "# to be sure that the variable is the same as the one from the objective we could also do\n",
-    "# a = objective.extract_variables()[0]\n",
-    "\n",
-    "# this is the new objective\n",
-    "L = E**2 + (-a**2).apply(tq.numpy.exp)*E\n",
-    "\n",
-    "compile_and_evaluate(L);\n",
-    "\n",
-    "# check how many (unique) expectation values are in the objective\n",
-    "print(L)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "At last, lets take our last objective but sample from it. \n",
-    "This means that in the evaluation of the expectation value the measurements on the underlying circuit are sampled.  \n",
-    "Feel free to play with the number of samples."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# For completeness we initialize the variable again here\n",
-    "a = tq.Variable(\"a\")\n",
-    "# to be sure that the variable is the same as the one from the objective we could also do\n",
-    "# a = objective.extract_variables()[0]\n",
-    "\n",
-    "# this is the new objective\n",
-    "L = E**2 + (-a**2).apply(tq.numpy.exp)*E\n",
-    "\n",
-    "compile_and_evaluate(L, samples=1000);\n",
-    "\n",
-    "# check how many (unique) expectation values are in the objective\n",
-    "print(L)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Derivatives of Objectives\n",
-    "\n",
-    "Derivatives of objectives are objectives themselves.\n",
-    "They can be simply created by applying `tq.grad` on a objective.  \n",
-    "\n",
-    "Lets take first objective and plot its derivative.\n",
-    "The first is easy to check since the derivative should just be the shifted sinus curve.\n",
-    "Feel free to change the objective and play around.\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "L = E\n",
-    "\n",
-    "dLda = tq.grad(L, \"a\")\n",
-    "d2Ld2a = tq.grad(dLda, \"a\")\n",
-    "print(\"Objective:\\n\", L)\n",
-    "compile_and_evaluate(L);\n",
-    "print(\"First Derivative:\\n\",dLda)\n",
-    "compile_and_evaluate(dLda);\n",
-    "print(\"Second Derivative:\\n\",d2Ld2a)\n",
-    "compile_and_evaluate(d2Ld2a);\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# another example\n",
-    "L = E**2 + (-a**2).apply(tq.numpy.exp)*E\n",
-    "dLda = tq.grad(L, \"a\")\n",
-    "d2Ld2a = tq.grad(dLda, \"a\")\n",
-    "print(\"Objective:\\n\", L)\n",
-    "compile_and_evaluate(L);\n",
-    "print(\"First Derivative:\\n\",dLda)\n",
-    "compile_and_evaluate(dLda);\n",
-    "print(\"Second Derivative:\\n\",d2Ld2a)\n",
-    "compile_and_evaluate(d2Ld2a);\n",
-    "\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# All in one\n",
-    "\n",
-    "At last we will create a small toy objective and use the phoenics optimizer to find local minima.  \n",
-    "\n",
-    "As expectation value we will use an entangled circuit with one CNOT gate and one Ry rotation and an arbitrary chosen Hamiltonian.\n",
-    "\n",
-    "Our objective is defined as\n",
-    "\n",
-    "$$\\displaystyle\n",
-    "L = \\langle H \\rangle_{U(a)} + e^{-\\left(\\frac{\\partial}{\\partial a} \\langle H \\rangle_{U_{a}}\\right)^2 }\n",
-    "$$\n",
-    "\n",
-    "with \n",
-    "\n",
-    "$$\n",
-    "H = -X(0)X(1) + \\frac{1}{2}Z(0) + Y(1)\n",
-    "$$\n",
-    "\n",
-    "and \n",
-    "\n",
-    "$$\n",
-    "U = e^{-\\frac{e^{-a^2}}{2} Y(0)} \\text{CNOT}(0,1)\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# All in one\n",
-    "\n",
-    "a = tq.Variable(\"a\")\n",
-    "U = tq.gates.Ry(angle=(-a**2).apply(tq.numpy.exp)*pi, target=0)\n",
-    "U += tq.gates.X(target=1, control=0)\n",
-    "\n",
-    "H = tq.QubitHamiltonian.from_string(\"-1.0*X(0)X(1)+0.5Z(0)+Y(1)\")\n",
-    "\n",
-    "E = tq.ExpectationValue(H=H, U=U)\n",
-    "dE = tq.grad(E, \"a\")\n",
-    "\n",
-    "objective = E + (-dE**2).apply(tq.numpy.exp)\n",
-    "\n",
-    "param, values = compile_and_evaluate(objective, steps=100, start =-5, stop=5);"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# We need to specify the phoenics config here\n",
-    "# the only change is that we are changing the interval for periodic boundary conditions to [-3,3] istead df [0, 2pi]\n",
-    "# not that the original interval would also work here\n",
-    "# we are restricting the search to 10 iterations here\n",
-    "# check out the notebook on phoenics for more information\n",
-    "phoenics_config = {'general': {'auto_desc_gen': 'False', 'batches': 5, 'boosted': 'False', 'parallel': 'False'}, 'parameters': [{'name': a, 'periodic': 'True', 'type': 'continuous', 'size': 1, 'low': -3., 'high': 3.}], 'objectives': [{'name': 'Energy', 'goal': 'minimize'}]}\n",
-    "result = tq.minimize(method='phoenics', objective = objective, phoenics_config = phoenics_config, maxiter=10)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# plot the points phoenics visited\n",
-    "# the information is in the optimizer history\n",
-    "# we have 'angles' and `energies' giving us information about every evaluation\n",
-    "import matplotlib.pyplot as plt\n",
-    "points = {}\n",
-    "energies = result.history.energies\n",
-    "angles = result.history.angles\n",
-    "for it, energy in enumerate(energies):\n",
-    "    angle = angles[it][tq.Variable(\"a\")]\n",
-    "    points[angle] = energy\n",
-    "\n",
-    "plt.plot(param, values, linestyle=\"--\")\n",
-    "plt.plot(list(points.keys()), list(points.values()), marker = \"o\", linestyle=\" \", label=\"phoenics\")\n",
-    "plt.legend()\n",
-    "plt.show()\n",
-    "    \n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In case you want to play with different optimizers (see also the SciPyOptimizers and FAQ notebooks)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "tq.show_available_optimizers()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "tequila-3.6",
-   "language": "python",
-   "name": "tequila-3.6"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.6.9"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}
diff --git a/tutorials/Chemistry.ipynb b/tutorials/Chemistry.ipynb
deleted file mode 100644
index a969eda2..00000000
--- a/tutorials/Chemistry.ipynb
+++ /dev/null
@@ -1,1046 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Tequila Chemistry Basics\n",
-    "\n",
-    "Here we show the basics of the tequila chemistry module.  \n",
-    "In order for this to work you need to have psi4 installed in the same python environment as tequila.  \n",
-    "If you are in a conda environment installing psi4 is easy:\n",
-    "`conda install psi4 -c psi4`  \n",
-    "But better check the [psi4 website](http://www.psicode.org/) for up to date instructions.\n",
-    "\n",
-    "In some cases, problems with the environment were observed which are suspected to originate from conflicts between psi4 and tequila dependcies. Usually the safest way is to install psi4 **first** and then install tequila.  \n",
-    "\n",
-    "Basic functionality is currently also provided with PySCF which might be easier to install. \n",
-    "\n",
-    "At the moment we only support automatized handling of closed-shell molecules\n",
-    "\n",
-    "This tutorial will give an overview over:\n",
-    "\n",
-    "- Initialization of molecules within tequila\n",
-    "- Usage of different qubit encodings from openermion (JW, BK, BKSF, Tapered-BK)\n",
-    "- Using basic functionality of Psi4 with tequila\n",
-    "- Setting up active spaces\n",
-    "- Constructing UCC based quantum circuits with tequila\n",
-    "\n",
-    "**There might be issues with psi4 and jupyter, currently the workarround is to reload the kernel before a cell gets executed, or run as a regular python script**  \n",
-    "(issue seems to be resolved, leaving this warning in, just in case)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import tequila as tq"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Initialize Molecules\n",
-    "\n",
-    "Molecules can be initialized by passing their geometries as string or the name of a `xyz` file."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "<class 'tequila.quantumchemistry.psi4_interface.QuantumChemistryPsi4'>\n",
-      "Qubit Encoding\n",
-      "transformation=<function jordan_wigner at 0x7f66d9b5b320>\n",
-      "basis_set       : sto-3g          \n",
-      "geometry        : H 0.0 0.0 0.0\n",
-      "Li 0.0 0.0 1.6 \n",
-      "description     :                 \n",
-      "multiplicity    : 1               \n",
-      "charge          : 0               \n",
-      "closed_shell    : True            \n",
-      "name            : molecule        \n",
-      "\n",
-      "Psi4 Data\n",
-      "Point Group (full) : c_inf_v         \n",
-      "Point Group (used) : c2v             \n",
-      "nirrep          : 4 \n",
-      "irreps          : ['A1', 'A2', 'B1', 'B2'] \n",
-      "mos per irrep   : [4, 0, 1, 1]    \n",
-      "\n",
-      "The Orbitals are:\n",
-      "0 : 0A1 energy = -2.348839 \n",
-      "1 : 1A1 energy = -0.285276 \n",
-      "2 : 2A1 energy = +0.078216 \n",
-      "3 : 0B1 energy = +0.163950 \n",
-      "4 : 0B2 energy = +0.163950 \n",
-      "5 : 3A1 energy = +0.547769 \n"
-     ]
-    }
-   ],
-   "source": [
-    "import tequila as tq\n",
-    "molecule = tq.chemistry.Molecule(geometry = \"H 0.0 0.0 0.0\\nLi 0.0 0.0 1.6\", basis_set=\"sto-3g\")\n",
-    "print(molecule)\n",
-    "\n",
-    "# lets also print some information about the orbitals\n",
-    "# we need it later\n",
-    "\n",
-    "print(\"The Orbitals are:\")\n",
-    "for orbital in molecule.orbitals:\n",
-    "    print(orbital)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "You can initialize a tequila `QubitHamiltonian` from a molecule with `make_hamiltonian`.\n",
-    "The standard transformation is the `jordan-wigner` transformation.  \n",
-    "You can use other transformations by initializing the molecule with the `transformation` keyword."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Hamiltonian has 631 terms\n",
-      "Hamiltonian has 12 qubits\n"
-     ]
-    }
-   ],
-   "source": [
-    "import tequila as tq\n",
-    "H = molecule.make_hamiltonian()\n",
-    "# the LiH Hamiltonian is already quite large, better not print the full thing\n",
-    "print(\"Hamiltonian has {} terms\".format(len(H)))\n",
-    "print(\"Hamiltonian has {} qubits\".format(H.n_qubits))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Hamiltonian has 631 terms\n",
-      "Hamiltonian has 12 qubits\n"
-     ]
-    }
-   ],
-   "source": [
-    "molecule = tq.chemistry.Molecule(geometry = \"H 0.0 0.0 0.0\\nLi 0.0 0.0 1.6\", basis_set=\"sto-3g\", transformation=\"bravyi_kitaev\")\n",
-    "H = molecule.make_hamiltonian()\n",
-    "print(\"Hamiltonian has {} terms\".format(len(H)))\n",
-    "print(\"Hamiltonian has {} qubits\".format(H.n_qubits))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "trafo_args =  {'active_orbitals': 12, 'active_fermions': 4}\n",
-      "trafo_args =  {'active_orbitals': 12, 'active_fermions': 4}\n",
-      "Hamiltonian has 631 terms\n",
-      "Hamiltonian has 10 qubits\n"
-     ]
-    }
-   ],
-   "source": [
-    "molecule = tq.chemistry.Molecule(geometry = \"H 0.0 0.0 0.0\\nLi 0.0 0.0 1.6\", basis_set=\"sto-3g\", transformation=\"symmetry_conserving_bravyi_kitaev\")\n",
-    "H = molecule.make_hamiltonian()\n",
-    "print(\"Hamiltonian has {} terms\".format(len(H)))\n",
-    "print(\"Hamiltonian has {} qubits\".format(H.n_qubits))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Using different Qubit Encodings of OpenFermion"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The different qubit encodings of openfermion can be applied by passing the keyword `transformation` to the molecule and setting it to the name of the corresponding openfermion function.  \n",
-    "\n",
-    "Some of those transformation might require additional keywords. Following `psi4` conventions those should be given to the `Molecule` initialization with the prefix `transformation__`. For most of them, `tequila` is however able to assign the keys automatically (see above for the `symmetry_conserving_bravyi_kitaev` transformation, that tapers off two qubits.\n",
-    "\n",
-    "In the following we provide some examples using various transformations from openfermion"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Jordan-Wigner\n",
-      " -0.0421+0.1777Z(0)+0.1777Z(1)-0.2427Z(2)-0.2427Z(3)+0.1706Z(0)Z(1)+0.0448Y(0)X(1)X(2)Y(3)-0.0448Y(0)Y(1)X(2)X(3)-0.0448X(0)X(1)Y(2)Y(3)+0.0448X(0)Y(1)Y(2)X(3)+0.1229Z(0)Z(2)+0.1677Z(0)Z(3)+0.1677Z(1)Z(2)+0.1229Z(1)Z(3)+0.1763Z(2)Z(3)\n",
-      "lowest energy =  -1.1361894540879054\n",
-      "Bravyi-Kitaev\n",
-      " -0.0421+0.1777Z(0)+0.1777Z(0)Z(1)-0.2427Z(2)-0.2427Z(1)Z(2)Z(3)+0.1706Z(1)+0.0448Y(0)Z(1)Y(2)Z(3)+0.0448X(0)Z(1)X(2)+0.0448X(0)Z(1)X(2)Z(3)+0.0448Y(0)Z(1)Y(2)+0.1229Z(0)Z(2)+0.1677Z(0)Z(1)Z(2)Z(3)+0.1677Z(0)Z(1)Z(2)+0.1229Z(0)Z(2)Z(3)+0.1763Z(1)Z(3)\n",
-      "lowest energy =  -1.136189454087905\n",
-      "trafo_args =  {'active_orbitals': 4, 'active_fermions': 2}\n",
-      "trafo_args =  {'active_orbitals': 4, 'active_fermions': 2}\n",
-      "Symmetry conserving Bravyi-Kitaev\n",
-      " -0.2879+0.4205Z(0)+0.4205Z(1)+0.0115Z(0)Z(1)+0.1790X(0)X(1)\n",
-      "lowest energy =  -1.1361894540879054\n"
-     ]
-    }
-   ],
-   "source": [
-    "import tequila as tq\n",
-    "import numpy\n",
-    "geomstring = \"H 0.0 0.0 0.0\\nH 0.0 0.0 0.7\"\n",
-    "basis_set = \"sto-3g\"\n",
-    "\n",
-    "# Jordan-Wigner (this is the default)\n",
-    "mol = tq.chemistry.Molecule(geometry=geomstring, basis_set=basis_set, transformation=\"jordan_wigner\")\n",
-    "H = mol.make_hamiltonian()\n",
-    "print(\"Jordan-Wigner\\n\", H)\n",
-    "eigenValues = numpy.linalg.eigvalsh(H.to_matrix())\n",
-    "print(\"lowest energy = \", eigenValues[0])\n",
-    "\n",
-    "# Bravyi-Kitaev\n",
-    "mol = tq.chemistry.Molecule(geometry=geomstring, basis_set=basis_set, transformation=\"bravyi_kitaev\")\n",
-    "H = mol.make_hamiltonian()\n",
-    "print(\"Bravyi-Kitaev\\n\", H)\n",
-    "eigenValues = numpy.linalg.eigvalsh(H.to_matrix())\n",
-    "print(\"lowest energy = \", eigenValues[0])\n",
-    "\n",
-    "# symmetry_conserving_bravyi_kitaev\n",
-    "# this transformation will taper off two qubits of the Hamiltonian\n",
-    "# it needs additional information on the number of spin-orbitals and the active_fermions/electrons in the system\n",
-    "mol = tq.chemistry.Molecule(geometry=geomstring, basis_set=basis_set,\n",
-    "                              transformation=\"symmetry_conserving_bravyi_kitaev\")\n",
-    "H = mol.make_hamiltonian()\n",
-    "print(\"Symmetry conserving Bravyi-Kitaev\\n\", H)\n",
-    "eigenValues = numpy.linalg.eigvalsh(H.to_matrix())\n",
-    "print(\"lowest energy = \", eigenValues[0])\n",
-    "\n",
-    "# Symmetry "
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Setting active spaces\n",
-    "\n",
-    "You can define active spaces on your molcule by passing down a dictionary of active orbitals.  \n",
-    "The orbitals are grouped into the irreducible representation of the underlying symmetry group (see the printout of `print(molecule)` above).\n",
-    "\n",
-    "Lets take the LiH molecule from above but initialize it with an active space containing the second two A1 orbitals (meaning the first 0A1 orbital is frozen) and the B1 orbital"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Hamiltonian has 62 terms\n"
-     ]
-    }
-   ],
-   "source": [
-    "import tequila as tq\n",
-    "active_orbitals = {\"A1\":[1,2], \"B1\":[0]}\n",
-    "molecule = tq.chemistry.Molecule(geometry = \"H 0.0 0.0 0.0\\nLi 0.0 0.0 1.6\", basis_set=\"sto-3g\", active_orbitals=active_orbitals)\n",
-    "H = molecule.make_hamiltonian()\n",
-    "print(\"Hamiltonian has {} terms\".format(len(H)))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Lets make the active space even smaller, so that we can print out the full Hamiltonian"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Hamiltonian has 15 terms\n",
-      "-7.4711+0.1352Z(0)+0.1352Z(1)-0.0310Z(2)-0.0310Z(3)+0.1218Z(0)Z(1)+0.0059Y(0)X(1)X(2)Y(3)-0.0059Y(0)Y(1)X(2)X(3)-0.0059X(0)X(1)Y(2)Y(3)+0.0059X(0)Y(1)Y(2)X(3)+0.0617Z(0)Z(2)+0.0675Z(0)Z(3)+0.0675Z(1)Z(2)+0.0617Z(1)Z(3)+0.0782Z(2)Z(3)\n"
-     ]
-    }
-   ],
-   "source": [
-    "import tequila as tq\n",
-    "active_orbitals = {\"A1\":[1], \"B1\":[0]}\n",
-    "molecule = tq.chemistry.Molecule(geometry = \"H 0.0 0.0 0.0\\nLi 0.0 0.0 1.6\", basis_set=\"sto-3g\", active_orbitals=active_orbitals)\n",
-    "H = molecule.make_hamiltonian()\n",
-    "print(\"Hamiltonian has {} terms\".format(len(H)))\n",
-    "print(H)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Computing classical methods with Psi4\n",
-    "\n",
-    "We can use psi4 to compute the energies (and sometimes other quantities) with the `compute_energy` function.\n",
-    "Here are some examples. Note that the energies are computed within the active space if one is set.\n",
-    "\n",
-    "Note also that not all active spaces can be represented by psi4 which will mean you can/should not use the classical psi4 methods with those (a warning will be printed). You will still get the right active space hamiltonian however.\n",
-    "\n",
-    "Active spaces which will not work for psi4 methds are the ones where the orbitals of individual irreps are not in one block ( e.g. {`\"A1\":[1,3]`} )"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "There are known issues with some psi4 methods and frozen virtual orbitals. Proceed with fingers crossed for mp2.\n",
-      "{(1, 0, 1, 0): -0.026069395810974533, (2, 0, 2, 0): -0.026069395810972833}\n",
-      "{(1, 0, 1, 0): -0.027418022914682542, (2, 0, 2, 0): -0.027418022914682535}\n"
-     ]
-    }
-   ],
-   "source": [
-    "import tequila as tq\n",
-    "active_orbitals = {\"A1\":[1], \"B1\":[0], \"B2\":[0]}\n",
-    "molecule = tq.chemistry.Molecule(geometry = \"H 0.0 0.0 0.0\\nLi 0.0 0.0 1.6\", basis_set=\"sto-3g\", active_orbitals=active_orbitals)\n",
-    "\n",
-    "mp2 = molecule.compute_energy(method=\"mp2\")\n",
-    "\n",
-    "# Note there are known issues for some methods when the active space as frozen virtuals as is the case here\n",
-    "# detci based methods are fine again \n",
-    "fci = molecule.compute_energy(method=\"fci\")\n",
-    "\n",
-    "# for most coupled-cluster like models you can compute amplitudes\n",
-    "# Amplitudes are computed in c1 and in the full space, this is why the active space troubles from above usually don't hold\n",
-    "# Note that amplitudes are in closed-shell\n",
-    "amplitudes = molecule.compute_amplitudes(\"mp2\")\n",
-    "\n",
-    "# you can export a parameter dictionary which holds the indices of the amplitude as keys and values as values\n",
-    "# for this small active space that is only one amplitude for mp2\n",
-    "variables = amplitudes.make_parameter_dictionary()\n",
-    "print(variables)\n",
-    "\n",
-    "# similar for ccsd since the singles are 0 due to symmetry (that changes if you change the active space)\n",
-    "amplitudes = molecule.compute_amplitudes(\"ccsd\")\n",
-    "variables = amplitudes.make_parameter_dictionary()\n",
-    "print(variables)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Hello World \"H2\" optimization with LiH in an active space"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Lets do a small hand-constructed VQE like it would be done for the Hydrogen molecule in STO-3G, just that we use our active space LiH molecule from the cell above.\n",
-    "For consistency reasons we initialize everything again.  \n",
-    "\n",
-    "Check the `BasicUsage` and `SciPyOptimizers` tutorial notebooks for more information about then"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Optimizer: <class 'tequila.optimizers.optimizer_scipy.OptimizerSciPy'> \n",
-      "backend         : qulacs\n",
-      "device          : None\n",
-      "samples         : None\n",
-      "save_history    : True\n",
-      "noise           : None\n",
-      "\n",
-      "Method          : BFGS\n",
-      "Objective       : 1 expectationvalues\n",
-      "gradient        : 2 expectationvalues\n",
-      "\n",
-      "active variables : 1\n",
-      "\n",
-      "E=-7.19702401  angles= {a: 0.0}  samples= None\n",
-      "E=-7.19766373  angles= {a: -0.0234220027923584}  samples= None\n",
-      "E=-7.20203763  angles= {a: -0.11711001396179199}  samples= None\n",
-      "E=-7.24749228  angles= {a: -0.49186205863952637}  samples= None\n",
-      "E=-7.68640044  angles= {a: -1.9908702373504639}  samples= None\n",
-      "E=-7.59671569  angles= {a: -7.986902952194214}  samples= None\n",
-      "E=-7.86212174  angles= {a: -3.129600457337474}  samples= None\n",
-      "E=-7.59889693  angles= {a: -1.7104055550334691}  samples= None\n",
-      "E=-7.86268191  angles= {a: -3.0777237637496633}  samples= None\n",
-      "E=-7.86268890  angles= {a: -3.0712456201159126}  samples= None\n",
-      "Optimization terminated successfully.\n",
-      "         Current function value: -7.862689\n",
-      "         Iterations: 3\n",
-      "         Function evaluations: 10\n",
-      "         Gradient evaluations: 10\n",
-      "VQE : -7.8626889f\n",
-      "FCI : -7.8626889f\n"
-     ]
-    }
-   ],
-   "source": [
-    "import tequila as tq\n",
-    "# define the active space\n",
-    "active_orbitals = {\"A1\":[1], \"B1\":[0]}\n",
-    "\n",
-    "# define the molecule\n",
-    "molecule = tq.chemistry.Molecule(geometry = \"H 0.0 0.0 0.0\\nLi 0.0 0.0 1.6\", basis_set=\"sto-3g\", active_orbitals=active_orbitals)\n",
-    "\n",
-    "# make the hamiltonian\n",
-    "H = molecule.make_hamiltonian()\n",
-    "\n",
-    "# define a hand designed circuit\n",
-    "U = tq.gates.Ry(angle=\"a\", target=0) + tq.gates.X(target=[2,3])\n",
-    "U += tq.gates.X(target=1, control=0)\n",
-    "U += tq.gates.X(target=2, control=0)\n",
-    "U += tq.gates.X(target=3, control=1)\n",
-    "\n",
-    "# define the expectationvalue\n",
-    "E = tq.ExpectationValue(H=H, U=U)\n",
-    "\n",
-    "# optimize\n",
-    "result = tq.minimize(objective=E, method=\"BFGS\", initial_values={k:0.0 for k in E.extract_variables()})\n",
-    "\n",
-    "# compute a reference value with psi4\n",
-    "fci = molecule.compute_energy(method=\"fci\")\n",
-    "\n",
-    "print(\"VQE : {:+2.8}f\".format(result.energy))\n",
-    "print(\"FCI : {:+2.8}f\".format(fci))\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "# some more information from the optimization\n",
-    "result.history.plot(\"energies\", baselines={\"fci\":fci})"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Unitary Coupled-Cluster Style Construction\n",
-    "\n",
-    "Here we show how to initialize in the style of unitary coupled-cluster.  \n",
-    "See also the overview article [arxiv.org/abs/2011.03057](https://arxiv.org/abs/2011.03057) for more details about the underlying methods.\n",
-    "\n",
-    "In the next example we are gonna compute the `mp2` amplitudes and build a UCC type circuit from them.  \n",
-    "Here we use the cc2 amplitudes only to define an order on the trotterized gates and remove small amplitudes as classical prescreening.\n",
-    "\n",
-    "We use again an active space to make the computation fast.\n",
-    "\n",
-    "First we start with the manual construction and then show how to use in build convenience functions of tequila to.\n",
-    "\n",
-    "An important function is the `make_excitation_generator` function of the molecule.  \n",
-    "This initializes a `QubitHamiltonian` which can be used to define a unitary gate which acts as excitation operation of electrons.\n",
-    "\n",
-    "$$\\displaystyle\n",
-    "U(\\theta) = e^{-i\\frac{\\theta}{2} G_{iajbkc\\dots}}\n",
-    "$$\n",
-    "\n",
-    "In fermionic language the generator is defined as\n",
-    "\n",
-    "$$\n",
-    "G_{ia,jb,jc,\\dots} =  i ( a^\\dagger_a a_i a^\\dagger_b a_j a^\\dagger_c a_k \\dots - h.c. )\n",
-    "$$\n",
-    "\n",
-    "The `make_excitation_generator` function gives back this generator in the qubit representation (depends on the chosen `transformation` of the molecule) and takes the indices as list of tuples  \n",
-    "  \n",
-    "$$\n",
-    "\\texttt{make_excitation_generator(indices=[(a,i),(b,j),...])} \\longrightarrow G_{ia,jb,jc,\\dots}\n",
-    "$$\n",
-    "\n",
-    "You can use those generators to initialize \\textit{formally} Trotterized Gates (one step is exact):  \n",
-    "$$\n",
-    "\\texttt{tq.gates.Trotterized(generators=[generator], angles=[\"a\"], steps=1)} \\longrightarrow U(\\theta) = e^{-i\\frac{\\theta}{2} G_{iajbkc\\dots}}\n",
-    "$$\n",
-    "\n",
-    "The last part was the general construction of gates over their parameters. In the case of Unitary coupled-cluster you can define fermionic gates directly, \\textsc{tequila} will then be able to compute analytical gradients with substantially reduced cost (see this article for an in-depth description: [arxiv.org/abs/2011.05938](https://arxiv.org/abs/2011.05938)). The fermionic gate is initialized over the same list of index-tuples that initialize generators:\n",
-    "\n",
-    "$$\n",
-    "\\texttt{make_excitation_gate(indices=[(a,i),(b,j),...])} \\longrightarrow U(\\theta) = e^{-i\\frac{\\theta}{2} G_{iajbkc\\dots}}\n",
-    "$$\n",
-    "\n",
-    "Angles can be either numeric types (such as 1.0, 1.5, numpy.pi/2) for fixed angles, any hashable type (such as \"a\", \"xyz\", (1,2,3) ) for variables, or a tequila objective for variable dependent transformations (see also the BasicUsage tutorial here). \n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Manual Construction"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "MP2 Amplitudes:\n",
-      " {(1, 0, 1, 0): -0.026069395810974533}\n",
-      "This is our circuit:\n",
-      "circuit: \n",
-      "X(target=(0,))\n",
-      "X(target=(1,))\n",
-      "FermionicEx(target=(0, 1, 2, 3), control=(), parameter=Objective with 0 unique expectation values\n",
-      "variables = [a]\n",
-      "types     = [])\n",
-      "\n",
-      "Optimizer: <class 'tequila.optimizers.optimizer_scipy.OptimizerSciPy'> \n",
-      "backend         : qulacs\n",
-      "device          : None\n",
-      "samples         : None\n",
-      "save_history    : True\n",
-      "noise           : None\n",
-      "\n",
-      "Method          : BFGS\n",
-      "Objective       : 1 expectationvalues\n",
-      "gradient        : 2 expectationvalues\n",
-      "\n",
-      "active variables : 1\n",
-      "\n",
-      "E=-7.86132988  angles= {a: 0.01}  samples= None\n",
-      "E=-7.86253976  angles= {a: -0.05013059616088867}  samples= None\n",
-      "E=-7.86268890  angles= {a: -0.03515792946196591}  samples= None\n",
-      "Optimization terminated successfully.\n",
-      "         Current function value: -7.862689\n",
-      "         Iterations: 2\n",
-      "         Function evaluations: 3\n",
-      "         Gradient evaluations: 3\n",
-      "VQE : -7.8626889f\n",
-      "FCI : -7.8626889f\n",
-      "MP2 Amplitudes: {(1, 0, 1, 0): -0.026069395810974533}\n",
-      "Optimized UCC Amplitudes: a : -0.03515792946196591\n",
-      "\n"
-     ]
-    }
-   ],
-   "source": [
-    "import tequila as tq\n",
-    "threshold = 1.e-6\n",
-    "\n",
-    "# define the active space\n",
-    "active_orbitals = {\"A1\":[1], \"B1\":[0]}\n",
-    "\n",
-    "# define the molecule\n",
-    "molecule = tq.chemistry.Molecule(geometry = \"H 0.0 0.0 0.0\\nLi 0.0 0.0 1.6\", basis_set=\"sto-3g\", active_orbitals=active_orbitals)\n",
-    "# make the hamiltonian\n",
-    "H = molecule.make_hamiltonian()\n",
-    "\n",
-    "# compute classical amplitudes\n",
-    "amplitudes = molecule.compute_amplitudes(method=\"mp2\")\n",
-    "\n",
-    "# in this example there is only one closed-shell MP2 amplitude, therefore manual construction is reasonable in this tutorial\n",
-    "# first we make a dictionary out of the non-zero MP2 amplitudes\n",
-    "ampdict = amplitudes.make_parameter_dictionary(threshold=threshold)\n",
-    "print(\"MP2 Amplitudes:\\n\", ampdict)\n",
-    "# lets get the indices of the only amplitude which is there manually\n",
-    "indices = list(ampdict.keys())[0]\n",
-    "\n",
-    "# the (1, 0, 1, 0) index in closed shell leads to the (2, 0, 3, 1) and (3, 1, 2, 0) excitations on the qubits\n",
-    "# but first we need to initialize the hartree fock state\n",
-    "U = molecule.prepare_reference()\n",
-    "\n",
-    "# UCC excitation gates can be directly initialized as follows:\n",
-    "# This will lead to significantly reduced cost in gradient evaluation (see text cell above)\n",
-    "# We also illustrate here how to define transformed angles by scaling the angle with 2.0\n",
-    "# (this makes it comarable to the MP2 amplitude, since it cancels out the conventional factor of 1/2 in the definition of the gates)\n",
-    "a = tq.Variable(\"a\")\n",
-    "U += molecule.make_excitation_gate(indices=[(3, 1),(2, 0)], angle=2.0*a)\n",
-    "\n",
-    "print(\"This is our circuit:\")\n",
-    "print(U)\n",
-    "\n",
-    "# lets form the expectation value\n",
-    "E = tq.ExpectationValue(H=H, U=U)\n",
-    "\n",
-    "# optimize\n",
-    "result = tq.minimize(objective=E, method=\"BFGS\", initial_values={k:0.01 for k in E.extract_variables()})\n",
-    "\n",
-    "# compute a reference value with psi4\n",
-    "fci = molecule.compute_energy(method=\"fci\")\n",
-    "print(\"VQE : {:+2.8}f\".format(result.energy))\n",
-    "print(\"FCI : {:+2.8}f\".format(fci))\n",
-    "print(\"MP2 Amplitudes:\", ampdict) # indices in spatial orbital notation\n",
-    "print(\"Optimized UCC Amplitudes:\", result.variables) # indices in spin-orbital notation\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Automatic Construction"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Optimizer: <class 'tequila.optimizers.optimizer_scipy.OptimizerSciPy'> \n",
-      "backend         : qulacs\n",
-      "device          : None\n",
-      "samples         : None\n",
-      "save_history    : True\n",
-      "noise           : None\n",
-      "\n",
-      "Method          : BFGS\n",
-      "Objective       : 1 expectationvalues\n",
-      "gradient        : 4 expectationvalues\n",
-      "\n",
-      "active variables : 1\n",
-      "\n",
-      "E=-7.86186477  angles= {(1, 0, 1, 0): 0.0}  samples= None\n",
-      "E=-7.86259809  angles= {(1, 0, 1, 0): -0.0468440055847168}  samples= None\n",
-      "E=-7.86268890  angles= {(1, 0, 1, 0): -0.03516504106977361}  samples= None\n",
-      "Optimization terminated successfully.\n",
-      "         Current function value: -7.862689\n",
-      "         Iterations: 2\n",
-      "         Function evaluations: 3\n",
-      "         Gradient evaluations: 3\n",
-      "VQE : -7.8626889f\n",
-      "FCI : -7.8626889f\n"
-     ]
-    }
-   ],
-   "source": [
-    "import tequila as tq\n",
-    "threshold = 1.e-6\n",
-    "\n",
-    "# define the active space\n",
-    "active_orbitals = {\"A1\":[1], \"B1\":[0]}\n",
-    "\n",
-    "# define the molecule\n",
-    "molecule = tq.chemistry.Molecule(geometry = \"H 0.0 0.0 0.0\\nLi 0.0 0.0 1.6\", basis_set=\"sto-3g\", active_orbitals=active_orbitals)\n",
-    "\n",
-    "# make the hamiltonian\n",
-    "H = molecule.make_hamiltonian()\n",
-    "\n",
-    "# make the UCCSD ansatz (note that this will be without singles since it starts from mp2)\n",
-    "U = molecule.make_uccsd_ansatz(initial_amplitudes=\"mp2\", threshold=threshold, trotter_steps=1)\n",
-    "\n",
-    "# define the expectationvalue\n",
-    "E = tq.ExpectationValue(H=H, U=U)\n",
-    "\n",
-    "# optimize\n",
-    "result = tq.minimize(objective=E, method=\"BFGS\", initial_values={k:0.0 for k in E.extract_variables()})\n",
-    "\n",
-    "# compute a reference value with psi4\n",
-    "fci = molecule.compute_energy(method=\"fci\")\n",
-    "\n",
-    "print(\"VQE : {:+2.8}f\".format(result.energy))\n",
-    "print(\"FCI : {:+2.8}f\".format(fci))\n",
-    "    \n",
-    "    "
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Pi System of Benzene\n",
-    "Here is the \\pi-system of Benzene, computed with the [UpCCGSD](https://pubs.acs.org/doi/10.1021/acs.jctc.8b01004) ansatz. The fermionic gradient techniques from [arxiv.org/abs/2011.05938](https://arxiv.org/abs/2011.05938) allow us to compute analytical gradients with a cost factor of 2 (this is the same cost as the cheapest 2-point numerical stencils). We neglect the singles here to speed-up the computation - so essentially this is UpCCGD. You can increase the `order` (in other words, the number of UpCCGD layers) to yield better energies. You can also try to build a batched optimization by re-using results from previous optimizations (get the optimized variables over `result.variables`)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "There are known issues with some psi4 methods and frozen virtual orbitals. Proceed with fingers crossed for mp2.\n",
-      "Optimizer: <class 'tequila.optimizers.optimizer_scipy.OptimizerSciPy'> \n",
-      "backend         : qulacs\n",
-      "device          : None\n",
-      "samples         : None\n",
-      "save_history    : True\n",
-      "noise           : None\n",
-      "\n",
-      "Method          : BFGS\n",
-      "Objective       : 1 expectationvalues\n",
-      "gradient        : 30 expectationvalues\n",
-      "\n",
-      "active variables : 15\n",
-      "\n",
-      "E=-227.88792153\n",
-      "E=-227.91711515\n",
-      "E=-227.92873702\n",
-      "E=-227.92990736\n",
-      "E=-227.93052215\n",
-      "E=-227.93056604\n",
-      "E=-227.93057449\n",
-      "Optimization terminated successfully.\n",
-      "         Current function value: -227.930574\n",
-      "         Iterations: 6\n",
-      "         Function evaluations: 7\n",
-      "         Gradient evaluations: 7\n",
-      "VQE : -227.93057f\n",
-      "MP2 : -227.9475f\n",
-      "CISD: -227.98666f\n",
-      "FCI : -227.99711f\n"
-     ]
-    }
-   ],
-   "source": [
-    "import tequila as tq\n",
-    "threshold = 1.e-6\n",
-    "active = {\"B1u\": [0], \"B3g\": [0, 1], \"B2g\": [0], \"Au\": [0], \"b1u\": [1]}\n",
-    "molecule = tq.quantumchemistry.Molecule(geometry=\"data/benzene.xyz\", basis_set='sto-3g', active_orbitals=active)\n",
-    "H = molecule.make_hamiltonian()\n",
-    "\n",
-    "U = molecule.make_upccgsd_ansatz(order=1, include_singles=False)\n",
-    "\n",
-    "# define the expectationvalue\n",
-    "E = tq.ExpectationValue(H=H, U=U)\n",
-    "\n",
-    "# compute reference energies\n",
-    "mp2 = molecule.compute_energy(\"mp2\")\n",
-    "cisd = molecule.compute_energy(\"detci\", options={\"detci__ex_level\": 2})\n",
-    "fci = molecule.compute_energy(\"fci\")\n",
-    "\n",
-    "# optimize\n",
-    "result = tq.minimize(objective=E, method=\"BFGS\", initial_values=0.0, print_level=2)\n",
-    "\n",
-    "print(\"VQE : {:+2.8}f\".format(result.energy))\n",
-    "print(\"MP2 : {:+2.8}f\".format(mp2))\n",
-    "print(\"CISD: {:+2.8}f\".format(cisd))\n",
-    "print(\"FCI : {:+2.8}f\".format(fci))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "result.history.plot(\"energies\", baselines={\"fci\":fci, \"cisd\": cisd, \"mp2\":mp2}, filename=\"benzene_result_bfgs\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Noisy optimization of an active space molecule with tapered qubit embeding\n",
-    "\n",
-    "This example shows the combination of several features of tequila in a few lines.  \n",
-    "Note that you will need to have `qiskit` installed for this.  \n",
-    "If not: replace the `backend` and set `device=None` (there will be no specialized noise emulation in that case, see our tutorial on noise model on how to construct your own!)\n",
-    "\n",
-    "- automatic handling of active spaces\n",
-    "- consitent usage of qubit encodings (here the symmetry_conserving_bravyi_kitaev encoding from openfermion which reduces the number of qubits by 2)\n",
-    "- custom circuit construction\n",
-    "- unitary cluster circuits\n",
-    "- optimization of measurements (here the Hamiltonian will be grouped into two commuting groups, this can be seen by the optimizer output which holds two expectation values). See the [MeasurementGroups](https://github.com/aspuru-guzik-group/tequila/blob/master/tutorials/MeasurementGroups.ipynb) tutorial for more background information.\n",
-    "- interface to different quantum backends (you will need qiskit to run this cell)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "trafo_args =  {'active_orbitals': 12, 'active_fermions': 4}\n",
-      "trafo_args =  {'active_orbitals': 4, 'active_fermions': 2}\n",
-      "Optimizer: <class 'tequila.optimizers.optimizer_scipy.OptimizerSciPy'> \n",
-      "backend         : qulacs\n",
-      "device          : None\n",
-      "samples         : None\n",
-      "save_history    : True\n",
-      "noise           : None\n",
-      "\n",
-      "Method          : COBYLA\n",
-      "Objective       : 2 expectationvalues\n",
-      "\n",
-      "active variables : 1\n",
-      "\n",
-      "E=-7.19702387  angles= {a: 0.0}  samples= None\n",
-      "E=-7.33012819  angles= {a: 1.0}  samples= None\n",
-      "E=-7.64648247  angles= {a: 2.0}  samples= None\n",
-      "E=-7.85523319  angles= {a: 3.0}  samples= None\n",
-      "E=-7.76445484  angles= {a: 4.0}  samples= None\n",
-      "E=-7.84895802  angles= {a: 3.5}  samples= None\n",
-      "E=-7.82776165  angles= {a: 2.75}  samples= None\n",
-      "E=-7.86143017  angles= {a: 3.125}  samples= None\n",
-      "E=-7.86244774  angles= {a: 3.25}  samples= None\n",
-      "E=-7.85826778  angles= {a: 3.375}  samples= None\n",
-      "E=-7.86100483  angles= {a: 3.3125}  samples= None\n",
-      "E=-7.86268139  angles= {a: 3.21875}  samples= None\n",
-      "E=-7.86258984  angles= {a: 3.1875}  samples= None\n",
-      "E=-7.86267614  angles= {a: 3.203125}  samples= None\n",
-      "E=-7.86265326  angles= {a: 3.2265625}  samples= None\n",
-      "E=-7.86268759  angles= {a: 3.21484375}  samples= None\n",
-      "E=-7.86268902  angles= {a: 3.2109375}  samples= None\n",
-      "E=-7.86268473  angles= {a: 3.20703125}  samples= None\n",
-      "E=-7.86268759  angles= {a: 3.208984375}  samples= None\n",
-      "E=-7.86268902  angles= {a: 3.2119375}  samples= None\n",
-      "Optimizer: <class 'tequila.optimizers.optimizer_scipy.OptimizerSciPy'> \n",
-      "backend         : qiskit\n",
-      "device          : fake_rome\n",
-      "samples         : 10000\n",
-      "save_history    : True\n",
-      "noise           : None\n",
-      "\n",
-      "Method          : COBYLA\n",
-      "Objective       : 2 expectationvalues\n",
-      "\n",
-      "active variables : 1\n",
-      "\n",
-      "E=-7.19702387  angles= {a: 0.0}  samples= 10000\n",
-      "E=-7.32791853  angles= {a: 1.0}  samples= 10000\n",
-      "E=-7.64811182  angles= {a: 2.0}  samples= 10000\n",
-      "E=-7.85427999  angles= {a: 3.0}  samples= 10000\n",
-      "E=-7.76262712  angles= {a: 4.0}  samples= 10000\n",
-      "E=-7.85026312  angles= {a: 3.5}  samples= 10000\n",
-      "E=-7.82797718  angles= {a: 2.75}  samples= 10000\n",
-      "E=-7.86140490  angles= {a: 3.125}  samples= 10000\n",
-      "E=-7.86260271  angles= {a: 3.25}  samples= 10000\n",
-      "E=-7.85750961  angles= {a: 3.375}  samples= 10000\n",
-      "E=-7.86095858  angles= {a: 3.3125}  samples= 10000\n",
-      "E=-7.86324453  angles= {a: 3.21875}  samples= 10000\n",
-      "E=-7.86271811  angles= {a: 3.1875}  samples= 10000\n",
-      "E=-7.86283731  angles= {a: 3.203125}  samples= 10000\n",
-      "E=-7.86209965  angles= {a: 3.2265625}  samples= 10000\n",
-      "E=-7.86232805  angles= {a: 3.21484375}  samples= 10000\n",
-      "E=-7.86293221  angles= {a: 3.220703125}  samples= 10000\n",
-      "E=-7.86276293  angles= {a: 3.21775}  samples= 10000\n",
-      "Optimizer: <class 'tequila.optimizers.optimizer_scipy.OptimizerSciPy'> \n",
-      "backend         : qulacs\n",
-      "device          : None\n",
-      "samples         : None\n",
-      "save_history    : True\n",
-      "noise           : None\n",
-      "\n",
-      "Method          : COBYLA\n",
-      "Objective       : 2 expectationvalues\n",
-      "\n",
-      "active variables : 1\n",
-      "\n",
-      "E=-7.86186457  angles= {(0, ((0, 2), (1, 3)), None): 0.0}  samples= None\n",
-      "E=-7.72876072  angles= {(0, ((0, 2), (1, 3)), None): 1.0}  samples= None\n",
-      "E=-7.68934298  angles= {(0, ((0, 2), (1, 3)), None): -1.0}  samples= None\n",
-      "E=-7.80994129  angles= {(0, ((0, 2), (1, 3)), None): -0.5}  samples= None\n",
-      "E=-7.85732555  angles= {(0, ((0, 2), (1, 3)), None): 0.24999999999999997}  samples= None\n",
-      "E=-7.85635090  angles= {(0, ((0, 2), (1, 3)), None): -0.12499999999999999}  samples= None\n",
-      "E=-7.86267853  angles= {(0, ((0, 2), (1, 3)), None): 0.06249999999999999}  samples= None\n",
-      "E=-7.86219120  angles= {(0, ((0, 2), (1, 3)), None): 0.125}  samples= None\n",
-      "E=-7.86243439  angles= {(0, ((0, 2), (1, 3)), None): 0.031249999999999993}  samples= None\n",
-      "E=-7.86267900  angles= {(0, ((0, 2), (1, 3)), None): 0.078125}  samples= None\n",
-      "E=-7.86264801  angles= {(0, ((0, 2), (1, 3)), None): 0.0859375}  samples= None\n",
-      "E=-7.86268663  angles= {(0, ((0, 2), (1, 3)), None): 0.07421875}  samples= None\n",
-      "E=-7.86268902  angles= {(0, ((0, 2), (1, 3)), None): 0.0703125}  samples= None\n",
-      "E=-7.86268616  angles= {(0, ((0, 2), (1, 3)), None): 0.06640625}  samples= None\n",
-      "E=-7.86268854  angles= {(0, ((0, 2), (1, 3)), None): 0.068359375}  samples= None\n",
-      "E=-7.86268854  angles= {(0, ((0, 2), (1, 3)), None): 0.0713125}  samples= None\n",
-      "Optimizer: <class 'tequila.optimizers.optimizer_scipy.OptimizerSciPy'> \n",
-      "backend         : qiskit\n",
-      "device          : fake_rome\n",
-      "samples         : 10000\n",
-      "save_history    : True\n",
-      "noise           : None\n",
-      "\n",
-      "Method          : COBYLA\n",
-      "Objective       : 2 expectationvalues\n",
-      "\n",
-      "active variables : 1\n",
-      "\n",
-      "E=-7.86185074  angles= {(0, ((0, 2), (1, 3)), None): 0.0}  samples= 10000\n",
-      "E=-7.72668314  angles= {(0, ((0, 2), (1, 3)), None): 1.0}  samples= 10000\n",
-      "E=-7.68907213  angles= {(0, ((0, 2), (1, 3)), None): -1.0}  samples= 10000\n",
-      "E=-7.80885315  angles= {(0, ((0, 2), (1, 3)), None): -0.5}  samples= 10000\n",
-      "E=-7.85614920  angles= {(0, ((0, 2), (1, 3)), None): 0.25}  samples= 10000\n",
-      "E=-7.85703373  angles= {(0, ((0, 2), (1, 3)), None): -0.125}  samples= 10000\n",
-      "E=-7.86282635  angles= {(0, ((0, 2), (1, 3)), None): 0.0625}  samples= 10000\n",
-      "E=-7.86291409  angles= {(0, ((0, 2), (1, 3)), None): 0.125}  samples= 10000\n",
-      "E=-7.86130190  angles= {(0, ((0, 2), (1, 3)), None): 0.15625}  samples= 10000\n",
-      "E=-7.86234283  angles= {(0, ((0, 2), (1, 3)), None): 0.109375}  samples= 10000\n",
-      "E=-7.86158419  angles= {(0, ((0, 2), (1, 3)), None): 0.1328125}  samples= 10000\n",
-      "E=-7.86303949  angles= {(0, ((0, 2), (1, 3)), None): 0.12109375}  samples= 10000\n",
-      "E=-7.86273146  angles= {(0, ((0, 2), (1, 3)), None): 0.1171875}  samples= 10000\n",
-      "E=-7.86206484  angles= {(0, ((0, 2), (1, 3)), None): 0.119140625}  samples= 10000\n",
-      "E=-7.86176157  angles= {(0, ((0, 2), (1, 3)), None): 0.12209375}  samples= 10000\n",
-      "VQE         = -7.86268902\n",
-      "VQE (noisy) = -7.86324453\n",
-      "UCC         = -7.86268902\n",
-      "UCC (noisy) = -7.86303949\n"
-     ]
-    }
-   ],
-   "source": [
-    "import tequila as tq\n",
-    "# define the active space\n",
-    "active_orbitals = {\"A1\":[1], \"B1\":[0]}\n",
-    "samples = 10000\n",
-    "if 'qiskit' in tq.INSTALLED_SIMULATORS:\n",
-    "    backend = \"qiskit\"\n",
-    "    device = \"fake_rome\"\n",
-    "else:\n",
-    "    backend = None\n",
-    "    device = None\n",
-    "\n",
-    "# define the molecule\n",
-    "molecule = tq.chemistry.Molecule(geometry = \"H 0.0 0.0 0.0\\nLi 0.0 0.0 1.6\",\n",
-    "                                 basis_set=\"sto-3g\",\n",
-    "                                 active_orbitals=active_orbitals,\n",
-    "                                 transformation=\"symmetry_conserving_bravyi_kitaev\")\n",
-    "\n",
-    "fci = molecule.compute_energy(\"fci\")\n",
-    "\n",
-    "H = molecule.make_hamiltonian()\n",
-    "\n",
-    "# Toy circuit (no deeper meaning)\n",
-    "U = tq.gates.Ry(angle=\"a\", target=0)\n",
-    "U += tq.gates.X(target=1, control=0)\n",
-    "E = tq.ExpectationValue(H=H, U=U, optimize_measurements=True)\n",
-    "\n",
-    "vqe = tq.minimize(method=\"cobyla\", objective=E, initial_values=0.0)\n",
-    "noisy_vqe = tq.minimize(method=\"cobyla\", objective=E, samples=samples, backend=backend, device=device, initial_values=0.0)\n",
-    " \n",
-    "# The same with UpCCGSD\n",
-    "UpCCGSD = molecule.make_upccgsd_ansatz(include_singles=False)\n",
-    "E2 = tq.ExpectationValue(H=H, U=UpCCGSD, optimize_measurements=True)\n",
-    "ucc = tq.minimize(method=\"cobyla\", objective=E2, initial_values=0.0)\n",
-    "noisy_ucc = tq.minimize(method=\"cobyla\", objective=E2, samples=samples,  backend=backend, device=device, initial_values=0.0)\n",
-    "\n",
-    "print(\"VQE         = {:2.8f}\".format(min(vqe.history.energies)))\n",
-    "print(\"VQE (noisy) = {:2.8f}\".format(min(noisy_vqe.history.energies)))\n",
-    "print(\"UCC         = {:2.8f}\".format(min(ucc.history.energies)))\n",
-    "print(\"UCC (noisy) = {:2.8f}\".format(min(noisy_ucc.history.energies)))\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "tequila-3.6",
-   "language": "python",
-   "name": "tequila-3.6"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.6.9"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}
diff --git a/tutorials/ChemistryBasisSetFreeVQE.ipynb b/tutorials/ChemistryBasisSetFreeVQE.ipynb
deleted file mode 100644
index e6d5eb32..00000000
--- a/tutorials/ChemistryBasisSetFreeVQE.ipynb
+++ /dev/null
@@ -1,300 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Basis Set Free VQE calculations with Tequila"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import tequila as tq\n",
-    "import numpy\n",
-    "\n",
-    "# global variables\n",
-    "# symmetry_conserving_bravyi_kitaev will result in a underlying 2-qubit simulation instead of 4 (for all vqe calculations)\n",
-    "transformation = \"jordan_wigner\" # alternatives: bravyi_kitaev, symmetry_conserving_bravyi_kitaev (will taper 2 qubits), bravyi_kitaev_tree\n",
-    "data_directory=\"data/h2_pnos/\""
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "This tutorial illustrates one of the explicit calculations of [arxiv.org/abs/2008.02819](https://arxiv.org/abs/2008.02819). We restrict ourselves to a minimal calculation of the Hydrogen molecule since this will execute within a jupyter environment without taking to much resources.\n",
-    "\n",
-    "Note that you can use this tutorial without having `madness` installed. If you want to compute the MRA-PNOs yourself, checkout our tutorial on the `tequila`-`madness` interface!.\n",
-    "\n",
-    "In this notebook we will compute the Hydrogen molecule in a minimal representation (2 spatial orbitals i.e. 4 spin-orbitals) using standard Gaussian basis sets (GBS) and the basis-set-free MRA-PNO representation. In the end we will show a comparisson with a large GBS computation that would require around 120 qubits.\n",
-    "\n",
-    "This notebook illustrates how to:\n",
-    "- define custom molecules from integral values\n",
-    "- use the in-build UpGCCSD ansatz in `tequila`\n",
-    "- compare to classical methods like FCI\n",
-    "- manually diagonalize a qubit Hamiltonian\n",
-    "\n",
-    "\n",
-    "The Hamiltonians are computed with a modified pno code of [`madness`](https://github.com/m-a-d-n-e-s-s/madness) which will be public soon (feel free to contact [me](mailto:jakob.kottmann@utoronto.ca) for early access or more information). The `madness` PNO-Code is described in more detail here [/doi.org/10.1063/1.5141880](https://doi.org/10.1063/1.5141880).\n",
-    "\n",
-    "The main difference in usage will be, that we will create the Hamiltonians directly from integral files that were originally obtained with `madness` and are for this tutorial provided in the `data` directory. Those integrals can be used to create `tequila` molecule objects which can then be handeled in the same way as other `tequila` molecules - for example obtained with the `psi4` backend. See the general [chemistry tutorial](https://github.com/aspuru-guzik-group/tequila/blob/master/tutorials/Chemistry.ipynb). Note however, that access to the classical `psi4` methods is not possible.\n",
-    "\n",
-    "We begin with reading in the `.npy` files which hold the molecular integrals obtained from the direct-determined PNOs that are stored in the `data/h2_pnos` directory for Hydrogen molecules in minimal representation (2 spatial-orbitals i.e. 4 spin-orbitals) and different bond lengths R in the directories `h2_R_4so`. Theese integral files can be passed to the `tequila` molecule object.\n",
-    "\n",
-    "We define a function here to reuse it later when we compute the whole potential energy surface (PES)."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def initialize_molecule(R):\n",
-    "    geomstring = \"H 0.0 0.0 0.0\\nH 0.0 0.0 {R}\".format(R=R)\n",
-    "    directory = data_directory + \"h2_{:1.1f}_4so/\".format(R)\n",
-    "    \n",
-    "    # load the integral files\n",
-    "    one_body_integrals = numpy.load(directory+\"one_body_integrals.npy\")\n",
-    "    two_body_integrals = numpy.load(directory+\"two_body_integrals.npy\")\n",
-    "    # resort from Mulliken notation to openfermion convetions\n",
-    "    two_body_integrals = numpy.einsum(\"psqr\", two_body_integrals)\n",
-    "    \n",
-    "    # compute the nuclear repulsion (optional)\n",
-    "    angstrom_to_bohr=1.8897\n",
-    "    nuclear_repulsion = 1.0/(angstrom_to_bohr*R)\n",
-    "\n",
-    "    \n",
-    "    molecule = tq.chemistry.Molecule(geometry=geomstring,\n",
-    "                                     one_body_integrals=one_body_integrals,\n",
-    "                                     two_body_integrals=two_body_integrals,\n",
-    "                                     nuclear_repulsion=nuclear_repulsion,\n",
-    "                                     transformation=transformation,\n",
-    "                                     backend=\"base\") # necessary if psi4 or others are installed\n",
-    "    \n",
-    "    return molecule\n",
-    "    "
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Next we define the 1-UpCCGSD calculation used in [arxiv.org/abs/2008.02819](https://arxiv.org/abs/2008.02819) as a function to be called later for the whole PES"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def compute_upgccsd_energy(molecule, method=\"BFGS\", *args, **kwargs):\n",
-    "    U = molecule.make_upccgsd_ansatz()\n",
-    "    H = molecule.make_hamiltonian()\n",
-    "    E = tq.ExpectationValue(H=H, U=U)\n",
-    "    \n",
-    "    result = tq.minimize(objective=E, method=method, initial_values=0.0, *args, **kwargs)\n",
-    "    \n",
-    "    return result.energy"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Now lets compute all MRA datapoints in two simple lines (remove the `silent=True` key to get live updates about the individual VQE simulatins)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "points = [0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.4, 2.0, 3.0, 4.0]\n",
-    "mra_vqe = {R:compute_upgccsd_energy(initialize_molecule(R), silent=True) for R in points}    "
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Here are the results of our basis-set-free calculations"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "import matplotlib.pyplot as plt\n",
-    "plt.figure()\n",
-    "plt.plot(list(mra_vqe.keys()), list(mra_vqe.values()), marker=\"o\", label=\"UpCCGSD(2,4)\")\n",
-    "plt.legend()\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "For the case that psi4 is installed within your environment we can compute also the STO-3G energies in exact diagonalization (or with the VQE using the function above, but for this size the results will be the same, we compute both to illustrate that).\n",
-    "See the [paper](https://arxiv.org/abs/2008.02819) for the numbers close to the complete basis set limit (CBS), which is the exact solution with respect to electron correlation (FCI) and one-particle basis and larger MRA caluclations.\n",
-    "Set `no_compute=True` to avoid recomputing and save time."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "no_compute = True\n",
-    "# in case you have psi4 installed you can compute the reference values here\n",
-    "if \"psi4\" in tq.quantumchemistry.INSTALLED_QCHEMISTRY_BACKENDS and not no_compute:\n",
-    "    def initialize_psi4_molecule(R):\n",
-    "        geomstring = \"H 0.0 0.0 0.0\\nH 0.0 0.0 {R}\".format(R=R)\n",
-    "        molecule = tq.chemistry.Molecule(basis_set=\"sto-3g\", geometry=geomstring, transformation=transformation)\n",
-    "        return molecule\n",
-    "    gbs_fci = {R:initialize_psi4_molecule(R).compute_energy(\"fci\") for R in points}\n",
-    "    gbs_vqe = {R:compute_upgccsd_energy(initialize_psi4_molecule(R), silent=True) for R in points}\n",
-    "else:\n",
-    "    # otherwise, here they are\n",
-    "    gbs_vqe = {0.5: -1.05515979168155, 0.6: -1.1162859536932939, 0.7: -1.1361894250426225, 0.8: -1.1341473711383794, 0.9: -1.120560281221029, 1.0: -1.1011503300331484, 1.1: -1.0791929437201784,1.2: -1.0567407365989585,1.3: -1.0351862019508562,1.4: -1.015467897671673,2.0: -0.9486410371613808,3.0: -0.9336318373138941,4.0: -0.9331713618417009}\n",
-    "    gbs_fci = {0.5: -1.0551597946880178,0.6: -1.1162860069722242,0.7: -1.1361894540879063,0.8: -1.1341476666428472,0.9: -1.1205602812268745,1.0: -1.1011503301329566,1.1: -1.079192944852247,1.2: -1.05674074617943,1.3: -1.035186266306758,1.4: -1.0154682491653277,2.0: -0.9486411121296501,3.0: -0.933631844555985,4.0: -0.9331713618435854}\n",
-    "    \n",
-    "# close to CBS: FCI/cc-pVQZ calculation\n",
-    "# can be computed with the tequila psi4 interface in the same way as STO-3G (but takes time)\n",
-    "close_to_cbs = {0.5:-1.10338122, 0.6:-1.15531049,0.7:-1.1725277, 0.8:-1.17182109,0.9:-1.16178264,1.0:-1.14710242,1.1:-1.13045400,1.2:-1.11340654,1.3:-1.09689852,1.4:-1.08149165,2.0:-1.02143838,3.0:-1.00109047,4.0:-0.99995503}"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Here are the comparisson plots. We use the notation (number_of_electrons, number_of_spin_orbitals) to indicate the sizes of the Hamiltonians.  \n",
-    "In this case we have minimal sizes (the smallest size where a treatment beyond mean-field is possible) which results in 4 spin-orbitals (and usually 4 qubits)."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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RWVgKQJCXM0N6tefqrj5Ed/GmYzv1oJ3SPBqdCIQQI4HZQG8gSkq5p4Z2twH/BrTACinl3PLlocBGwAfYCzwipSxtbFyK9ZWW5PP8Z8P4hxLmd32A66ImWzskq5NSciq9sErHn0lGgemfe4CnEzf08CO6qw9Xd/Ghk7fq+BWTzBUrcArvi2v0QPOywp270MUdxGf8+EZvvynOCOKAe4H/1NRACKEF3gduARKB3UKIb6SUh4F5wCIp5UYhxHLgceCDJohLsaIyfTHTN93GDop5o9Mwhl73qrVDsgopJWcyCstr9WSy83Qm6fklALT3cOTabr7lR/w+BHu71KsSZWvV3J2VLXMK70vSlCkELVqEa/RACnfuMr9uCo1OBFLKI1BnKdUo4KSU8nR5243A3UKII8AQ4KHydmswnV2oRNCGGQ1lvLppGL8Y85jhfy333DTf2iG1GCkl8ZlF5iP+naczSc0zdfz+7o5c3cXH3PGH+LTtjv9Czd1ZWZuUEqQEgwFpNJb/lGA0IA0GMBpNPy9qY6x8z/y7sXw9I0hj9fXN2yxvU76O14MPkPjMM3jedx95335r/p6bQkvdIwgCzlV5nQgMxHQ5KEdKWVZlucVCJUKICcAEgOBg9RRqayWNRt7+7E6+K8vg2XYRjL798s7pUkrOZRVX6/hTcnUA+Lo5moZylnf8XXxdL6uO/0LO/friO3Ei5yZOxGXAAIr27sXzrrvQxR2k+J9/Kjs8gxFptNThVXSg5W2kEap2mEbjxZ1redvq6zegTfk+KttY2ofpNUbLk8O0tOy1a/Gd+HSTJQGoZyIQQvwEdLDw1stSys1NFk0tpJQfAh8CREZGWnE+IaUm0mhk0Zf/x6cliYx1684Tw9dYO6RmkZhdxI5Tmew8ncXOKhOy+Lg6mEb0dPXh6i7edPVzu2w7fkNuLrojR9AdOmz6efgwpWfOUDHVV+H27QDkfPqp5Q1oNKDVmuac0GpN31OV12gEQqMFrcb0U6OpbKvRlK+vqWwjKt8T9vYIRweoY32h1VS2EVW3p0VoBGi0lW2qxqPVgqhcX2g1ULG+tsq+Lly/4j1L65tjsrC+VgtCoIs7ROrcubR74H6yN2zEJWpgy54RSClvbuR+koBOVV53LF+WCXgJIezKzwoqlitt0IrvHmNV4Qnudwxiyj2fXzYTyyTnFJd3/Kaj/sRsU8ffzsWe6C4+PHlDF6K7+NDd//Lr+KWUlKWloztyGN3hw5SUd/765GRzG7uAAJzCwvAYNgy0WrJWr8br3nvJ/eorAubOxXVg1MUdsdIghTt3kbZgAR2XLME1eiCug66tdhmusVrq0tBuoHv5CKEk4EHgISmlFEL8CvwfppFDjwItcoahNK31WyayJHs/w+18ebmVzy729f6kWmvmn8/VseN0BjtPmW7wJmQVAeDlYs/AUG/GXxtKdFcfevi7o7mMZtSSUqJPTKx2lK87cgRDRoa5jUNICM4RV9DuoVE49u6NU1gYdu3aAZjvCXT8979xjR6I2w03NGlnZct0cQerfY+u0QMJWrQIXdzBJvluhWzkrM1CiHuA9wA/IAeIlVIOFUIEYhomOqy83TBgMabhoyullHPKl3fBlAS8gf3Aw1LKktr2GRkZKffssThKVbGCr39+iVcTf2CIxoP/9+DP2Nm33idcv96fdNEsWk52GkZGdqTMKNlxKpOzmaaO38PJjoFdTEM5o7v40KvD5dPxy7IySs+cMXX2h4+YOv4jRzDm55sa2Nnh2LUrTmFhOPXujVOfMBx79kLr5lrjNtWoodZPCLFXShl50fLGJgJrUImg9fjxz7eYfmojA4ULSx/8GQfH1j0lYU2TgAO4O9kxMNTb/ORu7wCPy2IOXWNJCSXHT5gv7+iOHKHk6DFkiel4Szg54dizR2Wn3zsMxx7d0TiqInWXm5oSgXqyWLlkf+76Ny+d2kg/HFg88odWnwTAdL3fEgHE/uvWNt/xGwoKKTl2tNrlnZJTp6DMNDBP4+6OU+/etHvwQZz6mDp+h9BQhJ3qCmyZ+ttXLsnu2JVMOfwR3bHj/Xs34+Lia+2Q6lRmMOJkr612WahCoJdzm0sCZdnZlTdwyy/xlMbHm0fuaH18cAoLw23wYPPlHfuOHS+7G9pK46lEoDRY3OHPeHb/uwRKDctHfI6HZ6e6V7KykjIDz22IpVhvwE4jKDNWXhJ1ttcyfWhPK0ZXOyklZampldfzyy/vlKWkmNvYBwbi1CcMj7vuLL/EE4adv5/q9JV6UYlAaZATJ7fy1K7ZeEkNH92xDm/vbtYOqU7FpQaeXLeXP46n86/hYXi7OtQ6asiapNGIPiGhctROecdvyM42NRACh9BQXK680nyU79SrF1ovL+sGrrRpKhEoNVoZt5Lw3AyiYtZCbiIJnh14zFOLQQg+uuVD2rfvZ+0Q65Sn0/P46t3sjc9m/n39uP8q09lLa+j4pV5PyenykTvmcfpHMRYWmhrY2+PYvRtuQ240H+U79eyBxrXmkTuKcilUIlBqFJ6bwbRja1hYkk6wVsMYDw35GsEb/tfTqdPV1g6vTlmFpYxZuYujKfksGdWf4f0CrRaLUaej5PjxasM1S44dQ5aaKo8KZ2ecevXC8+67zTdxHbt1QzioCeWV5qcSgVKjqJi1LCxJZ6q/6UZwrkbDqxlZjMj+A4ZZObg6pObpeHjFLhKyivhoTCQ39vJvsX0b8vNNHX2Vyzslp0+b6tUAGk9P08idhx82X95x6NzZVF5AUaxAJQKlZrmJRCHpqC/jkJMjd+cXcH9BIVBk7chqdS6riNErdpFZUMLqsVFc3dWn2fZVlplZ7Qau7vBh9AkJ5vft/PxMI3duvsl8ecc+KFDdxFVaFZUIlJp5duS7sgwOOTrQu6SEP1yciXFyJMqx5Y6uG+pkWgEPr9hFsd7A+ieiiejUNDdRpZSUJSeXd/ZVRu6kpprb2HfqhFPv3njdey9OYb1x6t0bOz+/Jtm/ojQnlQiUGsVEjeG1E2uxl5KlqRmctbdjmr8fC3uOIcrawVkQl5TLmJUxaITg0yej6dXB46I29SmDII1GSs/GV7+Je/gIhtxc0woaDY5du+AyMKryJm7vXmg9Lt6forQFKhEoNfq1NJ1S4PHCEvwNRvzd/FnYcwxxnr6tLhHsOZvF2NW78XCyZ934gYT6Wh5Zc+HkKQXbt5M09QW8Ro7k/JtvmY74jx5FFpkufwl7exx79MD91ltNR/lhYTj26IHGWU0cr1w+VK0hpUZPr4nmgLGALfduadUPjf15Ip0Ja/fSwdOJdeMHEuRVeyed/9tvJD33PBp392qVNTUuLqaKmuVVNZ3CeuPYtSvC3r65P4KitAhVa0hpkN2xK9lOIVP9BrbqJLDt0Hme/e9+uvi58snjA/Fzr71QWll2NhlL30eWlmLIyMC5f4Rp9E5Y+cidVlw+W1Gai/pXr1xEGo0s3r8Uf4Nk1E0LrR1Ojb7an8jE9fsIC/Rg44ToupNAejoJYx5Fd/QoGldXfCc+TenZeOx8fHEMDVVJQLFZ6l++cpFfdi7ggEbPxE5DcXJuZ+1wLFq3M56pm/4hKsSbdeMH4uVS+4NX+uRkzj78MCUJCWicnOi4dCl+kycTtGgRSVOmULhzVwtFriitj0oESjVleh1Ljq4nxCC4e/Aca4dj0X9+P8UrX8dxY09/Vo29CjfH2q9wlp49y9mHH8aQlY3XvffScelSizM9KYqtUvcIlGq+/eNfnNZK3u06qtXNNCal5N3/Hee9X04yvF8Aix6IwF5b+7GM7vhxEh5/HMoMdF6zGqewsIvauEY33STgitIWqUSgmJXoclkW/wN9hT03XzPD2uFUYzRK3vjuMKv/PsuDV3Vizj1965w/oPhgHOfGj0c4OBD8yVocu7X+SqmKYg0qEShmG3+exnmtYE6/Z1rVjVODUTLjiwN8tjeRx68N5ZU7etdZoqFo717OTXgSrZcXwatX4dCp9Y58UhRrU4lAASA/L4mP0nYwSONKVP/WM9F4aZmRKZ/G8v3BFJ6/uTvP3dS9ziRQ8NdfJD4zCfuAAIJXrcS+Q4cWilZR2iaVCGxY1fkGVmnyyPXy5CaffqyMW8m48HHWDo/iUgNPr9/Lb8fSeeWO3oy/rkud6+T//DNJz0/BoUsXgld+jJ1P8xWcU5TLRes5/1daXMV8Az/qM1jn4U5UcTHvpf1NeG5G3Ss3s3ydnkdXxfD78XTevqdvvZJA7rffkTj5ORzDetN5zWqVBBSlnlQisGFRMWtZmJbOLD8fdEJw1MGBhWnpphnJrCi7sJSHV+xiX3w2ix+I4KGBwXWvs2kTyS++iMuVVxL88Uo1daOiNIC6NGTLchMJstNQKgRSCEblFRClKwFdotVCSsvT8cjHMZzJLGT5w1dyc1j7OtfJXL2atLnzcL3+OjouWYLGqXUNe1WU1k4lAlvm2ZF3HIuRwOjcPDZ5uBGl01ltvoHE7CIeXrGLtPwSVj92Fdd08621vZSSjA8+IGPJe7jfeitBCxeoqR0V5RKoS0M2bGuf2/jdxZkbioqZkZXDwrQMpvn7ERM1psVjOZVewMjlO8gqLGXd+IH1SgJpCxeSseQ9PEeMIOjd/6eSgKJcIpUIbNj69F1ogJkl9oAgytGfhT0fJc6z9k64qR1OzuP+5TvQG4xsnHA1A4Jrr28kjUbOv/EGWR+vpN1Dowh4ew7CTp3cKsqlUv97bFRG+hGOlGZzl2MHgqb8ZF4eVf6npeyNz2bsqhhcHe1YN34gXf3cam0vy8pIefllcjd/g8/4x/F74QU1/6+iNJJKBDZq9W8z0Qt44trZVovhr5MZPLF2D37ujqwfP5CO7VxqbS9LS0maNp38H3/E7/nn8HnySZUEFKUJqERgg7KyTrKp4CS3O/gRHHytVWL46XAqE/+7j1AfVz55PAp/j9pH+hh1OhInT6bwjz9pP3MG3o8+2kKRKsrlTyUCG/TJrzPQCZhwzStW2f83/yQz9dNY+gR6sHpsFO1ca7/JaygoJPHppynas4cOb75Bu5EjWyhSRbENKhHYmNycs2zIO8qt9t50Cb2pxfe/ISaBWV8d5KoQbz5+NBJ3p9rnAzbk5JAw4Ul0hw4RuGABnsPvaKFIFcV2qERgY9b/OpNCjWBC9MwW3/eKP0/z1vdHGNzTjw9GX4mzg7bW9mUZGSQ8Pp7S06fpuOTfuN/U8olLUWxBo4aPCiFGCiEOCSGMQojIWtrdJoQ4JoQ4KYSYUWX5aiHEGSFEbPmfiMbEo9QuPy+JdTkHGaLxoEe321tsv1JKFv3vOG99f4Q7+gbw4SORdSYBfUoK8Q8/QmlCAh2Xf6CSgKI0o8aeEcQB9wL/qamBEEILvA/cAiQCu4UQ30gpD5c3mS6l/LyRcSj1sOG3GeRrBBOueqHF9iml5K3vj/Dx9jOMvLIjc+/rV+eEMqUJCSQ8NhZDXh7BH6/AZcCAFopWUWxToxKBlPIIUNcQvijgpJTydHnbjcDdwOHaVlKaVlFBGp9k7uc6rRt9et3bIvs0GCUvf3WQjbvP8dg1IfxreBiaOpJAycmTJIwdh9TrCV69GufwPi0Sq6LYspZ4sjgIOFfldWL5sgpzhBAHhBCLhBCONW1ECDFBCLFHCLEnPT29uWK9bH3620xyNIInBzzfIvsrLTPy3Mb9bNx9jmeHdOO1O+tOAsWHDhH/yBgkks6frFVJQFFaSJ1nBEKInwBLUzy9LKXc3Mj9zwTOAw7Ah8BLwBuWGkopPyxvQ2RkpGzITqpOwEJuInh2JCZqDHGevq1iApbmVlyUxer0XURrXLgi/MFm359Ob2Di+n38cjSNGbf34qkbuta5TtG+/ZybMAGNhzudV63CoXPnZo9TURSTOs8IpJQ3SynDLfypbxJIAqpOGNuxfBlSyhRpUgKsopmqG1RMwBJTkgZIYkrSmHZsTauYgKW5rIxbScxf82FROF8s70eWRnC9Z09Wxq1s1v0WlJQxdtVufj2WxlsjwuuVBAp37CDh8cex8/EhZP16lQQUpYW1xKWh3UB3IUSoEMIBeBD4BkAIEVD+UwAjMN18bnIVE7BMau/HHR0DmObv2yomYGlOFcnvr9I0Vnm606OklI+y9jVr8hnhz1cAACAASURBVMspMk0oE3M2i0X3R/BwdN0dev4vv3Luyadw6NiRzus+wT4goNniUxTFssYOH71HCJEIXA18L4TYVr48UAjxA4CUsgyYBGwDjgCbpJSHyjexXghxEDgI+AJvNSaeGuUmEqUroXdJKQn29tyXXz4BS671JmBpbhXJb6q/H2l2diTb2TVr8kvPL+HBD3dyODmPD0YPYET/oDrXyfvhBxInT8axZ086f7IWOz+/ZolNUZTaNXbU0FfAVxaWJwPDqrz+AfjBQrshjdl/vXl2JKYkjWOOplIGn7q7cXWx9SZgaRG5ifRHoim/mzI6L7/ZZh9Lyinm4RW7OJ+r4+PHIrmue90des4XX5Dyyqu4XHklHZd/gNat9qqjiqI0H5uYjyAmagzT/P2YkZkFwP35BVabgKXFeHZkmZcnBVoNQwsK2eThRoyTI3h2bNLdnMkoZOQHf5ORX8Inj0fVKwlkrf2ElJdfwXXQIDp99KFKAopiZTaRCOI8fVnY81Hu0HpjJyVGraNVJmBpSbuueoSVXh4E6vXMT89sltnHjqTkMXL5DnRlRjZMiCYyxLvOdTKW/4fUt9/G/Zab6bjsfTTOzk0Wj6Iol8Ymag2Zh4gOepHQVVdw0sOHqYNebNEJWFrad3lHMQrBpEIDGvPsY6Yhs03xuWPP5fDoyhic7bWsGz+Qbv7utbaXUpL+7iIyP/oIj7vuJPDtt9WsYorSStjc/8TuDu3YX3L5DhutkJB2gACj5LaJ/4C9acKXppp9bMepTMav2Y2Pm2lCmU7edUwoYzSSOudtstevx+uBB+jw2r8QGps4GVWUNsHm/jd2d+9MilZQkJ9i7VCazb5/1rJPlPJowPXY29feSTfUr0fTeGxVDIFeznz21NV1JwGDgZSXXyF7/Xq8x46lw+zXVBJQlFbG5s4Iuvn3g+x9nIz/lYjwh6wdTrNY+c8HtDNK7r2h8aNxv96fxIJtx0jOKcbLxZ6cIj3hQZ6sGReFdx0TysjSUpJefIn8rVvxfXYSvhMnqqklFaUVsrlDs24dBwFwMmWPlSNpHsdPbuF3WcBD3hE4u9R987Y2X+9PYuaXB0nKKUYC2UV6hICHBnaqMwkYdToSn51M/tat+L/4In7PPKOSgKK0UjaXCAIDInE2Sk5mn7B2KM1i1a75OBslo5rgbGDBtmMU6w3VlhklLP3lVK3rGQsLOffkUxT88QcdXn8dn3FjGx2LoijNx+YuDWm0dnTDnpPF560dSpNLSophiz6d0W5d8fQKafT2knOKG7QcwJCby7kJT1IcF0fg/Hl43nlno+NQFKV52dwZAUA3Jx9OGGvuzNqqNdtfRwCPXPd6k2wvwMvJ4vJAL8tj/8uysoh/bCy6w4cJWrxIJQFFaSNsMxF4diFLI8jMOG7tUJpMZsZxviyK507HDnTo0DQzfvYL8rxombO9lulDe160XJ+aappa8swZOi5bhscttzRJDIqiND/bTAT+po7y1Lk/rBxJ01n/xyuUCngselaTbG/32Sx+PJxKZGcvgrycEUCQlzPv3Nv3ooJypYmJxI9+mLLUVIJXfITbddc2SQyKorQMm7tHANA9+AY49AEnzu8livHWDqfRCvJT2Jh7mJvsvOgS2vg6frnFep7fGEvHdi6sGhuFu5N9jW1LTp82TS2p0xG8ehXOffs2ev+KorQsm0kEVcfDB3g64tneyImc2ke/tBWf//4q+RrBuAHPNXpbUkpmfXWQ1Dwdnz99Ta1JQHfkCAmPjweNhuC1a3Hq2aPR+1cUpeXZxKWhC8fDJ+eW0KHUjqNFbX/u49KSfNam7WQgTvTtM7LR2/tsbyLfH0hhyi09iOjkVWO74thY4h99DOHoSMi6T1QSUJQ2zCYSgaXx8M4lHpzRlCKNRitFdemqTkP57Xs9SdcKBnl0a/Q0lKfTC5j9zSGu7uJT6xSThTt3ET/ucbTtvAhZ9wkOISGN2q+iKNZlE4nA0rh3Y0kHijQazp/fb4WIGqdiGsqdJWms8vKgc2kpq7IPNGoaytIyI5M37sfBTsOiByLQaiw/BVzw+++ce/JJHIIC6fzJJ9gH1T0TmaIorZtNJAJL496zdaEAnDi3vaXDabSKaSifb+9HvL09GY2YhvLr/UkMmvsLPV7ZQlxSHvf2D6KDp+n5gcwVKyjcucvcNm/rVs5NfAatlxfBa9di738Zz/CmKDbEJhLB9KE9cbbXVluWYTCNbjmZ9o81Qmqc3ESu0pXgbDTNQzk6N/+S5mCueu+kwoaYc3y9PwkAp/C+JE2ZQuHOXeR8+RVJU6aCEHSY/Rp27do13edRFMWqbCIRjOgfxDv39iWw/EjXzdGOWSOG4G+QnMw7a93gLoVnRz72dCfDTssNhUV8donTUFq6d1KsN7Bg2zEAXKMHErRoEYmTJpEyaxZotXR6fynuN97YZB9FURTrs4lEAKZk8PfMmwgP8qB/sBcj+gfRXevKydIsa4fWYLuueoSl7bzwNhhYlJZxydNQ1qeWkGO3rsiyMgB8xo3D7YYbLj1wRVFaJZtJBBXCAz2JS8pFSkk3lwBOiTIMZaXWDqtBthWdxSAETxWUYm+ehrLhczB7uVh+RqDinoqUknPPTkbqdHg98AA5n31W7Z6BoiiXB5t5oKxCeJAnG3efIymnmO4+vSgtOsW5xB2EhLSdI93ElL34GCT3PLEbnE3X6hs6DWVavo4SvQEhQMrK5VVrCaX9v3fR7d+P1wMPEPD6bDxuv52kKVMIWrQI1+iBTfeBFEWxKts7IygvpBaXlEe3QFPXeSLxL2uG1CBxhz9jB8WM8YvCyfnSbthKKZn1ZRxlEmbc1tNiLSF9cjLZa9fi0KMHHf71KlB5z0AXd7AJP5GiKNZmc2cEvTq4o9UI4pJyueG6wYidkpMZcbSVWpkf7V2Mh1HywI1vX/I2vtyXxE9HUnnljt6Mv64LT97Qrdr70mgk+eWXwc6OTu8vRWgrR1y5Rg9UZwOKcpmxuTMCJ3st3f3diEvOxdnFm05GwYn8c9YOq15OnNzKL8Y8Rnv1xdWtwyVtIyW3mNnfHiIqxJuxg0Ittsn+7waKduyk/Ysv4tCpU2NCVhSlDbC5RACmy0PmG8b2HpzU51o7pHpZsWsuzkbJ6BvfuaT1pZS8+PkBygySBSP7WXx6uOTMGdIWLsT1uuvweuD+xoasKEobYJOJoG+QJxkFpaTmldDNrSMJGiMlutadDBIStrNVn8ED7t0veRrK/8Yk8OeJDGbd0ZvOPq4XvS/LykiZMRPh4EDAW2+qyeYVxUbYZCIID/IAIC4pl+4+YRiE4GzCn1aOqnYr/3oDO2DM9Zc2KX1CZhFzvj/Cdd19eXhgsMU2mR+vpPiff+jw6qvYt2/fiGgVRWlLbDIR9A7wQCPgYFIu3YKuBuBEcusdH3/+fCybS5K5xzkYP/8+DV7faJRM+/wftEIw775+5iP9qrWEdEePkr50Kc6RkejPn2/S+BVFad1sMhG4ONjR1c+NQ8m5dO44CDspOZl5xNph1WjNH6bhm+Oue6NB61UUlOsy6wdizmQx/IqAagX4KmoJFWzfTvJLM9A4O1N68qSaZUxRbIxNJgIw3TA+mJSLvaMrIVLLycIka4dkUWbGcT4vPMMdDh0IDIys93qWCsp9vT/JXFAOqtYSepaSY8fAaCRo8WI1PFRRbEyjEoEQYqQQ4pAQwiiEqLGXEkKsFEKkCSHiLljuLYT4nxDiRPnPFitpGR7kSWpeCWn5Orrbe3GyrKCldt0g636fRYmAx695pUHrWS4oZzQXlKugcXND6nQAeI95RCUBRbFBjT0jiAPuBf6oo91q4DYLy2cAP0spuwM/l79uEeGBphvGh5Ly6O7RmSQtFBa0jmvjFTOQ5S0KY2PeEW4pLiE9KaZBM5DVp6Cc1OtJmmoqLe39+DiyN2xUtYQUxQY1KhFIKY9IKY/Vo90fgKUyn3cDa8p/XwOMaEw8DdHHXGoil25+/QA4efa3ltp9rSpmIFtoV0yBRsPVhYVMO7amQTOQ+bk7Wlxe9R7B+TffRJ+QgO8zz9B++nSCFi0yzz+gKIrtsPY9gvZSypTy388DNY5ZFEJMEELsEULsSU9v2KTzF860BSD272VC0l/EJefSreMgAE6m7G7QdptLVMxa3krP4Gt3V4L1epZ4ezVoBjKDUeLqoL1oedWCcqUJCeR88SVOA/rj+8xEQNUSUhRbVWciEEL8JISIs/Dn7qYMREopAVnL+x9KKSOllJF+fn4N2nbVmbZkWRmFO3eRNGUKoncYcUl5BAVehbNRcjL7eGM/RtPITeSQowNSCBLs7bk/r6BBM5Ct+fssZzKLGD2wk8WCclJKUl57DY2zMx0XLar24Jhr9EB8xo9vpg+mKEprVGfROSnlzc24/1QhRICUMkUIEQCkNcdOKo50zz35JMLJEaHRErRoET6lviT9cJQcnZGu2HOiuHXcI8jwDGCFpwZ7KRmXk8cmDzeidDqiHOueI/hsRiHztx1lSC9/3hrR1+LTwblffU3Rjp10eO1f6sGxVkCv15OYmIiu/Ka9ojSWk5MTHTt2xN7e8pwjF7J29dFvgEeBueU/NzfXjlyjB+I8oD9FO3biPXYsrtEDCT9puuYel5RLN0cf/tS1jkTwurcHpbKQOemZ3FVYRJROxzR/Pxb2HFPrnANGo+TFLw5gr9Xw9j2Wk0BZZiZp8+bhPGAAXg880HwfQqm3xMRE3N3dCQkJUWU9lEaTUpKZmUliYiKhoZYLS16oscNH7xFCJAJXA98LIbaVLw8UQvxQpd0GYAfQUwiRKIR4vPytucAtQogTwM3lr5tF4c5d6OJMo1crZtoy3zBOzqWbZxcytYKsrJPNFUK9xMf/yR+ykMHChbvsfKABM5Ct2xVPzJksXr0jjA7l8zNfKPXtdzAWFRHwxusIjbVvESkAOp0OHx8flQSUJiGEwMfHp0FnmI06I5BSfgV8ZWF5MjCsyutRNayfCdzUmBjqo+KeQOC8eSROfAb3oUPNM20Fe7twKCmP0T2ugIwdnIr/HW/vbnVvtJks+XMWjhJeG74WfHuZl9c1A9m5rCLmbjnK9T38GBlpeRL7gt9/J+/77/GdNAnHbtb7jMrFVBJQmlJD/z3ZxCGhLu4gQYsW4T5kCA6dO2PMyzWPjgkP8jDVHAo2TVV5InWf1eI8eOgzfjTk8JhXX3yrJIG6SCl56YsDaIRg7r2WLwkZCwtJef11HLp2xWfCE00ZtqIobZxNJAKf8ePNT8w6hYdTHHfIPDomPMiThKwiHFy742mUnMw5ZZUYpdHIu7vn4W2UPHrLogat+9+YBP4+lcmsYb2rPSdQVdq//01ZynkC3nwTjYNDU4SsWElFDanQGd8zaO4v1cqGXKqzZ88SHh5ebdns2bNZuHBhrett2bKFyMhIwsLC6N+/Py+88IL5vbVr1xIeHk7fvn3p379/tW29++679OrVi759+3LFFVcwdepU9Ho9ACtXrqRv377069eP8PBwNm823Tp87LHHCA0N5YorrqBHjx6MGTOGxMTqI+nmzp3L+vXrmT17NkIITp6svNS7ePFihBDs2bMHgJCQEPN+brjhBuLj46tta8SIEURHR1/0mRcvXszataah3NOnT6dXr17069ePe+65h5ycnBq/q7y8PDp27MikSZPMy26++Ways7Nr/Y5bgk0kgqqcwsMpS0mhLMN0ozg80HSf4PD5fLoJJ07qGvaMQlP5c/e/2SNKeDrgxnrNPla1M3jlqzi6+7syKqpyNrGqz04UHzhA9ifrcBtyI8X79jbbZ1CaX9UaUhJIyilm5pcHmyQZNFRcXByTJk1i3bp1HD58mD179tCt/JLjli1bWLx4MT/++CMHDx5k586deHqa/q8tX76cH3/8kZ07d3Lw4EF2796Nv78/xcXFJCYmMmfOHLZv386BAwfYuXMn/fr1M+9zwYIF/PPPPxw7doz+/fszZMgQSktLze9v27aNW2+9FYC+ffuyceNG83ufffYZffpUr97766+/cuDAAQYPHsxbb1WWeM/JyWHv3r3k5uZy+vRp8/KysjJWrlzJQw89BMAtt9xCXFwcBw4coEePHrzzTs2TRr366qtcf/311ZY98sgjLFu2rH5feDOy9qihFuccbvqHoDt0CLcbbqiczD45l27O/vxQlIA0Glv0RqqhrJRFh1cTLOG+m+bV2b6iM6haSyghq5jNscmM6B8EVD47EbhwAWnz5qPx8qJ47z68HxnTbJ9DabzXvz3E4eS8Gt/fn5BDqcFYbVmx3sCLnx9gQ0yCxXXCAj147c6Gly+vMHjwYK644gp+//13c0cYFRXF/Pnzefnll+nVy3QZU6vV8vTTTwPwzjvvsHDhQgIDAwFwdHTkiSdMlyTnzJnDH3/8gZeXFwAODg7MmGGqLnPy5Enc3d1xc3MDwM3Nzfx7VUIIpkyZwldffcWWLVu4++67ycvLo7S0lIrnjEaMGMHmzZt55ZVXOHXqFJ6enjUOp7z66qtZsmSJ+fWXX37JnXfeSfv27dm4cSOzZs0C4JdffmHAgAHY2Zm6zoqkAxAdHc3nn39ucft79+4lNTWV2267zXxGAnDXXXdx3XXX8fLLL9f8F9ACbO6MwLF3GAhBcfkIIm9XB4K8nPk+YQP2BgP5GkHqHD9YFE7MX/MbVN/nUn3z+yuc1BiZ3P1+7O1d6mxvqaBcSVn1gnLVKosePw56vaosehm4MAnUtbypFBUVERsby7Jlyxg3bhxgOiO48sorLbav6b28vDwKCgpqHNZ4xRVX0L59e0JDQxk7dizffvttrXENGDCAo0ePAvDTTz9x002VY088PDzo1KkTcXFxbNy4kQdqGS69detWRoyorHCzYcMGRo0axahRo9iwYYN5+V9//VXjZ165ciW33377RcuNRiMvvPCCxcts7dq1o6SkhMzMzFo/Z3OzuTMCrZsrDl26oIs7ZF7WJ9ADx9QUNnsngkbDCQc7EkrSTPV+ej7arPHoirN5P/4H+gp7bh1Uv6OC+hSUA7APCkSWnzaryqJtQ11H7oPm/lKttHiFIC9nPn3y6kveb02jTCqWjxplGvh3/fXXk5eXV+u18IbYtm0bL730Ejk5Ofz3v//lmmuuYevWrezevZuff/6ZKVOmsHfvXmbPnm1xfVNBApOtW7cyduzYau8/+OCDbNy4kW3btvHzzz+zatWqau/feOONZGVl4ebmxptvvglAamoqJ06c4Nprr0UIgb29PXFxcYSHh5OSkkLv3r0vimPOnDnY2dkxevToi95btmwZw4YNo2NHy6P5/P39SU5OxsfHp9bvqjnZ3BkBmC4PVTxTAKY5jF/K3cqcNFNWXuPpzjR/3wbV97lU63+aSqpWMKX/s/W+HBXgZfkZgao3iqWUJE19AQwG2o0ZoyqLXiamD+2Js331OlJVa0hdKh8fn4tuWmZlZeHra3p25cJEIYSgT58+7N1r+Z5TTe95eHjg5ubGmTNnABg6dCixsbGEh4ebr/ULIYiKimLmzJls3LiRL774osa49+/fb+6YY2JiiIqqPsh6+PDhfPLJJwQHB+Ph4XHR+r/++ivx8fFERETw2muvAbBp0yays7MJDQ0lJCSEs2fPms8KnJ2dLxqfv3r1ar777jvWr19vMaHu2LGDpUuXEhISwrRp01i7dq35UhiYniNxdrY8yKOl2GQicOoTTll6OvpUU0WL8CBPAkUGNxYX42Y0ssvZucH1fS5Fbs5ZPs7YzfXCjasixtV7vagQ74uWXdgZZCxdiu7gQdo99BAdZs1UlUUvEyP6B/HOvX0t1pBqDDc3NwICAvjll18AUxLYunUr1157LQCffvopANu3b8fT0xNPT0+mT5/O22+/zfHjphpdRqOR5cuXAzBz5kymT5/O+fJpT0tLS1mxYoX5vaefftp8ViGlNHeuycnJ7NtXOYQ7NjaWzp07XxSvlJIlS5aQkpLCbbfdxqFDh+jVqxdabfUk6eLiwrx582q9Bm9nZ2ceCZSVlcWGDRvYunUrZ8+e5ezZs+zdu9d807l3797VRiJt3bqV+fPn88033+DiUnlZNykpyXyZav369SQkJHD27FkWLlzImDFjmDt3rvlznD9/npCQkBrjawk2d2kIwKnKDWP79v6EB3mSLH1Jds6n4sr7eg/3etf3aYiVcSsJz80gKmYtH2nzKfBw5yafCFbGrWRceN3J4GRaAVvizhMW4E5usZ7kHB2BXs5MH9rT3BkYCgrIWr0G+86daT9rJlC9sqi6RNS2jegf1OiO35K1a9fyzDPPMHXqVABee+01unbtCphq1/Tv3x+9Xs/Klab7Zv369WPx4sWMGjWKoqIihBAMHz4cgGHDhpGamsrNN9+MlBIhhPnewtNPP01hYSEDBw7E0dERNzc3Bg0aRP/+/cnJyWHatGkkJyfj5OSEn5+fObmAabjmm2++SVFREdHR0fz66684ODiwZcsWbrvN0pQnpstDdQkICGDUqFG8//77xMfHVxs2GhoaiqenJ7t27eL222/nkUceMb83adIkSkpKuOWWWwDTDePly5eTkpJivqFcm7179xIdHV2vts1KStnm/lx55ZWyMQyFhfJw7zCZ9u8l5mVPzntKXvtxmNw+10/evKKXvPPDHvK6j8Pkru3zGrWvC+3aPk9e93GY/H5+e9l/VR85YVnXeu9HX2aQd733p4x4fZtMzSuusV3KW3Pk4V69ZdGBA00ZutJMDh8+bO0QanXDDTfI3bt3WzuMWt18880yOTm5RfY1YsQIefz48VrbvPfee3Lz5s11bmvy5Mnyp59+aqrQqrH07wrYIy30qTZ5aUjj4oJj164UH6q8T5DgH8CAnMEMcvBnYnYuZxwceMijV531fRoqKmYtC9PSecXPFyNwyNGh3vcilv12in8Sc3lrRF/83S3fJyiOO0T2+vW0GzVKTUKv2Iz//e9/BAQEtMi+5s6dS0pKSq1tJk2axF133VXntsLDw6uNdLIWm0wEYHqwTBd3yDzq4JagB/k2fRhFz8Ry53OnCTUItuSd4NFeDzftjnMTSbSzQy8EBiF4sJ73IuKSclny8wnuvCKQO/pZ/gcvDQbOz56N1scbvynPN23cis367bffiIyscUpym9OzZ8+LHgy7VBXPVlibDSeCPhgyMykrv5kVHuSJUcKRlDzs7J14tseDnNZKvv391Sbd72Gv9rzp442dlEzIzmWThxsxTo7gaXloGUBJmYGpm2LxdnXgzbtrHl6YvXEjurg42s+YgdbdvUnjVhTl8mWzicC5vK5KxYNlfc1zGJue6rz5mhn0MWpZFv89pSX5TbLP3JyzPONhh0HAwtQMns3JZWFaBtP8/YiJqvmJ33f/d5zjqQXMu68fXi6W6wTpU9NIX7QY12uuwWPYMIttFEVRLLHZRODYsyfY2ZkfLGvv4YivmwMHk3IBEBoNz/V7ihStYNMv0xu9P6OhjJnfPEiWRjDT+ypucvCltrkGqtYS+s/vp7m6izc39qp5BFPavLnI0lI6/OtVVdJYUZQGscnhowAaJyccu3c3P1gmhKBPoCdx5YkA4Oorn2Jg3Md8dH479xScr1cxuJp8+N1j/CkLeSVgCA8MXVLtvQvnGrBUS2j/uRy+3p9kcdhgwZ/byfthC77PTsLByuORFUVpe2z2jAAqnzCuuGHcN8iTE2kF6Kp0wM9FvkiWRrD2pxdq2kyd/t79PsuyYxlu58v9tyyus72lWkI6fWUtoaqVRY06HefffBO79u1Ba7N53bYc2ASLwmG2l+nngU2N3uTlVob62LFjDB48mIiICHr37s2ECRPYtm0bERERRERE4ObmRs+ePYmIiGDMGNNl2e3btxMVFUWvXr3o1asXH374YY2f+9VXX6Vfv35ERERw6623kpycbH5v69at5u1ERETwwAMPkJBQWRDw+eef548//gBg9OjR9OzZk/DwcMaNG2f+DixJSEjAzc3N/D2WlpZy/fXXU1ZWVuvfUX3YdCJw6hOOITcXfZKphG9hqR6DUdL71a3mOu99+4zkJo0Ha7L/ITur4XMVpCTv5aW4D+gqtbx6z2f1KiNRVy2hisqihTt3kfnhh+gTEjAWFeISEdHg+JQ25sAm+HYy5J4DpOnnt5ObJBk0VGsuQz158mSmTJlCbGwsR44c4dlnnzWXs4iNjSUyMpL169cTGxvL2rVrOX/+PA899BDLly/n6NGjbN++nf/85z98//33Fj/79OnTOXDgALGxsQwfPpw33njD/J08++yzrFmzhqNHjxIbG8vo0aM5e/YsAJmZmezcudM86mj06NEcPXqUgwcPUlxcbH762pKpU6dWK2rn4ODATTfdZH7quzFs+hDSqbw2uS4ujh/SBf/ddQ6gWp13gGevmc2vf05hxc9TmT5yc723X1qSz9Rt4ykDFg9ZiotL/Z5J8HN3JC2/5KLlFbWEzJVFJ0/GWFCAcHCg43tL1RPDl4MtM+D8wZrfT9wNhgv+beiLYfMk2LvG8jod+sLtlz4deFssQ52SklKtyFvfOp6pef/993nssccYMGAAAL6+vsyfP5/Zs2dzxx13XNS+at2iwsJC8325efPmMWvWrGqF6ao+T/DFF19UewJ6WJWBHVFRURed4VT4+uuvCQ0NxdXVtdryESNGMHPmTIvF7hrCps8IHHv2AHt7dIcOsWDbMUrKLq7zvmDbMbp2vYU7HTqwsfAU51P217i9lXEriflrvvm0ff6KAcRpyrjRrz+dO19Xr5jydXpMqai6C2sJuURdhcbVFYxG2j00SiUBW3FhEqhreRNpa2Wop0yZwpAhQ7j99ttZtGhRndVSDx06dFG8kZGRHDp0qIY14OWXX6ZTp06sX7/efEZw6NAhczKxpKYy1nq9nk8++cRimYyCggLmzZtnLopXVXh4OLt3765xf/Vl04lA4+CAU48eFMfFu2e69gAAHotJREFU1Xk5ZuLguUjgg99erHF74bkZTDu2hpiSNL51c+ZTNyccjUZGtKvfE75SSqZ99g+ZhXom3ti11sJiaQsXUpaSgtvgweRu/kYVk7tc3D4Xxn5f8x/PTpbX8+xU8zr1OBuwZhnqiIgIQkJC+Pvvv9FqtWzdupXPP/+cHj16MGXKlBpLUMPFZagrLp2MHTuWI0eOMHLkSH777Teio6MpKWnaZDlnzhzOnTvH6NGjWbp06UXvZ2ZmEhERQY8ePczX9VNSUswT51Q1ceJErr/+eq677uIDxtmzZzNlyhSLZ0ZarRYHBwfy8xs3xN2mEwFUPmEc6Fl7aefAwEjC7b35qiSF04t6mm/UVZ285opda3gmK4dn2/vxqq8PdlLyXmr9S1l/8Pspth1KZebtvXhxaC/+mjGEM3Pv4K8ZQ6olgbwffyRr1Woce/ak4wfLVGVRW3LTv8D+gpLF9s6m5Y1wOZahDgwMZNy4cWzevBk7OzviqpSev1BYWNhF8e7du9c8teXYsWOJiIiodimnwujRo80x9unTx1w91cfHh9jYWCZMmEBBQQFguYz166+/Tnp6Ou+++67F2Hbt2sWLL75ISEgIixcv5u23366WeEpKSnBystx/1ZdKBOF9MObnMyvC/aI67/ZaUe1yzJj2g5DAG85GCgWsM2Yz6fgadu1exr2rrmCgt+AtP2+KNBoMQjAqN5+r61nK+o/j6Szcdozh/QJ4/FrLp80VMt5fBhoNQYsWIYSoVllUucz1ux/uXFJ+ZiBMP+9cYlreCJdbGeqtW7eaR+CcP3+ezMxMgoJqrtj6zDPPsHr1amJjYwHT0fxLL73Eiy+argCsWrWK2NhYfvjhBwBOnDhhXnfz5s3m+yQvvvgic+bM4ciRI+b3i4qKzL9fWMZ6xYoVbNu2jQ0bNqCpMpAkJibGPJrpzz//NJfEfv7555k1axaTJk0yx+nr61vjFJz1ZdM3i6HyCeNrjem8c28EC7YdIzmnGK1G4Opgx23hlc8O3HzwW+60L+RbdzeiQypP0Y8aigjTejA4PwM7fQnrPd0ZlVfAJg83BhcX11nK+lxWEZM37qe7vzvz/69frQ+EFfz+OyXHjuH77CQcu1QmDNfogeo+ga3od3+jO35LLqcy1D/++CPPPfec+Uh5wYIFdOhQ83NAAQEBrFu3jieeeIL8/HyklPz/9s48rKpy3+OfVxARp5LBSI4zCQiKZjjkSdHMW85DdrASz8mbU9mkZlZ67ZTmFYW8mdXJ0rTyHE0th+optXJIyAlnSI1UUCRUUCYRfvePvVmyYW/cyFY28n6eZz3P3mu9e63vetms336n7+/555+nf//+VstPnTqVhIQEatSoQdOmTQ2NISEhvPPOO4wcOZLMzEy8vLxo0qQJM2fOBKBv37588MEHjB49GoCxY8fStGlTunQxZZcbMmQI06dP5+TJk3Ylq9myZYvVwexyY82S1Nm3itpQF6fwyhU5EtJWzr5taQO9/bc0afryelm45bdrO2c0kMv/00CGf+AvwUuCZfK7zSX1jTulcEYDEblmMR0721tkRn2Jne19XYvpnCtX5ZF3fpbgGd/KibTLZWotyMqS38J7yrFH+kpBXt6N37TGqdA21BXnVtpQV5T7779fLly4UGaZSZMmSXx8/HXPNXjwYElISLB6TNtQlwNVsya1AgMsUlcCdG3lxYOBjXhvy3HSiqZyNvDjUC03zri6MuZCBjtru5NU0xVlNow72MCLqNaR5haAbfuIIkSEaWsOcCglk5jHQmnuVcdquSLS/u9d8lNS8H1jJjXcrHsOaTTVkVtpQ11R5s2bZ7HAzBpz5861WD9hjStXrjBo0CDuueeeCmuq9l1DALXbBJOxdi1SWGix4OuVRwLoE/0z0T8kMmtwCHFhI00J7c+lEZabR1huLpN8vIlqPZIwuJZh7P5rM4tK2keAyUJi7ncJRhLyPkGN6BXYqEyNOYcOcX7pUu547DE8bEzZ02huBj/++GNlS7it6NTJMV24bm5uxjhCRan2LQIwzRwqzM7minn1XxEtvevyROemrIg7SWLqpXL/4rdGkY9QcrHpqj//lsbavck2PyNXr3L29em4eDbE56UXy3t7Go1GUya6RYDlCuNaLVpYHHuulz+r95zmrQ1HWPoP+37xl4U1H6Ecs4+QrTy055ctJ/fwYRrHxOBSbEWjRqPROALdIgBqtWyBcnc3chMU5846bkzs5c9PiWn8mHCuQtcREYuWQHFsLWi7cjqZtAULqBseTr0+D1Xo+hqNRmMNHQgA5eqKe2CgkZugJCO7NKOZpwezNh7hakGh1TLXI+9qAZNX7bd5vGjhGlxzFxURzs6ciVKK+v37cX7x4hu6tkaj0ZSFDgRm3IODyT1yBCkoKHXMzbUGUx8OIDH1Mv/edarc5z53KZeID3eyavdp+gQ1onZNy2ov6SNU5C6atmABWVu30mDQIFL/+SbuwToZfXXn44MfE3cmzmJf3Jk4Y3X7jeLi4mJYNIeGhhpumXFxcTzwwAO0bt2a9u3bM3r0aLKzs1myZImxqAlM1gkPPfQQhYWFTJw40bCfvu+++/j999/p1KkToaGhNGnSBG9vb4vrZGRkMHLkSFq1akXLli0ZOXIkGRkZVnXGxcUZn23Xrh1r1qwxjqWmpjJixAhatGjBvffeS5cuXSyO7927l6eeegqAzz77jLZt2xISEkLXrl2Jj48vs34GDBhgYdM9adIkY/HdbYG1OaX2bsCjwCGgEOhYRrmPgXPAwRL7/wdIBvaZt0fsua4j1xEUcXHtWjncOkByExOtHi8sLJRHF+2QoNe/kc6zfpBmL6+XrrM3yZo9p8s87/5TF6XzrB8k4LVvZMN+0zznNXtOS9fZm8o8R8b338vhgEBJ+OsDktC5i1z+ZWfFb1LjlJRnHUFsSqz89Yu/SmxKrNX3N0qdOnVK7Tt79qw0adJEduzYYexbuXKlnD17Vj755BOZMGGCsf/jjz+WqKgo+fzzz2Xo0KFSUFAgIiKnTp2S8+fPG+VKfk5EZOjQoTJjxgzj/fTp02XYsGFWdWZlZUl+fr6IiKSkpIi3t7fk5+dLYWGhdO7cWRYtWmSUTUpKkgULFhjvhw0bJvv27RMRke3btxu6Nm7cKGFhYTbr5ssvv5SIiAhp06aNxbl79+5t8zPOQHnWEVR0sPggMAT44DrllgDvAtZMd6JFpOzsF7cAdyOH8SFq+fuXOq6Uopu/J3FJ58m6Ymo1FLeqLhroLZoamnIxhzs8apKZk89dDWqzalwX2tzdwChra2AYTME5Y/UaUIqCc+fwGj9OrxquJsyJm8PR80fLLOPt4c2Y78fg7eFNWnYaLe5owaL4RSyKX2S1fEDDAF4Oe7ncWhYuXEhkZKSx6hVg2LBhVst+++23zJgxg2+//RZfX1/DLqG4FbQ1jh07xu7duy089adPn06rVq04fvy4sbK5CA8PD+N1bm6usQp/8+bNuLm5MXbsWON406ZNefbZZwG4dOkS+/fvp127dgB07drVKNe5c2eb9s+XL19m/vz5fPjhhwwffm01d9OmTUlPT+fs2bNlrliuKlSoa0hEjohIgh3lfgbOV+RaNxu3Zs2o4eFRamFZcf79a+kvS05+ATO+PsTX8SnM/uYIL3+5n+SLOQhwITsfAcb2aGEEAXu4uGIFlzdvRtWqhdf4cVz4YoU2lNMY1Herj7eHN2eyzuDt4U19t4rPJMvJyTG6XAYPHgyUbTNdnIKCAhISEggKCmL48OGsW7eO0NBQXnrpJfbutW3bDnD48GFCQ0MNjyC41k1lywI6NjaWNm3aEBISwvvvv4+rq+t17Z937dpVKgNbEYsXL7ZI+FKc119/nZdeeskiABXRoUMHtm/fXtbtVRmcYfroM0qpkcAu4CURuWCtkFLqaeBpgCZNmjhchHJxwT0oqMxAYGtmT0ZOPhO/sP6FLxR4/8cTPNm5mV068n77jbOzZoOrK37vLaRuly54hHUi+YUXaBwdrVsGtzn2/HKPOxPHpJ8mMabtGP6T8B/GtRtHmG95JjGXpnbt2obhWnmJjY01Fkn5+fmRkJDA5s2b2bx5M7169WLlypVGngBH0KlTJw4dOsSRI0eIjIy0+hCfMGEC27Ztw83NjV9//dWm/fOWLVtYvHgx27ZtK3Vs3759HD9+nOjoaGPMpDg+Pj4WKSqrMtdtESilflBKHbSyDXTA9RcBLYFQ4Awwz1ZBEflQRDqKSEdrf1BH4B4cTO7Ro4iNvKHFZ/YU56767nz/wgPYsoqzFUBKUpiXR/KkyShXVxrPn0ddc5Ncu4tqiigKAlHdo3im/TNEdY9i0k+TSg0gO4KybKaLU9LwrVatWjz88MPMnTuXadOmsXbtWpufDQoKYt++fRQWXpuNV1hYyL59+wgKCmLNmjVGS2XXrl0Wnw0MDKRu3bocPHjQwv4ZTN1amzZtIi0tDbBu/7x//35Gjx7NV199haenZyltv/zyC7t27aJZs2Z069aNxMREevToYRzPzc21yxiuKnDdQCAiD4pIsJXN/pyNts+dKiIFIlII/Ivyrc1yKOkffYRyd0fy8sg7bspNnLUzlvRiOUQn92ldyqq6dk0Xpj4cgH+jejYDha39JTk3bx55CQn4xURT/yHLNQN1OnfC0+xYqKm+HEw/SFT3KKMFEOYbRlT3KA6m227J3ijPPPMMS5cuJTb2Wrfk6tWrSU1NtSi3adMmHnzwQQD27Nlj/EouLCxk//79Vm2ki2jVqhXt27fnzTffNPa9+eabdOjQgVatWjF48GCLPMO///67kaz9jz/+4OjRozRr1oyePXuSm5vLokXXxknKsn8+efIkQ4YMYdmyZaW8enr16kVycjLjxo0jJSWFpKQktm3bxj333GNht5GYmGizu6mqUanTR5VSxV2iBmMafK4U3INDuPDF54BphXHWzliSX3jBYsrmoPaNmT0kxGbmMFuBovjUUFtc/uknLny6jDuffJK63bs77sY0txX/CP5HqW6gMN+waz5XDqRRo0asWLGCSZMm0bp1awIDA/nuu++oV6+eUSYtLQ13d3dj37lz5+jfvz/BwcG0bdsWV1dXi2mm1li8eDGJiYm0bNmSli1bkpiYyGIba2a2bdtGu3btjLGM9957Dy8vL5RSrF27lp9++onmzZsTFhZGZGQkc+bMASAgIICMjAwjk9cbb7xBeno648ePJzQ0lI4dOwKm4HXs2DEaNmxYpub8/HyOHTtmfK7KY20qkb0bpof3aSAPSAW+M++/G9hYrNwXmLp+8s3lnzLvXwYcAPYDXwO+9lz3ZkwfFRG5tGOHHA4IlGOP9L3hKZv2TA0tSX5amiR0vV+O9x8gBbm5NyJdU4Vxdhvqsli2bJnMnj27smXYxfz58+Vf//pXmWUOHDggL7zwwnXPtXr1annttdccJe2mUJ7po8p0rGrRsWNHKdlf6CiSIkaQs3cvDQYN5O63r5/rtaJIYSGnxowlOy6OZiv/g7sDLGU1VYsjR44Y6RY1N4/c3FxWrlzJk08+WeFzrVy5kt69e3PHHXc4QNnNwdr3Sim1W0RKNWP0yuJiZO2M5crvv1Ojbl0y1q3j8i2YGnZh+XKytm7FZ8pkHQQ0mpuIu7u7Q4IAwKOPPurUQaC86EBgpmhMoHFMDHf/7xwoKOT0M886fP5+kY8QQO7Ro5ybG4V7u3YUZts3s0ij0WgcjQ4EZnIPHjDm6dfr2ZO64eFIQQFZOxzbKijyEbr8888kT5qE8qhN/h9/UDtE+whpNJrKwRkWlDkFJadmNnr1VbL69SPvxAmHXqdO507cPX8ep8eMRa5coUbdujR+d4FeKKbRaCoN3SKwgZtfY7zGj+fyD5u4tGWLw84rBQVkrl+PXLkCQMORT+ogoNFoKhUdCMrAc1Qkbi1bkvrmWxTmVLwPX/LzSZk8hYwvV6Pc3fEcp32ENOWj+BhTESUXPt4IjrKhdjTZ2dl4enqSmZlpsX/QoEGGUd3atWtp27YtAQEBBAcHs2rVKsDkgVT8nkJDQ/Hy8uKxxx4zzjNs2DBOnDhBdnY2ffv2JSAggDZt2jB16lSreo4ePUqXLl2oVasWUVHXvDJPnTpFeHg4QUFBtGnThnfeecc4dv78eXr37o2/vz+9e/fmwgWTi8769euZPn26YyqqolibU+rs281aR2CNyztj5XDrAEmNjq7QeQpyc+XkuPFyuHWAHAltb6xRuPzLTm0zXc0pzzqCkt8XR31/HGVDfTOIiIiQJUuWGO8vXrwonp6ekpWVJfv27ZOWLVvKiRMnRETkxIkT0qJFC9m1a1ep86SkpIifn58cOHBAREQOHjwogwYNEhGTvfXmzZtFRCQvL0+6desmGzduLHWO1NRUiYuLk2nTpsncuXMtzr17924REcnMzBR/f385dOiQiIhMnjzZWGsxe/ZsmTJlioiYrO1DQ0MlKyurYhVkg1tpQ33bU6dTGPUH9Cd98cc0GDCgVE5jeyjMzjbNQNqxg7q9etLwyZFGd1BxHyHdRaQ5O2sWeUfKtqF29fHh5OjRuPr4cPXcOWq1bMmfCxfy58KFVsvXCgzgrmnTyq3lRmyoAebMmcPy5cupUaMGDz/8MG+//TbHjh1j7NixpKWl4eLiwsqVK0tZTI8aNQp3d3d27dpFZmYm8+fPp1+/fkRERPDee+8RGRkJwJo1a+jTpw8eHh5ERUUxbdo0mjdvDkDz5s2ZNm0a8+bN4/PPPzfOLSJERkYyefJkwxbis88+Y+BAk2Wah4cH4eHhALi5udGhQwer1tQ+Pj74+PiwYcMGi/2+vr74+pqMEurVq0dgYCDJyckEBQXx1VdfGdYUkZGR9OjRgzlz5qCUokePHqxfv97C4roy0F1DdtBoyhRq1K7N2Tf+WbRS2m4KLl3i5H8/TdbOnfjOmsVfFi4s9cDXPkKa8uBSv74pCKSk4Orjg0t957Gh/uabb/jqq6+IjY0lPj6eKVOmAPD4448zYcIE4uPj2bFjh/HQLElSUhJxcXFs2LCBsWPHkpubS58+fdizZw/p6ekArFixgoiICAAOHTpUSmPHjh05fPiwxb7o6GhcXV2N/AQA27dvt3p/Fy9eZN26dTfsmJqUlMTevXsNR9bU1FTjfu+66y4Lr6aOHTuydevWG7qOI9EtAjtw9fLC54XnOTvzDTLXb6BB/35Wy6V/9BHuwSHGg/7qhQskRYwg/+RJGs+Lor4Nz3ONpgh7frkXrXkpylXhNWFChVuTjrKh/uGHH/j73/9u+Pc3bNiQS5cukZycbAQYd3d3m+caPnw4NWrUwN/fnxYtWnD06FFCQ0MZMGAAq1atYujQoezdu5c+ffrYrS8+Pp6YmBh+/fVXI5ENYNWa+urVq0RERDBx4kRa3EDr//LlywwdOpSYmBjqWwnQSikLDc5iZa1bBHZyx/DhuDZqxNl//pOCYgNXxQfqitYIZO2M5WpaGknDHiU/KQmvic/qIKBxCMbCx+hovCdOpHF0tPGdczQ3akNtL6+++qrRCimi+EOy+PuIiAhWrFjBqlWrGDhwIDVr1gRMNtYlNe7evdswg8vJyeHxxx9n0aJFNGrUyKKcNWvqp59+Gn9/f55//vly309+fj5Dhw7l8ccfZ8iQIcb+Ro0acebMGcAUfHx8fIxjzmJlrQOBnSgXFzzHjaMwM5OUV0y/2kz/lM/j2tiP3MRElKsLd44cyenx4znerz/5ycn4TJmMd7H0eRpNRSi+8BFubq6KG7Gh7t27N5988olhAX3+/Hnq1auHn5+fkZcgLy+P7Oxs3nrrLcNiuoiVK1dSWFjI8ePHOXHiBK1bm5x7e/TowW+//cbChQuNbiEwJZGfPXu2McspKSmJmJgYJk+ebBzv3r07ffv2LXV/Ja2pX3vtNTIyMoiJibEot2bNGl555ZUy60pEeOqppwgMDOTFF1+0ODZgwACWLl0KwNKlS41xCXAiK2trI8jOvt3KWUMlOTl+gmnmT/v2crh1QJlb8tRXKk2npurgDO6j1mYNiYjs2LFDunXrJvfcc48EBATI008/LVlZWcasoXPnzkl4eLjFZ2bPni2BgYHSrl07eeUV0/9AYmKihIeHS0hIiHTo0EGOHz9e6lqRkZEyZswYuffee8Xf31/WrVtncfy5554TX19fKSgosNj/5ZdfSnBwsPj7+0vNmjVl27ZtIiKSnJwsgAQEBEi7du2MbcSIESIi8umnn8qrr74qIiKnTp0qVbbIqXTu3Lkya9YsERE5c+aMNG7cWOrVqycNGjSQxo0bS0ZGhmzdulUACQkJMT6/YcMGERH5888/pWfPntKqVSvp1auXpKenG9r79u0r+/fvt+MvVH60++hNpODSJf4YGUnekSO4h4ZSr2dPXOrXx6VBfWrUr8+Vk6dIi4nhzuHDubhqlU4vqbkuVdl9dPny5Zw+fdrmvPvyMGrUKPr162dzZpI9TJ06ldjYWL777jvc3NzKLJuTk0N4eDjbt2+3yJlckieeeILo6GirqS4rQmpqKiNGjGDTpk0OPW8R5XEf1YPF5ST30GGunj1rDNTVbtvWeNBn7YzlzwUL8HvnHep07kSd++/XuYY1tzVPPPFEZUuw4O1yWMfXrl2bmTNnkpycXGYe9OXLlztCWilOnjzJvHk2s/PeUnQgKAfFB+rqdO5UKql8Wf23OhBoNGWzZMmSW37N8sw+cjT33XdfpV27JDoQlIPrPeitrQWo07mTDgKa6yIipWbMaDQ3Snm7/HUgKAf6Qa+5Gbi7u5Oeno6np6cOBpoKIyKkp6eXuV6jJDoQaDSVjJ+fH6dPnyYtLa2ypWhuE9zd3fHz87O7vA4EGk0lU7NmTcMrR6OpDPSCMo1Go6nm6ECg0Wg01RwdCDQajaaaUyVXFiul0oA/bvDjXsCfDpRzs6lKequSVqhaequSVqhaequSVqiY3qYiUmqJdJUMBBVBKbXL2hJrZ6Uq6a1KWqFq6a1KWqFq6a1KWuHm6NVdQxqNRlPN0YFAo9FoqjnVMRB8WNkCyklV0luVtELV0luVtELV0luVtMJN0Fvtxgg0Go1GY0l1bBFoNBqNphg6EGg0Gk0157YNBEqp/1JKJSiljimlSqVPUkqNUkqlKaX2mbfS1qK3CKXUx0qpc0qpgzaOK6XUAvO97FdKdbjVGotpuZ7WHkqpjGL1Ov1Wayym5S9KqS1KqcNKqUNKqeeslHGmurVHr1PUr1LKXSkVp5SKN2udaaVMLaXUv811G6uUanbrlRpa7NHrNM8Esx4XpdRepdR6K8ccW7fW8ldW9Q1wAY4DLQA3IB4IKlFmFPBuZWs1a3kA6AActHH8EeAbQAGdgVgn1toDWF/ZdWrW4gt0ML+uByRa+R44U93ao9cp6tdcX3XNr2sCsUDnEmXGA++bX/8N+LeT63WaZ4JZz4vA59b+3o6u29u1RRAGHBOREyJyBVgBDKxkTTYRkZ+B82UUGQh8KiZ2AncopXxvjTpL7NDqNIjIGRHZY359CTgCNC5RzJnq1h69ToG5vi6b39Y0byVnngwElppfrwJ6qUpKuGCnXqdBKeUH9AU+slHEoXV7uwaCxsCpYu9PY/0faqi5O2CVUuovt0baDWHv/TgLXcxN8G+UUm0qWwyAuencHtMvweI4Zd2WoRecpH7NXRf7gHPA9yJis25F5CqQAXjeWpXXsEMvOM8zIQaYAhTaOO7Qur1dA4E9rAOaiUhb4HuuRVdNxdiDyc+kHfB/wNpK1oNSqi7wJfC8iGRWtp7rcR29TlO/IlIgIqGAHxCmlAquLC32YIdep3gmKKX6AedEZPetuubtGgiSgeLR3M+8z0BE0kUkz/z2I+DeW6TtRrju/TgLIpJZ1AQXkY1ATaWUV2XpUUrVxPRQ/UxEVlsp4lR1ez29zla/Zh0XgS3Af5U4ZNStUsoVaACk31p1pbGl14meCfcDA5RSSZi6tXsqpZaXKOPQur1dA8GvgL9SqrlSyg3TYMrXxQuU6AcegKk/1ln5GhhpnuHSGcgQkTOVLcoaSqm7ivoqlVJhmL5jlfLPb9axGDgiIvNtFHOaurVHr7PUr1LKWyl1h/l1baA3cLREsa+BSPPrYcBmMY9u3mrs0esszwQReUVE/ESkGaZn12YReaJEMYfW7W2ZqlJEriqlngG+wzSD6GMROaSUegPYJSJfAxOVUgOAq5gGP0dVll6l1BeYZoN4KaVOAzMwDWYhIu8DGzHNbjkGZAN/rxyldmkdBoxTSl0FcoC/VdY/P6ZfVk8CB8x9wwDTgCbgfHWLfXqdpX59gaVKKRdMweg/IrK+xP/YYmCZUuoYpv+xv1WCziLs0es0zwRr3My61RYTGo1GU825XbuGNBqNRmMnOhBoNBpNNUcHAo1Go6nm6ECg0Wg01RwdCDQajaaaowOBRqPRVHN0INBoNJpqzv8DmikM1ZeGyYQAAAAASUVORK5CYII=\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plt.figure()\n",
-    "plt.plot(list(mra_vqe.keys()), list(mra_vqe.values()), marker=\"o\", label=\"UpCCGSD/MRA(2,4)\")\n",
-    "plt.plot(list(gbs_vqe.keys()), list(gbs_vqe.values()), marker=\"o\", label=\"UpCCGSD/STO-3G(2,4)\")\n",
-    "plt.plot(list(gbs_fci.keys()), list(gbs_fci.values()), marker=\"x\", label=\"FCI/STO-3G(2,4)\")\n",
-    "plt.plot(list(close_to_cbs.keys()), list(close_to_cbs.values()), marker=\"x\", label=\"FCI/cc-pVQZ(2,120)\")\n",
-    "\n",
-    "plt.legend()\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "To provide a complete picutre here are the values from the exact diagonalization of the Hamiltonian in MRA reprentation\n",
-    "(we initialize the `tequila` molecule, create the hamiltonian, export it as matrix and diagonalize with `numpy`).\n",
-    "The UpGCCSD is as good for MRA as it is for GBS (compared with exact diagonalization within those representations)."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "mra_diag = {R:numpy.linalg.eigvalsh(initialize_molecule(R).make_hamiltonian().to_matrix())[0] for R in points}    "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plt.figure()\n",
-    "plt.plot(list(mra_vqe.keys()), list(mra_vqe.values()), marker=\"o\", label=\"UpGCCGSD/MRA(2,4)\")\n",
-    "plt.plot(list(mra_diag.keys()), list(mra_vqe.values()), marker=\"x\", label=\"Exact/MRA(2,4)\")\n",
-    "plt.legend()\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "tequila-chemistry",
-   "language": "python",
-   "name": "tequila-chemistry"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.7.7"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}
diff --git a/tutorials/ChemistryExcitedState.ipynb b/tutorials/ChemistryExcitedState.ipynb
deleted file mode 100644
index 9992d61c..00000000
--- a/tutorials/ChemistryExcitedState.ipynb
+++ /dev/null
@@ -1,505 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Example for an excited state calculation\n",
-    "\n",
-    "Short example of how to form the objectives for the ''hangman's'' approach to excited states.  \n",
-    "Here the states are sequentially computed and are kept orhogonal towards previous states by projection.  \n",
-    "\n",
-    "The method was for example applied in:\n",
-    "https://pubs.acs.org/doi/pdf/10.1021/acs.jctc.8b01004\n",
-    "\n",
-    "See also our overview article [arxiv.org/abs/2011.03057](http://arxiv.org/abs/2011.03057) and our article on optimized fermionic gradients [arxiv.org/abs/2011.05938](https://arxiv.org/abs/2011.05938) for more information.\n",
-    "\n",
-    "The overlap objective is formed from the quantum circuits of the optimized lower lying states $U_i$ and the current parametrized circuit $U(a)$ like this:\n",
-    "\n",
-    "$$\n",
-    "S_i^2(a) = \\|\\langle \\Psi_i \\rvert \\Psi(a) \\rangle\\|^2 = \\|\\langle 0 \\rvert U_i^\\dagger U(a) \\lvert 0 \\rangle\\|^2 = \n",
-    " \\langle 0 \\rvert U^\\dagger(a) U_i  P_0 U_i^\\dagger U(a) \\lvert\\rangle = \\langle P_0 \\rangle_{U_i^\\dagger U(a)} $$\n",
-    " \n",
-    "where $P_0 = \\lvert 0..0 \\rangle \\langle 0..0 \\rvert = \\otimes^n Q_+ =  \\frac{1}{2^n} \\otimes^n (1 + Z)$.\n",
-    "\n",
-    "Bound states can then be kept orthogonal by projecting lower lying states out which is equivalent as minimizing the objective:\n",
-    "\n",
-    "$$\n",
-    " L = \\langle H \\rangle_{U(a)} - E_i S_i^2(a)\n",
-    "$$\n",
-    "\n",
-    "\n",
-    "We will use an active space Beryllium Hydride molecule with two orbitals because the circuit template is easy to construct for this example and it executes fast.\n",
-    "\n",
-    "<img src=\"data/ex_solver_cartoon-1.png\" width=\"200\" height=\"200\" />"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "geomstring=\"be 0.0 0.0 0.0\\nh 0.0 0.0 {R}\\nh 0.0 0.0 -{R}\""
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Optimizing point R=0.7\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.08170491\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -14.15900421\n",
-      "Optimizing point R=0.8\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.36599843\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -14.48743629\n",
-      "Optimizing point R=0.9\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.54369428\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -14.70864582\n",
-      "Optimizing point R=1.0\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.65189560\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -14.85821915\n",
-      "Optimizing point R=1.1\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.71447523\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -14.95919037\n",
-      "Optimizing point R=1.2\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.74678206\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -15.02665710\n",
-      "Optimizing point R=1.3\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.75882309\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -15.07069683\n",
-      "Optimizing point R=1.4\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.75724857\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -15.09814167\n",
-      "Optimizing point R=1.5\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.74656111\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -15.11368465\n",
-      "Optimizing point R=1.6\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.72985528\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -15.12058067\n",
-      "Optimizing point R=1.7\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.70927740\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -15.12111282\n",
-      "Optimizing point R=1.8\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.68632055\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -15.11689854\n",
-      "Optimizing point R=1.9\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.66202362\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -15.10909748\n",
-      "Optimizing point R=2.0\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.63711497\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -15.09854221\n",
-      "Optimizing point R=2.1\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.61210615\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -15.08584404\n",
-      "Optimizing point R=2.2\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.58736645\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -15.07144165\n",
-      "Optimizing point R=2.3\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.56316904\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -15.05565071\n",
-      "Optimizing point R=2.4\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.53971717\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -15.03869534\n",
-      "Optimizing point R=2.5\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.51716630\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -15.02072334\n",
-      "Optimizing point R=2.6\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.49563432\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -15.00182438\n",
-      "Optimizing point R=2.7\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.47520982\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -14.98204422\n",
-      "Optimizing point R=2.8\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.45595568\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -14.96139622\n",
-      "Optimizing point R=2.9\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.43791611\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -14.93987083\n",
-      "Optimizing point R=3.0\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.42111687\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -14.91745281\n",
-      "Optimizing point R=3.1\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.40557042\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -14.89412975\n"
-     ]
-    }
-   ],
-   "source": [
-    "import tequila as tq\n",
-    "\n",
-    "fci_gs = []\n",
-    "fci_es = []\n",
-    "energies_gs = []\n",
-    "energies_es = []\n",
-    "P0 = tq.paulis.Projector(\"|00>\")\n",
-    "for R in [0.7 + 0.1*i for i in range(25)]:\n",
-    "    print(\"Optimizing point R={:2.1f}\".format(R))\n",
-    "    active = {\"b1u\": [0], \"b2u\": [0]}\n",
-    "    mol = tq.chemistry.Molecule(geometry=geomstring.format(R=R), basis_set=\"6-31g\", active_orbitals=active)\n",
-    "    H = mol.make_hamiltonian()\n",
-    "    results = []\n",
-    "    for i in range(2):\n",
-    "        U = tq.gates.Ry((i, \"a\"), 0)\n",
-    "        U += tq.gates.CNOT(0, 1) + tq.gates.CNOT(0, 2)\n",
-    "        U += tq.gates.CNOT(1, 3) + tq.gates.X([2, 3])\n",
-    "        E = tq.ExpectationValue(U, H)\n",
-    "        active_vars = E.extract_variables()\n",
-    "        angles = {angle: 0.0 for angle in active_vars}\n",
-    "        for data, U2 in results:\n",
-    "            S2 = tq.ExpectationValue(H=P0, U=U + U2.dagger())\n",
-    "            E -= data.energy * S2\n",
-    "            angles = {**angles, **data.angles}\n",
-    "        print(\"Starting to optimize state \", i)\n",
-    "        result = tq.optimizer_scipy.minimize(E, method=\"bfgs\", variables=active_vars, initial_values=angles, silent=True)\n",
-    "        print(\"finished with energy {:2.8f}\".format(result.energy))\n",
-    "        results.append((result, U))\n",
-    "    energies_gs.append(results[0][0].energy)\n",
-    "    energies_es.append(results[1][0].energy)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "import matplotlib.pyplot as plt\n",
-    "R =  [0.7 + 0.1*i for i in range(len(energies_gs))]\n",
-    "plt.figure()\n",
-    "plt.plot(R, energies_gs, marker=\"o\", label=\"VQE GS\")\n",
-    "plt.plot(R, energies_es, marker=\"o\", label=\"VQE ES\")\n",
-    "plt.legend()\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Here is the same calculation using the [UpCCGSD](https://pubs.acs.org/doi/10.1021/acs.jctc.8b01004) construction for the untitary circuit with \\textsc{tequila}s [optimized scheme for fermionic gradients](https://arxiv.org/abs/2011.05938).  \n",
-    "In addition we changed to numerical gradients in order to not spend to much time on computing in this notebook.  \n",
-    "Note that in this super restricted active space we do not need to change the reference (allthough we could speed up convergence by switching from the Hartree-Fock reference (in jordan_wigner encoding: $\\lvert 1100 \\rangle)$ to the double excited configuration ($\\lvert 0011 \\rangle$). \n",
-    "\n",
-    "Try it out by setting `include_reference=False` in `make_upccgsd` and adding the gates to prepare the reference manually."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Optimizing point R=0.7\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.08170497\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -14.15900421\n",
-      "Optimizing point R=0.8\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.36599853\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -14.48743439\n",
-      "Optimizing point R=0.9\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.54369454\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -14.70864582\n",
-      "Optimizing point R=1.0\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.65189604\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -14.85821915\n",
-      "Optimizing point R=1.1\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.71447564\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -14.95918560\n",
-      "Optimizing point R=1.2\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.74678225\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -15.02665520\n",
-      "Optimizing point R=1.3\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.75882312\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -15.07069683\n",
-      "Optimizing point R=1.4\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.75724857\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -15.09814167\n",
-      "Optimizing point R=1.5\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.74656115\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -15.11368179\n",
-      "Optimizing point R=1.6\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.72985545\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -15.12057972\n",
-      "Optimizing point R=1.7\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.70927757\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -15.12111282\n",
-      "Optimizing point R=1.8\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.68632048\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -15.11689758\n",
-      "Optimizing point R=1.9\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.66202368\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -15.10909748\n",
-      "Optimizing point R=2.0\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.63711399\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -15.09854412\n",
-      "Optimizing point R=2.1\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.61210472\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -15.08584499\n",
-      "Optimizing point R=2.2\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.58736515\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -15.07144260\n",
-      "Optimizing point R=2.3\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.56316923\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -15.05564880\n",
-      "Optimizing point R=2.4\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.53971719\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -15.03869534\n",
-      "Optimizing point R=2.5\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.51716630\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -15.02072334\n",
-      "Optimizing point R=2.6\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.49563265\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -15.00182533\n",
-      "Optimizing point R=2.7\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.47520834\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -14.98204517\n",
-      "Optimizing point R=2.8\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.45595480\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -14.96139526\n",
-      "Optimizing point R=2.9\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.43791527\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -14.93987083\n",
-      "Optimizing point R=3.0\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.42111621\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -14.91745281\n",
-      "Optimizing point R=3.1\n",
-      "Starting to optimize state  0\n",
-      "finished with energy -15.40557002\n",
-      "Starting to optimize state  1\n",
-      "finished with energy -14.89412975\n"
-     ]
-    }
-   ],
-   "source": [
-    "import tequila as tq\n",
-    "\n",
-    "fci_gs = []\n",
-    "fci_es = []\n",
-    "energies_gs = []\n",
-    "energies_es = []\n",
-    "P0 = tq.paulis.Projector(\"|00>\")\n",
-    "for R in [0.7 + 0.1*i for i in range(25)]:\n",
-    "    print(\"Optimizing point R={:2.1f}\".format(R))\n",
-    "    active = {\"b1u\": [0], \"b2u\": [0]}\n",
-    "    mol = tq.chemistry.Molecule(geometry=geomstring.format(R=R), basis_set=\"6-31g\", active_orbitals=active)\n",
-    "    H = mol.make_hamiltonian()\n",
-    "    results = []\n",
-    "    for i in range(2):\n",
-    "        # labeling ensures that tequila can distinguish the variables\n",
-    "        # singles can break the symmetry here falling into different states than the two above\n",
-    "        # (i.e. the open-shell singly excited manifold: in jordan_wigner those states are build from\n",
-    "        #  |1001> and |0110>)\n",
-    "        U = mol.make_upccgsd_ansatz(label=i, include_singles=False) \n",
-    "        E = tq.ExpectationValue(U, H)\n",
-    "        active_vars = E.extract_variables()\n",
-    "        angles = {angle: 0.0 for angle in active_vars}\n",
-    "        for data, U2 in results:\n",
-    "            S2 = tq.ExpectationValue(H=P0, U=U + U2.dagger())\n",
-    "            E -= data.energy * S2\n",
-    "            angles = {**angles, **data.angles}\n",
-    "        print(\"Starting to optimize state \", i)\n",
-    "        result = tq.optimizer_scipy.minimize(E, silent=True, method=\"bfgs\", method_options={\"finite_diff_rel_step\":1.e-4, \"eps\":1.e-4}, variables=active_vars, initial_values=angles)\n",
-    "        print(\"finished with energy {:2.8f}\".format(result.energy))\n",
-    "        results.append((result, U))\n",
-    "    energies_gs.append(results[0][0].energy)\n",
-    "    energies_es.append(results[1][0].energy)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "import matplotlib.pyplot as plt\n",
-    "R =  [0.7 + 0.1*i for i in range(len(energies_gs))]\n",
-    "plt.figure()\n",
-    "plt.plot(R, energies_gs, marker=\"o\", label=\"VQE GS\")\n",
-    "plt.plot(R, energies_es, marker=\"o\", label=\"VQE ES\")\n",
-    "plt.legend()\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "tequila-chemistry",
-   "language": "python",
-   "name": "tequila-chemistry"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.7.7"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}
diff --git a/tutorials/ChemistryMadnessInterface.ipynb b/tutorials/ChemistryMadnessInterface.ipynb
deleted file mode 100644
index 81ee8171..00000000
--- a/tutorials/ChemistryMadnessInterface.ipynb
+++ /dev/null
@@ -1,326 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Basis-Set-Free VQEs with the Tequila - Madness interface"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "This tutorial covers the basic usage of the `tequila`-`madness` interface.  \n",
-    "It is currently brief and stenographic since the interface is still under development.  \n",
-    "The current version is however powerful enough to reproduce all results from our [article](https://arxiv.org/abs/2008.02819)!"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "One of `tequila`s primary aims is to simplify usage of many specialized algorithms and programs. The underlying technology should however be acknowledged, so if you are using the interface please acknowledge/cite the following articles:\n",
-    "- Our initial [article](https://arxiv.org/abs/2008.02819) describing the interface and introducint MRA-PNOs to quantum computing.\n",
-    "- The original [article](https://doi.org/10.1063/1.5141880) that describes the underlying MRA-PNO-MP2 implementation in `madness`.\n",
-    "- The `madness` overview [article](https://doi.org/10.1137/15M1026171).\n",
-    "- The `tequila` overview [article](https://arxiv.org/abs/2011.03057).\n",
-    "- In case you are using our automatically differentiable framework for unitary coupled-cluster, please also cite the [article](https://arxiv.org/abs/2011.05938) describing this simulation.\n",
-    "- Please also cite the corresponding articles of the quantum simulators and optimizers that you are using within `tequila`.\n",
-    "\n",
-    "If you just want to play with the hydrogen molecule in a minimal basis-set-free representation without installing `madness`, there is a short tutorial on this as well!"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Installation of madness and depenencies\n",
-    "\n",
-    "Currently the necessary version of `madness` is available over a fork under: https://github.com/kottmanj/madness . It is not yet merged into the main repository of madness, but will be at some point in the near future.  \n",
-    "You find installation instructions in the [README](https://github.com/kottmanj/madness) respectively github page of this fork. `madness` can be a beast to install, feel free to contact [me](mailto:jakob.kottmann@utoronto.ca) if you are running into trouble.\n",
-    "\n",
-    "After you compiled madness from the fork (make sure the `tequila` branch was checked out - it is the default, but it doesn't hurt to check). There are two ways to let `tequila` know about is.\n",
-    "- export the path to the madness root (that is the directory where you compiled the code) as the environment variable 'MAD_ROOT_DIR'. E.g `export MAD_ROOT_DIR=/path/to/where/you/compiled/madness/`. You need to do this in your terminal (Linux or Mac) before you run your python script. `tequila` is then able to find the corresponding executable directly\n",
-    "- you provide the path to the `pno_integrals` executable yourself. E.g `tq.Molecule(..., executable=\"/path/to/madness/src/apps/pno/pno_integrals\")`.\n",
-    "\n",
-    "You can exploit the second option and provide the path to a customized script that will itself call `pno_integrals` in some way (this is for example an option if you are using windows and want to run madness over docker or some kind of virtual machine. See the above github fork of madness for more information on how to use it with docker).\n",
-    "\n",
-    "In the following I will use the second option and provide the path to madness on my laptop. I'll leave that in, since that might clarify the usage a bit."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "executable = \"/home/jsk/devel/madness/build-opt/src/apps/pno/pno_integrals\""
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Use Tequila to compute a QubitHamiltonian with madness\n",
-    "\n",
-    "Here is how you can create a simple QubitHamiltonian over the interface.  \n",
-    "Checkout the main chemistry tutorial and see what you can further do with this (the usage is equivalent).  \n",
-    "- Choose different qubit encodints over the `transformation` keyword (the default is Jordan-Wigner - see the main chemistry tutorial)\n",
-    "- the `name` keyword is optional, the default is just `molecule`, it will mostly affect the output files names\n",
-    "- the `n_pno` keyword specifies how many pnos shall be computed and used. Note that the total number of orbitals is always `n_pno` plus all occupied Hartree-Fock orbitals."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Starting madness calculation with executable:  /home/jsk/devel/madness/build-opt/src/apps/pno/pno_integrals\n",
-      "output redirected to helium_1pno_pno_integrals.out logfile\n",
-      "finished after 45.39036822319031s\n"
-     ]
-    }
-   ],
-   "source": [
-    "import tequila as tq\n",
-    "geomstring = \"He 0.0 0.0 0.0\"\n",
-    "mol = tq.Molecule(geometry=geomstring, n_pno=1, executable=executable, name=\"helium_1pno\")\n",
-    "H = mol.make_hamiltonian()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "<class 'tequila.quantumchemistry.madness_interface.QuantumChemistryMadness'>\n",
-      "Qubit Encoding\n",
-      "transformation=<function jordan_wigner at 0x7f4b09b9ed08>\n",
-      "\n",
-      "Parameters\n",
-      "basis_set       : custom          \n",
-      "geometry        : He 0.0 0.0 0.0  \n",
-      "description     :                 \n",
-      "multiplicity    : 1               \n",
-      "charge          : 0               \n",
-      "closed_shell    : True            \n",
-      "name            : helium_1pno     \n",
-      "\n",
-      "MRA Orbitals    :\n",
-      "orbital 0, occupied reference orbital (0,), energy -0.917962 \n",
-      "orbital 1, pno from pair (0, 0), MP2 occ 0.00437667 \n",
-      "\n",
-      "executable      : /home/jsk/devel/madness/build-opt/src/apps/pno/pno_integrals\n",
-      "htensor         : helium_1pno_htensor.npy\n",
-      "gtensor         : helium_1pno_gtensor.npy\n",
-      "\n"
-     ]
-    }
-   ],
-   "source": [
-    "# some information about the molecule\n",
-    "print(mol)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Read in already existing madness outputs\n",
-    "\n",
-    "If you give `n_pno=None` tequila will try to read in the orbital data form madness.  \n",
-    "The following files are required: `name_htensor.npy` (or `molecule_htensor.bin`) `name_gtensor.npy` (or `molecule_gtensor.bin`) and `pnoinfo.txt`. Note that the `.bin` files should not be copied between different computers. `name` can be specific as keyword (default is just `molecule`)."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "<class 'tequila.quantumchemistry.madness_interface.QuantumChemistryMadness'>\n",
-      "Qubit Encoding\n",
-      "transformation=<function jordan_wigner at 0x7f4b09b9ed08>\n",
-      "\n",
-      "Parameters\n",
-      "basis_set       : custom          \n",
-      "geometry        : He 0.0 0.0 0.0  \n",
-      "description     :                 \n",
-      "multiplicity    : 1               \n",
-      "charge          : 0               \n",
-      "closed_shell    : True            \n",
-      "name            : helium_1pno     \n",
-      "\n",
-      "MRA Orbitals    :\n",
-      "orbital 0, occupied reference orbital (0,), energy -0.917962 \n",
-      "orbital 1, pno from pair (0, 0), MP2 occ 0.00437667 \n",
-      "\n",
-      "executable      : /home/jsk/devel/madness/build-opt/src/apps/pno/pno_integrals\n",
-      "htensor         : helium_1pno_htensor.npy\n",
-      "gtensor         : helium_1pno_gtensor.npy\n",
-      "\n"
-     ]
-    }
-   ],
-   "source": [
-    "mol2 = tq.Molecule(geometry=geomstring, n_pno=None, executable=executable, name=\"helium_1pno\")\n",
-    "print(mol2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Use the PNO-UpCCD ansatz\n",
-    "Check our [article](https://arxiv.org/abs/2008.02819) for more details on the ansatz. \n",
-    "Note that the PNOs do not need to be directly determined over a basis-set-free approach for this ansatz, but this is currently the only implementation.  \n",
-    "Note, that the following four lines use all the technology mentioned in the first cell of this notebook. Please acknowledge it if you use it :-).\n",
-    "The used simulator is not specified hiere, so tequila will pick depending on what you have installed (you can see it in the printout)."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Starting madness calculation with executable:  /home/jsk/devel/madness/build-opt/src/apps/pno/pno_integrals\n",
-      "output redirected to molecule_pno_integrals.out logfile\n",
-      "finished after 9.489994764328003s\n",
-      "refs= [orbital 0, occupied reference orbital (0,), energy -0.917962 ]\n",
-      "Optimizer: <class 'tequila.optimizers.optimizer_scipy.OptimizerSciPy'> \n",
-      "backend         : qulacs\n",
-      "device          : None\n",
-      "samples         : None\n",
-      "save_history    : True\n",
-      "noise           : None\n",
-      "\n",
-      "Method          : BFGS\n",
-      "Objective       : 1 expectationvalues\n",
-      "gradient        : 6 expectationvalues\n",
-      "\n",
-      "active variables : 3\n",
-      "\n",
-      "E=-2.86152285  angles= {(0, ((0, 2), (1, 3)), None): 0.0, (0, (0, 2), None): 0.0, (0, (1, 3), None): 0.0}  samples= None\n",
-      "E=-2.85540235  angles= {(0, ((0, 2), (1, 3)), None): 0.2644369900226593, (0, (0, 2), None): 6.854534149169922e-06, (0, (1, 3), None): 6.854534149169922e-06}  samples= None\n",
-      "E=-2.87761682  angles= {(0, ((0, 2), (1, 3)), None): 0.12154174082914501, (0, (0, 2), None): 3.150512388571456e-06, (0, (1, 3), None): 3.150512388571456e-06}  samples= None\n",
-      "E=-2.87761855  angles= {(0, ((0, 2), (1, 3)), None): 0.12159293536327934, (0, (0, 2), None): -0.0016298963380842438, (0, (1, 3), None): -0.0016298963380842438}  samples= None\n",
-      "Optimization terminated successfully.\n",
-      "         Current function value: -2.877619\n",
-      "         Iterations: 2\n",
-      "         Function evaluations: 4\n",
-      "         Gradient evaluations: 4\n"
-     ]
-    }
-   ],
-   "source": [
-    "import tequila as tq\n",
-    "geomstring = \"He 0.0 0.0 0.0\"\n",
-    "mol = tq.Molecule(geometry=geomstring, n_pno=1, executable=executable)\n",
-    "U = mol.make_pno_upccgsd_ansatz(generalized=False)\n",
-    "H = mol.make_hamiltonian()\n",
-    "E = tq.ExpectationValue(H=H, U=U)\n",
-    "result = tq.minimize(method=\"bfgs\", objective=E, initial_values=0.0)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Customize the madness calculation\n",
-    "\n",
-    "The underlying madness calculation can be customized by giving the corresponding sub-programs as keywords combined with dictionaries that hold the parameters.\n",
-    "To get an idea what is there: Check the output file `name_pno_integrals.out` generated by a madness calculation with default parameters and also the input file `input` writen by tequila. Here is some example how to customize it (here we change the polynomial order of the MRA which needs to be set in the scf calculation and increase the maximum rank of the PNOs which will result in 4 computed PNOs where the most important one is used for the QubitHamiltonian - this is just to illustrate the API, neither will have a notable effect on the Helium Hamiltonian with 1 PNO.). Note that the `scf` section is called `dft` in madness for historic reasons."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Starting madness calculation with executable:  /home/jsk/devel/madness/build-opt/src/apps/pno/pno_integrals\n",
-      "output redirected to helium_1pno_alt_pno_integrals.out logfile\n",
-      "finished after 37.68571734428406s\n"
-     ]
-    }
-   ],
-   "source": [
-    "mol3 = tq.Molecule(geometry=geomstring, n_pno=1, executable=executable, name=\"helium_1pno_alt\", dft={\"k\":9}, pno={\"maxrank\":4})\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Compute orbitals with frozen-core approximation\n",
-    "You can freeze occupied HF orbitals in the MP2-PNO calculation by setting the freeze keyword (e.g. `pno={\"freeze\":1}` or you just set `frozen_core=True` when intializing the Molecule."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Starting madness calculation with executable:  /home/jsk/devel/madness/build-opt/src/apps/pno/pno_integrals\n",
-      "output redirected to molecule_pno_integrals.out logfile\n",
-      "finished after 16.654462337493896s\n"
-     ]
-    }
-   ],
-   "source": [
-    "mol = tq.Molecule(geometry=\"Be 0.0 0.0 0.0\", n_pno=1, executable=executable, frozen_core=True)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "tequila-3.6",
-   "language": "python",
-   "name": "tequila-3.6"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.6.9"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}
diff --git a/tutorials/FAQ.ipynb b/tutorials/FAQ.ipynb
deleted file mode 100644
index 38d61e86..00000000
--- a/tutorials/FAQ.ipynb
+++ /dev/null
@@ -1,819 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Frequently Asked Questions:\n",
-    "\n",
-    "### It is recommended to take a look at the `BasicUsage` notebook before looking at this"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "running build_ext\n",
-      "skipping '/Users/sumneralperin-lea/.pyxbld/temp.macosx-10.9-x86_64-3.6/pyrex/BayesianNetwork/kernel_prob_reshaping.cpp' Cython extension (up-to-date)\n",
-      "skipping 'BayesianNetwork.kernel_prob_reshaping' extension (up-to-date)\n",
-      "running build_ext\n",
-      "skipping '/Users/sumneralperin-lea/.pyxbld/temp.macosx-10.9-x86_64-3.6/pyrex/BayesianNetwork/kernel_evaluations.cpp' Cython extension (up-to-date)\n",
-      "skipping 'BayesianNetwork.kernel_evaluations' extension (up-to-date)\n"
-     ]
-    }
-   ],
-   "source": [
-    "import tequila as tq\n",
-    "import numpy"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Which optimization methods can I use?\n",
-    "\n",
-    "`tq.show_available_optimizers` shows you all installed modules no your systems and the methods which `tq.minimize` understands. Method names are not case sensitive when passed to `tq.minimize`.  \n",
-    "\n",
-    "In the end you see which modules are supported and which of them are actually installed on your system.  \n",
-    "The table with methods and modules will only show you the methods for modules that are currently installed within your environment.  \n",
-    "\n",
-    "Of course you can also use tequila objectives for your own optimizers.  \n",
-    "You don't need to use the modules here."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "available methods for optimizer modules found on your system:\n",
-      "method               | optimizer module\n",
-      "--------------------------\n",
-      "NELDER-MEAD          | scipy\n",
-      "COBYLA               | scipy\n",
-      "POWELL               | scipy\n",
-      "SLSQP                | scipy\n",
-      "L-BFGS-B             | scipy\n",
-      "BFGS                 | scipy\n",
-      "CG                   | scipy\n",
-      "TNC                  | scipy\n",
-      "TRUST-KRYLOV         | scipy\n",
-      "NEWTON-CG            | scipy\n",
-      "DOGLEG               | scipy\n",
-      "TRUST-NCG            | scipy\n",
-      "TRUST-EXACT          | scipy\n",
-      "TRUST-CONSTR         | scipy\n",
-      "adam                 | gd\n",
-      "adagrad              | gd\n",
-      "adamax               | gd\n",
-      "nadam                | gd\n",
-      "sgd                  | gd\n",
-      "momentum             | gd\n",
-      "nesterov             | gd\n",
-      "rmsprop              | gd\n",
-      "rmsprop-nesterov     | gd\n",
-      "lbfgs                | gpyopt\n",
-      "direct               | gpyopt\n",
-      "cma                  | gpyopt\n",
-      "phoenics             | phoenics\n",
-      "Supported optimizer modules:  ['scipy', 'phoenics', 'gpyopt', 'gd']\n",
-      "Installed optimizer modules:  ['scipy', 'gd', 'gpyopt', 'phoenics']\n"
-     ]
-    }
-   ],
-   "source": [
-    "tq.show_available_optimizers()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Which simulators/Quantum-Backends can I use?\n",
-    "\n",
-    "`tq.show_available_simulators` shows all simulators/quantum backends which are supported by tequila as well as which are installed within your current environment.  \n",
-    "\n",
-    "The default choice if you don't specify a backend when for example simulating a tequila objective with `tq.simulate` is the first entry of the supported backends which is installed on your system."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "backend         | wfn        | sampling   | noise      | devices    | installed \n",
-      "--------------------------------------------------------------------\n",
-      "qulacs          | True       | True       | True       | False      | True      \n",
-      "qiskit          | True       | True       | True       | True       | True      \n",
-      "cirq            | True       | True       | True       | True       | True      \n",
-      "pyquil          | True       | True       | True       | True       | True      \n",
-      "symbolic        | True       | False      | False      | False      | True      \n"
-     ]
-    }
-   ],
-   "source": [
-    "tq.show_available_simulators()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Can I avoid re-translation/compilation on my objectives/circuits?\n",
-    "\n",
-    "Yes you can. By calling `tq.compile` instead of `tq.simulate`.\n",
-    "This will give you back a callable objective.  \n",
-    "Check also the `basic usage` tutorial notebook"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "+0.7071|00> +0.6205|01> -0.3390i|11> \n",
-      "+0.7071|00> +0.3821|01> -0.5950i|11> \n",
-      "compiled circuit: <tequila.simulators.simulator_qulacs.BackendCircuitQulacs object at 0x130f8b400>\n",
-      "+0.7071|00> +0.6205|01> -0.3390i|11> \n",
-      "+0.7071|00> +0.3821|01> -0.5950i|11> \n",
-      "compiled objective: Objective with 1 unique expectation values\n",
-      "variables = [a]\n",
-      "types     = not compiled\n",
-      "1.1770184\n",
-      "1.2067055\n",
-      "compiled objective: Objective with 1 unique expectation values\n",
-      "variables = [a]\n",
-      "types     = [<class 'tequila.simulators.simulator_qulacs.BackendExpectationValueQulacs'>]\n",
-      "1.1770184\n",
-      "1.2067055\n"
-     ]
-    }
-   ],
-   "source": [
-    "U = tq.gates.H(target=1) + tq.gates.Rx(angle=\"a\", target=0, control=1)\n",
-    "\n",
-    "# simulate the wavefunction with different variables\n",
-    "wfn0 = tq.simulate(U, variables={\"a\": 1.0})\n",
-    "wfn1 = tq.simulate(U, variables={\"a\": 2.0})\n",
-    "\n",
-    "print(wfn0)\n",
-    "print(wfn1)\n",
-    "\n",
-    "# the same, but avoiding re-compilation\n",
-    "# Note that your compiled object is translated to a quantum backend\n",
-    "# if the backend was not set, tequila it will pick the default which depends\n",
-    "# on which backends you have installed. You will seee it in the printout of the\n",
-    "# compiled circuits\n",
-    "compiled_U = tq.compile(U)\n",
-    "wfn0 = compiled_U(variables={\"a\":1.0})\n",
-    "wfn1 = compiled_U(variables={\"a\":2.0})\n",
-    "\n",
-    "print(\"compiled circuit:\", compiled_U)\n",
-    "print(wfn0)\n",
-    "print(wfn1)\n",
-    "\n",
-    "\n",
-    "# With Objectives it works in the same way\n",
-    "H = tq.paulis.Y(0)\n",
-    "E = tq.ExpectationValue(H=H, U=U)\n",
-    "objective = E**2 + 1.0\n",
-    "\n",
-    "# simulate the objective with different variables\n",
-    "result0 = tq.simulate(objective, variables={\"a\": 1.0})\n",
-    "result1 = tq.simulate(objective, variables={\"a\": 2.0})\n",
-    "\n",
-    "print(\"compiled objective:\", objective)\n",
-    "print(result0)\n",
-    "print(result1)\n",
-    "\n",
-    "# compile and then simulate\n",
-    "compiled_objective = tq.compile(objective)\n",
-    "result0 = compiled_objective(variables={\"a\":1.0})\n",
-    "result1 = compiled_objective(variables={\"a\":2.0})\n",
-    "\n",
-    "print(\"compiled objective:\", compiled_objective)\n",
-    "print(result0)\n",
-    "print(result1)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# how can I run on a real quantum computer?\n",
-    "Tequila can both emulate -- and when possible, operate via -- real quantum devices.\n",
-    "For example:\n",
-    "IBM's Qiskit can be used to run on some of IBM's public accessible quantum computers.\n",
-    "All you need for this is an ibm account (Follow the instructions under \"Configure your IBM Quantum Experience credentials\" here: https://github.com/Qiskit/qiskit-ibmq-provider).  \n",
-    "Tequila also supports Rigetti's PyQuil and Google's Cirq, but currently there are no publicly available devices.\n",
-    "\n",
-    "Here is a small  example with Qiskit (you need to have qiskit installed, and an activaged IBMQ account for this).\n",
-    "Alternatively you can also externally initialize your chosen device, and pass this down instead of a string.\n",
-    "\n",
-    "You always need to set samples if you intend to run on a real (or emulated) backend.\n",
-    "\n",
-    "If you have special access rights you can initialize the `qiskit` quantum backend yourself and pass it down as `device` instead of the device name.  \n",
-    "`device = provider.get_backend(name)` \n",
-    "or as a dictionary with `qiskit` provider and devicename  \n",
-    "`device = {\"provider\":provider_instance, \"name\":device_name}`\n",
-    "\n",
-    "Here is a small toy example that minimizes the square of a one qubit expectation value (minimum is 0.0)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Optimizer: <class 'tequila.optimizers.optimizer_scipy.OptimizerSciPy'> \n",
-      "backend         : qiskit\n",
-      "device          : ibmq_ourense\n",
-      "samples         : 1000\n",
-      "save_history    : True\n",
-      "noise           : None\n",
-      "\n",
-      "Method          : COBYLA\n",
-      "Objective       : 1 expectationvalues\n",
-      "\n",
-      "active variables : 1\n",
-      "\n",
-      "E=+0.68889999  angles= {a: 1.0}  samples= 1000\n",
-      "E=+0.83539593  angles= {a: 2.0}  samples= 1000\n",
-      "E=+0.00270400  angles= {a: 0.0}  samples= 1000\n",
-      "E=+0.64963597  angles= {a: -1.0}  samples= 1000\n",
-      "E=+0.22657602  angles= {a: -0.5}  samples= 1000\n",
-      "E=+0.03240000  angles= {a: 0.25}  samples= 1000\n",
-      "E=+0.01537600  angles= {a: -0.125}  samples= 1000\n",
-      "E=+0.00313600  angles= {a: 0.0625}  samples= 1000\n",
-      "E=+0.00270400  angles= {a: -0.03125}  samples= 1000\n",
-      "E=+0.00025600  angles= {a: -0.00390625}  samples= 1000\n",
-      "E=+0.00250000  angles= {a: -0.01171875}  samples= 1000\n",
-      "E=+0.00115600  angles= {a: 0.0}  samples= 1000\n",
-      "E=+0.00001600  angles= {a: -0.005859375}  samples= 1000\n",
-      "E=+0.00010000  angles= {a: -0.0078125}  samples= 1000\n",
-      "E=+0.00057600  angles= {a: -0.006859375}  samples= 1000\n"
-     ]
-    }
-   ],
-   "source": [
-    "import tequila as tq\n",
-    "U = tq.gates.Ry(angle=\"a\", target=0)\n",
-    "H = tq.paulis.X(0)\n",
-    "E = tq.ExpectationValue(H=H, U=U)\n",
-    "\n",
-    "# simulate the square of the expectation value with a specific set of variables\n",
-    "result = tq.simulate(E**2, variables={\"a\":1.0}, samples=1000, backend=\"qiskit\", device='ibmq_ourense'\n",
-    "\n",
-    "# optimize using ond of IMB's quantum computers as quantum backend\n",
-    "# (check your ibm account for more information and keywords)\n",
-    "# note that the names of the computer might have changed  \n",
-    "result = tq.minimize(objective=E**2, method=\"cobyla\", initial_values={\"a\":1.0}, samples=1000, backend=\"qiskit\", device='ibmq_ourense')"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# how can I emulate a real quantum computer?\n",
-    "Emulation is performed similarly to running on real devices. All you need to do is pass down the right string to the 'device' keyword. For qiskit, these are the same as for regular backends, but have'fake_' at the beginning; I.E to emulate 'armonk;, set `device=\"fake_armonk\"`. For PyQuil, this is done by adding '-qvm' to the end of the chosen string, i.e, 'Aspen-8' becomes `device=Aspen-8-qvm'`. For Cirq, only emulation is currently possible; the only string options for cirq are 'foxtail','bristlecone','sycamore', and 'sycamore23'.\n",
-    "\n",
-    "When emulating, a few things about the real device will be mimicked, principally its native gate set and its connectivities. Emulation will NOT include noisy emulation by default; If you want to emulate noise, pass down the keyword `noise='device'`. Using this option without specifying a device will result in an error.\n",
-    "\n",
-    "Below, we will emulate pyquil's Aspen 8, with emulated noise. You need pyquil installed for this to work.\n",
-    "\n",
-    "additionally: when real backends cannot be accessed, emulation will be attempted, with a warning."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "sampling from pyquil yielded:  0.72931594\n",
-      "sampling from pyquil while emulating Aspen-8 yielded:  0.662596\n",
-      "Optimizer: <class 'tequila.optimizers.optimizer_scipy.OptimizerSciPy'> \n",
-      "backend         : pyquil\n",
-      "backend_options : {}\n",
-      "samples         : 1000\n",
-      "save_history    : True\n",
-      "noise           : None\n",
-      "\n",
-      "Method          : BFGS\n",
-      "Objective       : 1 expectationvalues\n",
-      "gradient        : 3 expectationvalues\n",
-      "\n",
-      "active variables : 1\n",
-      "\n",
-      "E=+0.69889605  angles= {a: 1.0}  samples= 1000\n",
-      "E=+0.00291600  angles= {a: 0.06450396776199341}  samples= 1000\n",
-      "E=+0.00270400  angles= {a: -0.07299610341382534}  samples= 1000\n",
-      "E=+0.00270400  angles= {a: -0.0670304288095181}  samples= 1000\n",
-      "E=+0.00883600  angles= {a: -0.07190446966909138}  samples= 1000\n",
-      "E=+0.00270400  angles= {a: -0.07299381043520212}  samples= 1000\n",
-      "E=+0.00336400  angles= {a: -0.07299541886967227}  samples= 1000\n",
-      "E=+0.01210000  angles= {a: -0.07299610340533144}  samples= 1000\n",
-      "E=+0.00270400  angles= {a: -0.07299610341382534}  samples= 1000\n",
-      "E=+0.00672400  angles= {a: -0.07299610341382534}  samples= 1000\n",
-      "E=+0.00577600  angles= {a: -0.07299610341382534}  samples= 1000\n",
-      "E=+0.01081600  angles= {a: -0.0670304288095181}  samples= 1000\n",
-      "E=+0.00960400  angles= {a: -0.07001326611167172}  samples= 1000\n",
-      "E=+0.01742400  angles= {a: -0.07150468476274853}  samples= 1000\n",
-      "E=+0.00774400  angles= {a: -0.07225039408828693}  samples= 1000\n",
-      "E=+0.01638400  angles= {a: -0.07262324875105614}  samples= 1000\n",
-      "E=+0.00774400  angles= {a: -0.07280967608244074}  samples= 1000\n",
-      "E=+0.00250000  angles= {a: -0.07290288974813304}  samples= 1000\n",
-      "E=+0.00025600  angles= {a: -0.0728562829152869}  samples= 1000\n",
-      "E=+0.00160000  angles= {a: -0.07283297949886382}  samples= 1000\n",
-      "E=+0.01081600  angles= {a: -0.07284463120707535}  samples= 1000\n",
-      "E=+0.00577600  angles= {a: -0.07285045706118112}  samples= 1000\n",
-      "E=+0.00547600  angles= {a: -0.07285336998823401}  samples= 1000\n",
-      "Warning: Desired error not necessarily achieved due to precision loss.\n",
-      "         Current function value: 0.002704\n",
-      "         Iterations: 2\n",
-      "         Function evaluations: 23\n",
-      "         Gradient evaluations: 13\n",
-      "optimizing while emulating Aspen-8 with noise yielded a best energy of:  0.002704000100493431\n"
-     ]
-    }
-   ],
-   "source": [
-    "U = tq.gates.Ry(angle=\"a\", target=0)\n",
-    "H = tq.paulis.X(0)\n",
-    "E = tq.ExpectationValue(H=H, U=U)\n",
-    "\n",
-    "# simulate the square of the expectation value with a specific set of variables\n",
-    "result = tq.simulate(E**2, variables={\"a\":1.0}, samples=1000, backend=\"pyquil\")\n",
-    "print('sampling from pyquil yielded: ', result)\n",
-    "result = tq.simulate(E**2, variables={\"a\":1.0}, samples=1000, backend=\"pyquil\",device='Aspen-8-qvm')\n",
-    "print('sampling from pyquil while emulating Aspen-8 yielded: ', result)\n",
-    "result = tq.optimizer_scipy.minimize(E**2, initial_values={\"a\":1.0}, samples=1000,\n",
-    "                                    backend='pyquil', device=\"Aspen-8-qvm\", \n",
-    "                                    noise='device')\n",
-    "print('optimizing while emulating Aspen-8 with noise yielded a best energy of: ', result.energy)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Can I compile Objectives into different backends?\n",
-    "Yes you can. Tequila will print a warning if this happens. Warnings can be ignored by filtering them out (see the python warnings documentation)  \n",
-    "\n",
-    "If a compiled circuit is used as input to compile then tequila will re-compile the circuit to the new backend (it it differs from the previous one)  \n",
-    "\n",
-    "If a compiled objective is used as input to compile then tequila will only compile non-compiled expectationvalues into the different backend. Already compiled expectation values will remain untouched  \n",
-    "\n",
-    "Note that you need at least two different backends for the following cell to execute.  \n",
-    "Just change the key to whatever you have installed."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "backend1 = \"qulacs\"\n",
-    "backend2 = \"cirq\"\n",
-    "\n",
-    "U = tq.gates.X(target=[0,1])\n",
-    "print(\"Example Circuit: \", U)\n",
-    "compiled_1 = tq.compile(U, backend=backend1)\n",
-    "compiled_2 = tq.compile(compiled_1, backend=backend2)\n",
-    "print(\"Circuit compiled to {} -> \".format(backend1), compiled_1)\n",
-    "print(\"Circuit compiled to {} -> \".format(backend1), compiled_1)\n",
-    "\n",
-    "H = tq.paulis.X(0)*tq.paulis.Y(1) + tq.paulis.X([0,1])\n",
-    "print(\"\\nmake objective with H = \", H)\n",
-    "objective = tq.ExpectationValue(H=H, U=U)\n",
-    "compiled_1 = tq.compile(objective, backend=backend1)\n",
-    "\n",
-    "print(\"\\nExpectationValues of objective 1:\")\n",
-    "print(compiled_1)\n",
-    "    \n",
-    "objective2 = compiled_1 + objective # Its recommended to avoid those hybrids, but in principle it works\n",
-    "\n",
-    "print(\"\\nExpectationValues of partly compiled objective:\")\n",
-    "print(objective2)\n",
-    "    \n",
-    "compiled_2 = tq.compile(objective2, backend=backend2)\n",
-    "print(\"\\nExpectationValues of hybdrid compiled objective:\")\n",
-    "print(compiled_2)\n",
-    "\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# How do I transform Measurements into Hamiltonians?\n",
-    "\n",
-    "We can not answer this question in general, but we can try to give a small example here.  \n",
-    "\n",
-    "Assume you have a quantum circuit with $4$ Qubits and you are measuring Qubit $0$ and $2$. \n",
-    "You define your cost function in the following way:\n",
-    "\n",
-    "$$\n",
-    "L(AB) = A + B, \\qquad A,B \\in \\left\\{ 0,1 \\right\\}  \n",
-    "$$\n",
-    "\n",
-    "meaning you accumulate the number of ones measured in your circuit.  \n",
-    "\n",
-    "The corresponding expectationvalue would be  \n",
-    "\n",
-    "$$\n",
-    "L = \\langle \\Psi \\rvert H \\lvert \\Psi \\rangle \\qquad H = 1 - \\frac{1}{2}\\left(Z(0) + Z(1)\\right) \n",
-    "$$\n",
-    "\n",
-    "The Hamiltonian could also be written as\n",
-    "\n",
-    "$$\n",
-    "H = 2\\lvert 11 \\rangle \\langle 11 \\rvert + \\lvert 10 \\rangle \\langle 10 \\rvert + \\lvert 01 \\rangle \\langle 01 \\rvert\n",
-    "$$\n",
-    "\n",
-    "Tequila provides the convenience function `tq.gates.Projector` to initialize Hamiltonians like that\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "2*tq.paulis.Projector(\"|11>\") + tq.paulis.Projector(\"|01>\") + tq.paulis.Projector(\"|10>\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The projector can also be initialized with more structured `QubitWaveFunction`s which can itself be initialized from array or string.  \n",
-    "Here are some examples"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "wfn = tq.QubitWaveFunction.from_string(\"1.0*|00> + 1.0*|11>\")\n",
-    "wfnx = tq.QubitWaveFunction.from_array(arr=[1.0, 0.0, 0.0, 1.0])\n",
-    "print(wfn == wfnx)\n",
-    "wfn = wfn.normalize()\n",
-    "print(wfn)\n",
-    "\n",
-    "P = tq.paulis.Projector(wfn=wfn)\n",
-    "print(\"P = \", P)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Apart from `Projector` there is also `KetBra` which intialized more general operators like\n",
-    "$$\n",
-    "\\lvert \\Psi \\rangle \\langle \\Phi \\rvert\n",
-    "$$\n",
-    "\n",
-    "Keep in mind that those are not hermitian.  \n",
-    "But they can be split up into their hermitian and anti hermitian part where both can then be used as hamiltonians for expectationvalues.\n",
-    "\n",
-    "If the `hermitian = True` key is set, the function returns the hermitian version of the operator (which is the same as the hermitian part of the old operator)\n",
-    "\n",
-    "$$\n",
-    "\\frac{1}{2}\\left(\\lvert \\Psi \\rangle \\langle \\Phi \\rvert + \\lvert \\Phi \\rangle \\langle \\Psi \\rvert \\right)\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "wfn1 = tq.QubitWaveFunction.from_string(\"1.0*|00> + 1.0*|11>\").normalize()\n",
-    "\n",
-    "op = tq.paulis.KetBra(bra=wfn1, ket=\"|00>\")\n",
-    "\n",
-    "H1, H2 = op.split()\n",
-    "\n",
-    "print(\"operator=\", op)\n",
-    "print(\"hermitian part      = \", H1)\n",
-    "print(\"anti-hermitian part =\", H2)\n",
-    "\n",
-    "H = tq.paulis.KetBra(bra=wfn1, ket=\"|00>\", hermitian=True)\n",
-    "print(\"hermitianized operator = \", H)\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Can I do basic operations on wavefunctions and operators without quantum backends?\n",
-    "\n",
-    "In principle yes. But keep in mind that tequila was not made for this.  \n",
-    "However, some of those operations might come in handy for debugging or small examples.  \n",
-    "\n",
-    "You can not execute circuits without a simulator since they are just abstract data types (no matrices or anything). Tequila has however its own small debug simulator `backend = symbolic` but there is no reason to use it if you have any other quantum backend installed.\n",
-    "\n",
-    "Hamiltonians can be converted to matrices.\n",
-    "\n",
-    "We give a few examples here"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "wfn = tq.QubitWaveFunction.from_string(\"1.0*|0> + 1.0*|1>\").normalize()\n",
-    "H = 1.0/numpy.sqrt(2.0)*(tq.paulis.Z(0) + tq.paulis.X(0))\n",
-    "wfn2 = wfn.apply_qubitoperator(H).simplify()\n",
-    "\n",
-    "print(\"|wfn>  = \", wfn)\n",
-    "print(\"H      = \", H)\n",
-    "print(\"H|wfn> = \", wfn2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "wfn1 = tq.QubitWaveFunction.from_string(\"1.0*|0> + 1.0*|1>\").normalize()\n",
-    "wfn2 = tq.QubitWaveFunction.from_string(\"1.0*|0> - 1.0*|1>\").normalize()\n",
-    "print(\"<wfn1|wfn2> = \", wfn1.inner(wfn2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "H = 1.0/numpy.sqrt(2.0)*(tq.paulis.Z(0) + tq.paulis.X(0))\n",
-    "print(H.to_matrix())"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Can I import an Hamiltonian from OpenFermion?\n",
-    "\n",
-    "Yes! OpernFermion is currently tequilas backend for Hamiltonians, which makes importing from it straight forward.\n",
-    "You just need to wrap the OpenFermion QubitOperator into tequilas QubitHamiltonian.\n",
-    "\n",
-    "We show a few examples"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from openfermion import QubitOperator\n",
-    "\n",
-    "# get OpenFermion QubitOperator from tequila QubitHamiltonian\n",
-    "H = tq.paulis.X(0)\n",
-    "of_operator = H.to_openfermion()\n",
-    "\n",
-    "print(\"{} = {}\".format(type(H), H))\n",
-    "print(\"{} = {}\".format(type(of_operator), of_operator))\n",
-    "\n",
-    "# init tequila QubitHamiltonian with OpenFermion QubitOperator\n",
-    "H = tq.QubitHamiltonian.from_openfermion(of_operator)\n",
-    "print(\"{} = {}\".format(type(H), H))\n",
-    "\n",
-    "# initialization from file os often read in the string form\n",
-    "of_string = str(of_operator)\n",
-    "tq_string = str(H)\n",
-    "\n",
-    "print(of_string)\n",
-    "print(tq_string)\n",
-    "\n",
-    "H = tq.QubitHamiltonian.from_string(string=of_string, openfermion_format=True)\n",
-    "print(H)\n",
-    "H = tq.QubitHamiltonian.from_string(string=tq_string, openfermion_format=False)\n",
-    "print(H)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Can I compile into a regular function instead of one which takes dictionaries?\n",
-    "\n",
-    "Not recommended but yes. The order of the function arguments is the order you get from `extract_variables`"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "U = tq.gates.Ry(angle=\"a\", target=0)\n",
-    "U += tq.gates.X(power = \"b\", target=1)\n",
-    "H = tq.QubitHamiltonian.from_string(\"X(0)Z(1)\")\n",
-    "E = tq.ExpectationValue(H=H, U=U)\n",
-    "\n",
-    "f = tq.compile_to_function(E)\n",
-    "\n",
-    "print(\"order is : \", E.extract_variables())\n",
-    "print(f(0.5, 1.0))\n",
-    "print(tq.simulate(E, variables={\"a\":0.5, \"b\":1.0}))\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "If you also want to fix the samples and other entries to your compiled objective you can build wrappers"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def mywrapper(compiled_obj, samples):\n",
-    "    return lambda *x: compiled_obj(*x, samples=samples)\n",
-    "\n",
-    "wrapped = mywrapper(f, samples=100)\n",
-    "\n",
-    "# don't expect same results, since samples are taken individually\n",
-    "print(wrapped(1.0, 0.5)) # always takes 100 samples\n",
-    "print(f(1.0, 0.5, samples=100)) # samples need to be given\n",
-    "print(f(1.0, 0.5, samples=1000)) # but sampling rate can be changed\n",
-    "print(f(1.0, 0.5)) # you can go back to full simulation which you cannot with the wrapped function"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# How do numerical gradients work?\n",
-    "\n",
-    "Yes this is possible by passing for example `gradient={'method':'2-point', 'stepsize': 1.e-4}` to the `tq.minimize` function.  \n",
-    "\n",
-    "The default is a central 2-point derivative stencil where `h` is the stepsize:\n",
-    "$$\\displaystyle\n",
-    "\\frac{\\partial f}{\\partial a} = \\frac{f(a+\\frac{h}{2}) - f(a-\\frac{h}{2})} {h}\n",
-    "$$\n",
-    "\n",
-    "\n",
-    "Other methods are:\n",
-    "`2-point-forward`: Forward derivative stencil:\n",
-    "\n",
-    "$$\\displaystyle\n",
-    "\\frac{\\partial f}{\\partial a} = \\frac{f(a+h) - f(a)} {h}\n",
-    "$$\n",
-    "\n",
-    "\n",
-    "`2-point-backward`: Backward derivative stencil:\n",
-    "\n",
-    "$$\\displaystyle\n",
-    "\\frac{\\partial f}{\\partial a} = \\frac{f(a) - f(a-h)} {h}\n",
-    "$$\n",
-    "\n",
-    "\n",
-    "You can also use your own numerical derivative stencil by passing a callable function as `method`.  \n",
-    "The function should have the signature which is given in the example below.\n",
-    "\n",
-    "Here is an example:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import tequila as tq\n",
-    "# form a simple example objective\n",
-    "H = tq.paulis.X(0)\n",
-    "U = tq.gates.Ry(angle=\"a\", target=0)\n",
-    "E = tq.ExpectationValue(U=U, H=H)\n",
-    "\n",
-    "# make it more interesting by using analytical gradients for the objective\n",
-    "# and numerical gradients to optimize it\n",
-    "\n",
-    "objective = tq.grad(E, 'a')**2 # integer multiples of pi/2 are minima\n",
-    "\n",
-    "# start from the same point in all examples\n",
-    "initial_values = {'a': 2.3}"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# optimize with analytical derivatives\n",
-    "result = tq.minimize(objective=objective, method=\"bfgs\", initial_values=initial_values)\n",
-    "#result.history.plot(\"energies\")\n",
-    "#result.history.plot(\"gradients\")\n",
-    "\n",
-    "# optimize with 2-point stencil\n",
-    "result = tq.minimize(objective=E, method=\"bfgs\", gradient={'method': '2-point', 'stepsize':1.e-4}, initial_values=initial_values)\n",
-    "#result.history.plot(\"energies\")\n",
-    "#result.history.plot(\"gradients\")\n",
-    "\n",
-    "# optimize with custom stencil\n",
-    "# here this is the same as the default\n",
-    "import copy\n",
-    "def mymethod(obj, angles, key, step, *args, **kwargs):\n",
-    "    left = copy.deepcopy(angles)\n",
-    "    left[key] += step / 2\n",
-    "    right = copy.deepcopy(angles)\n",
-    "    right[key] -= step / 2\n",
-    "    return 1.0 / step * (obj(left, *args, **kwargs) - obj(right, *args, **kwargs))\n",
-    "\n",
-    "result = tq.minimize(objective=E, method=\"bfgs\", gradient={'method': mymethod, 'stepsize':1.e-4}, initial_values=initial_values)\n",
-    "#result.history.plot(\"energies\")\n",
-    "#result.history.plot(\"gradients\")\n",
-    "\n",
-    "# optimize with a scipy method and use scipys 2-point\n",
-    "# the scipy protocol will have more function evaluations and less gradient evaluations for some methods\n",
-    "# the stepsize in scipy has to be passed with the `method_options` dictionary\n",
-    "# with the keyword `eps`\n",
-    "result = tq.minimize(objective=E, method=\"bfgs\", gradient='2-point', method_options={'eps':1.e-4}, initial_values=initial_values)\n",
-    "#result.history.plot(\"energies\")\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Can I use the numerical gradient protocols from SciPy?\n",
-    "\n",
-    "Yes you can for all scipy methods by passing `gradient='2-point'` to `tq.minimize`.  \n",
-    "See the scipy documentation for the stepsize and more options which can be passed with `method_options` dictionary where the key for the stepsize is usually `eps`. Note that not all scipy methods support numerical gradients,but cyou can always fall back to tequilas numerical gradients.\n",
-    "See the previous cell for an example."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.6.9"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}
diff --git a/tutorials/MeasurementGroups.ipynb b/tutorials/MeasurementGroups.ipynb
deleted file mode 100644
index 1e8334bd..00000000
--- a/tutorials/MeasurementGroups.ipynb
+++ /dev/null
@@ -1,346 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Optimize Measurements by grouping into commuting cliques\n",
-    "\n",
-    "Quantum mechanics allows simultaneuous measurements of all mutually commuting operators. VQE however permits only the measurements of a much more restricted set of operators, the qubit-wise commuting operators (Verteletskyi et al., “Measurement Optimization in the Variational Quantum Eigensolver Using a Minimum Clique Cover\" [J. Chem. Phys. 152, 124114 (2020)](https://doi.org/10.1063/1.5141458)). But through certain unitary transformations any group of mutually commuting operators can be tranformed into their qubit-wise commuting form (Yen et al., \"Measuring all compatible operators in one series of single-qubit measurements using unitary transformations\" [Chem. Theory Comput. 2020, 16, 4, 2400–2409](https://doi.org/10.1021/acs.jctc.0c00008)). \n",
-    "\n",
-    "## How to Use:\n",
-    "This is how the technique can be used in tequila. Note that you will only benefit from optimizing measurements when you are running on a real quantum backend or when you simulate with finite samples. The difference in timings is just an indicator that different processes happen, in this specific example we have an Hamiltonian with 4 terms where optimization of the measurements reduces those to 2 commuting groups (see the next section for details)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "backend         | wfn        | sampling   | noise      | installed \n",
-      "--------------------------------------------------------------------\n",
-      "qulacs          | True       | True       | True       | True      \n",
-      "qiskit          | True       | True       | True       | True      \n",
-      "cirq            | True       | True       | True       | True      \n",
-      "pyquil          | True       | True       | True       | True      \n",
-      "symbolic        | True       | False      | False      | True      \n",
-      "+1.0000Z(0)Z(1)+1.0000Y(0)Y(1)+1.0000X(0)X(1)+1.0000X(0)+1.0000Z(0)Z(1)Z(2)Z(3)Z(4)Z(5)Z(6)\n",
-      "0.0006999999999999229\n",
-      "time : 1.0035152435302734s\n",
-      "0.00050002337\n",
-      "time : 0.47684693336486816s\n"
-     ]
-    }
-   ],
-   "source": [
-    "import tequila as tq\n",
-    "import time\n",
-    "tq.show_available_simulators()\n",
-    "backend = None\n",
-    "\n",
-    "H = tq.paulis.Z([0,1]) + tq.paulis.Y([0,1]) + tq.paulis.X([0,1]) + tq.paulis.X(0) + tq.paulis.Z([0,1,2,3,4,5,6])\n",
-    "\n",
-    "U = tq.gates.ExpPauli(angle = \"a\", paulistring=tq.PauliString.from_string('X(0)Y(1)'))\n",
-    "U += tq.gates.X(target=[0,1,2,3,4,5,6])\n",
-    "\n",
-    "E1 = tq.ExpectationValue(H=H, U=U) \n",
-    "E2 = tq.ExpectationValue(H=H, U=U, optimize_measurements = True)\n",
-    "\n",
-    "print(H)\n",
-    "start = time.time()\n",
-    "print(tq.simulate(E1, variables={\"a\":1.0}, samples=100000, backend=backend))\n",
-    "print(\"time : {}s\".format(time.time()-start))\n",
-    "\n",
-    "start = time.time()\n",
-    "print(tq.simulate(E2, variables={\"a\":1.0}, samples=100000, backend=backend))\n",
-    "print(\"time : {}s\".format(time.time()-start))\n",
-    "\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Behind the Scenes"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import tequila as tq\n",
-    "import numpy as np\n",
-    "from tequila.hamiltonian import QubitHamiltonian, paulis\n",
-    "from tequila.grouping.binary_rep import BinaryHamiltonian"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The following examples shows how to partition a given Hamiltonian into commuting parts and how to find the unitary transformation needed to transform the commuting terms into qubit-wise commuting form that is easy to measure. \n",
-    "\n",
-    "The Hamiltonian is simply \n",
-    "$$ H = \\sigma_z(0)\\sigma_z(1) + \\sigma_y(0)\\sigma_y(1) + \\sigma_x(0)\\sigma_x(1) + \\sigma_x(0)$$\n",
-    "where $\\sigma_z(0)\\sigma_z(1)$, $\\sigma_y(0)\\sigma_y(1)$ does not commute with $\\sigma_x(0)$, so two separate measurements are needed."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "H = paulis.Z(0) * paulis.Z(1) + paulis.Y(0) * paulis.Y(1) + \\\n",
-    "    paulis.X(0) * paulis.X(1) + paulis.X(0) \n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Here we use the binary representation of the Hamiltonian for partitioning. The method commuting_groups gets back a list of BinaryHamiltonian whose terms are mutually commuting. \n",
-    "\n",
-    "Call to_qubit_hamiltonian to visualize."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "binary_H = BinaryHamiltonian.init_from_qubit_hamiltonian(H)\n",
-    "commuting_parts = binary_H.commuting_groups()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "2\n",
-      "+1.0000X(0)X(1)+1.0000X(0)\n",
-      "+1.0000Z(0)Z(1)+1.0000Y(0)Y(1)\n"
-     ]
-    }
-   ],
-   "source": [
-    "print(len(commuting_parts)) # Number of measurements needed\n",
-    "print(commuting_parts[0].to_qubit_hamiltonian())\n",
-    "print(commuting_parts[1].to_qubit_hamiltonian())"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The second group of terms $H_2$ are not currently qubit-wise commuting and cannot be directly measured on current hardware. They require further unitary transformation $U$ to become qubit-wise commuting. The following code identifies two bases (list of BinaryPauliString) that encodes the unitary transformation as\n",
-    "$$ U = \\prod_i \\frac{1}{\\sqrt{2}} (\\text{old_basis}[i] + \\text{new_basis}[i])$$\n",
-    "such that $UH_2U$ is qubit-wise commuting."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "qubit_wise_parts, old_basis, new_basis = commuting_parts[1].single_qubit_form()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Old Basis\n",
-      "+1.0000Z(0)Z(1)\n",
-      "+1.0000X(0)X(1)\n",
-      "\n",
-      "New Basis\n",
-      "+1.0000X(0)\n",
-      "+1.0000Z(1)\n"
-     ]
-    }
-   ],
-   "source": [
-    "def display_basis(basis):\n",
-    "    for term in basis:\n",
-    "        print(QubitHamiltonian.from_paulistrings(term.to_pauli_strings()))\n",
-    "print('Old Basis')\n",
-    "display_basis(old_basis)\n",
-    "print('\\nNew Basis')\n",
-    "display_basis(new_basis)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The transfromed term $UH_2U$ is qubit-wise commuting. "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "+1.0000X(0)-1.0000X(0)Z(1)\n"
-     ]
-    }
-   ],
-   "source": [
-    "print(qubit_wise_parts.to_qubit_hamiltonian())"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Get the circuit for the unitary transformation to implement the measurement scheme.\n",
-    "The next function illustrates what is happening if expectation values are formed with the `optimize_measurements` keyword meaning it does the same as `tq.ExpectationValue(H=H,U=U, optimize_measurements=True)`"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def optimize_measurements(H, U):\n",
-    "    binary_H = BinaryHamiltonian.init_from_qubit_hamiltonian(H)\n",
-    "    commuting_parts = binary_H.commuting_groups()\n",
-    "    result = tq.Objective()\n",
-    "    for cH in commuting_parts:\n",
-    "        qwc, Um = cH.get_qubit_wise()\n",
-    "        Etmp = tq.ExpectationValue(H=qwc, U=U+Um)\n",
-    "        result += Etmp\n",
-    "    \n",
-    "    return result\n",
-    "        "
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The new measurement scheme produces the same expectation values"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Without measurement grouping\n",
-      "1.2040990959786004\n",
-      "\n",
-      "With measurement grouping\n",
-      "1.204099\n"
-     ]
-    }
-   ],
-   "source": [
-    "U = tq.gates.ExpPauli(angle = \"a\", paulistring=tq.PauliString.from_string('X(0)Y(1)'))\n",
-    "E1 = tq.ExpectationValue(H=commuting_parts[1].to_qubit_hamiltonian(), U=U)\n",
-    "E2 = optimize_measurements(H=commuting_parts[1].to_qubit_hamiltonian(), U=U)\n",
-    "\n",
-    "variables = {\"a\" : np.random.rand(1) * 2 * np.pi}\n",
-    "print('Without measurement grouping')\n",
-    "print(tq.simulate(E1, variables))\n",
-    "print('\\nWith measurement grouping')\n",
-    "print(tq.simulate(E2, variables))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The get_qubit_wise methods always transforms the hamiltonian into the qubit-wise commuting form with only z on each qubit. This is done via extra single-qubit unitaries. "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "The qubit-wise commuting hamiltonian, but does not have all z\n",
-      "+1.0000X(0)X(1)+1.0000X(0)\n",
-      "\n",
-      "The same qubit-wise commuting hamiltonian with all z\n",
-      "+1.0000Z(0)Z(1)+1.0000Z(0)\n",
-      "\n",
-      "The corresponding single qubit unitaries\n",
-      "circuit: \n",
-      "Rz(target=(0,), parameter=-1.5707963267948966)\n",
-      "Rx(target=(0,), parameter=-1.5707963267948966)\n",
-      "Rz(target=(0,), parameter=-1.5707963267948966)\n",
-      "Rz(target=(1,), parameter=-1.5707963267948966)\n",
-      "Rx(target=(1,), parameter=-1.5707963267948966)\n",
-      "Rz(target=(1,), parameter=-1.5707963267948966)\n",
-      "\n"
-     ]
-    }
-   ],
-   "source": [
-    "print('The qubit-wise commuting hamiltonian, but does not have all z')\n",
-    "print(commuting_parts[0].to_qubit_hamiltonian())\n",
-    "\n",
-    "qwc, U = commuting_parts[0].get_qubit_wise()\n",
-    "print('\\nThe same qubit-wise commuting hamiltonian with all z')\n",
-    "print(qwc)\n",
-    "print('\\nThe corresponding single qubit unitaries')\n",
-    "print(U)"
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "tequila-3.6",
-   "language": "python",
-   "name": "tequila-3.6"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.6.9"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}
diff --git a/tutorials/Noise_tutorial.ipynb b/tutorials/Noise_tutorial.ipynb
deleted file mode 100644
index 05b4358c..00000000
--- a/tutorials/Noise_tutorial.ipynb
+++ /dev/null
@@ -1,469 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Hello, and welcome to this tutorial on simulating circuit noise in Tequila! In this tutorial, we will briefly detail what quantum noise is, its mathematical modeling, and how specific popular simulation packages handle noisy simulation, before diving in to building Tequila `NoiseModel`s and applying them to sampling different circuits."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# <center> What is noise?</center>\n",
-    "\n",
-    "In case you need a quick refresher: Real quantum systems undergo the effects of noise, a catch-all term for 'anything the user didn't ask the computer to do'. Such noise can be caused by a number of physical processes, including but not limited to: \n",
-    "\n",
-    " - **Thermal fluctuations**\n",
-    " - **Interaction with the environment**\n",
-    " - **Uncontrolled interaction between qubits (cross-talk)**\n",
-    " - **Imperfections in gate implementation**\n",
-    " \n",
-    "\n",
-    "\n",
-    "# <center> How is noise represented mathematically?</center>\n",
-    "\n",
-    "\n",
-    "Commonly, the effects of noise on quantum systems are treated as the evolution of the system's density matrix under Krauss maps. Krauss maps are mappings of the form $ A: \\rho \\rightarrow \\rho' = \\sum_{i} A_i \\rho A_{i}^{\\dagger}$, where $\\sum_{i} A_i  A_{i}^{\\dagger} = I$. These Krauss maps are parametrized, in general by probabilities.\n",
-    "\n",
-    "For example, bit flip noise -- which takes qubits from the 0 to the 1 state and vice versa-- is a krauss map with two operators, and a single probabilistic parameter, p. The operators are:\n",
-    "$$A_0 = \\sqrt{1-p} I,  A_1 = \\sqrt{p} X$$\n",
-    "**Note that the square root is present, so that bit flip map is:**\n",
-    "$$ A_{bf}(p): \\rho \\rightarrow (1-p) * I\\rho I + p * X\\rho X$$\n",
-    "other noise operations may be defined similarly.\n",
-    "\n",
-    "**Note that such krauss operators may only affect subsystems of the system;** one can have a single qubit undergo bit-flip noise in an 8 qubit state. In such cases, the krauss maps are merely the 1-qubit maps tensored with the identity on all other qubits. Multi-qubit krauss operators will involve tensor products of single qubit krauss operators.\n",
-    "\n",
-    "For example, the 2-qubit bit flip krauss map has 4 operators:\n",
-    "$$A_{00}=(1-p)I\\otimes I, A_{01}=\\sqrt{p-p^2}I\\otimes X,A_{10}=\\sqrt{p-p^2}X \\otimes I,A_{11}=pX\\otimes X$$\n",
-    "Which are just all the tensor products of $A_{0}$ and $A_{1}$."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# <center> 3. How is noise simulated? </center>\n",
-    "\n",
-    "Different simulation packages handle noise in radically different ways.\n",
-    "\n",
-    "*Cirq* and *Qulacs*, for example, use noise channels, parametrized operations which are inserted into circuits the same way regular, unitary gates are. \n",
-    "\n",
-    "*Pyquil* asks its users to define noisy gate operations, and then instantiate those. \n",
-    "\n",
-    "*Qiskit*, meanwhile, simply takes a dictionary-like object as an argument to its simulator, and applies the noise on the user-chosen gates.\n",
-    "\n",
-    "In tequila, we try to hew toward making users write as few lines of code as possible. We therefore implement a simple framework for the application of noise, meant to be compatible with all our supported platforms. To do this, we make a few assumptions:\n",
-    "\n",
-    "1. If noise is present, any gate may be affected by noise.\n",
-    "2. The noise that affects 1..k..n-qubit gates is independent of the noise on 1...k-1,k+1...n qubit gates.\n",
-    "3. Noise probabilities are independent of position in the circuit.\n",
-    "4. The number of qubits involved in a gate, not the operation performed, dictates what noises may occur.\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# <center>  Noise in Tequila: Overview </center>\n",
-    "\n",
-    "noise in Tequila is centered upon the `NoiseModel` class, itself used to store and combine `QuantumNoise` objects. \n",
-    "Each `QuantumNoise` internally designates what operation it will perform, with what probability (or probabilities), and on how many qubits. Only at the time of translation to a backend -- or in the case of *Qiskit*, at time of simulation -- do`NoiseModel`s and simulateables -- circuits, ExpectationValues, Objectives -- interact.\n",
-    "\n",
-    "Tequila at present supports six common quantum noise operations, all of which can at present be employed by all the noise-supporting simulation backgrounds. These six operations are:\n",
-    "\n",
-    "1. Bit flips, a probabilistic application of pauli X;\n",
-    "2. Phase flips, a probablistic application of pauli Z;\n",
-    "3. Amplitude damps, which take qubits in state |1> to |0>;\n",
-    "4. Phase damps, which are a different formalization of the phase flip;\n",
-    "5. Phase-Amplitude damps, which simultaneously perform said operations;\n",
-    "6. (Symmetric) depolarizing, which (equi)probabilistically performs pauli X, Y, and Z.\n",
-    "\n",
-    "in Tequila, custom members of the `QuantumNoise` class are not possible, and so they should be initialized by the constructor function for each supported channel, which creates a `NoiseModel` containing one operation. all six of which are shown in the import statement below.\n",
-    "\n",
-    "`NoiseModel`s combine with eachother through addition, creating a new `NoiseModel` with all the operations of the two summands. Note that in those simulators which employ noise channels, the order of the noises in the noise model will dictate the order of application in the circuit; users should be mindful of this.\n",
-    "\n",
-    "To use a `NoiseModel` to apply noise, one may provide a noise model to the *tq.compile*, *tq.simulate*, and optimization calls like *tq.minimize*, through the keyword `noise=my_noise_model`. Noise is only supported when sampling; if in the above functions the keyword *samples* is `None` (defaullt), noise cannot function.\n",
-    "\n",
-    "additionally, Tequila supports the use of device-noise-emulation for those backends which allow the emulation of specific real devices. If in compilation, simulation, or optimization, emulated backends have been selected (such as 'fake_vigo', for IBMQ), the known noise of this device may be employed. In these cases, the keyword assignment *noise='device'* should be used, if these known noise models are desired.\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "### first, we import tequila!\n",
-    "import tequila as tq\n",
-    "from tequila.circuit.noise import BitFlip,PhaseFlip,AmplitudeDamp,PhaseDamp,PhaseAmplitudeDamp,DepolarizingError"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We will first examine bit flip noise on a simple circuit with a simple Hamiltonian."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 33,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "simulating:  +0.5000-0.5000Z(1)\n",
-      "acting on: \n",
-      "0: ───X───@───\n",
-      "          │\n",
-      "1: ───────X───\n"
-     ]
-    }
-   ],
-   "source": [
-    "H=tq.paulis.Qm(1) ### this hamiltonian is 0 for a qubit that is 0, and 1 for a qubit that is 1.\n",
-    "U=tq.gates.X(0)+tq.gates.CNOT(0,1)\n",
-    "O1=tq.ExpectationValue(U=U,H=H)\n",
-    "\n",
-    "print('simulating: ',H)\n",
-    "print('acting on: ')\n",
-    "tq.draw(U)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Say that we wanted a noise model where 1-qubit gates and 2-qubit gates undergo bit flips, but with different probabilities."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "bf_1=BitFlip(p=0.1,level=1)\n",
-    "bf_2=BitFlip(p=0.3,level=2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    " `NoiseModel` objects, like those initialized above, can be combined into new `NoiseModel`s by simple addition."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "applying: NoiseModel with: \n",
-      "bit flip on 1 qubit gates, probs = [0.1],\n",
-      "bit flip on 2 qubit gates, probs = [0.3],\n",
-      "\n"
-     ]
-    }
-   ],
-   "source": [
-    "my_nm=bf_1+bf_2\n",
-    "print('applying:',my_nm)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "we will now sample our `Objective` O1, both with and without noise."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 35,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Without noise, E = 1.0\n",
-      "With noise, E = 0.6664\n"
-     ]
-    }
-   ],
-   "source": [
-    "E=tq.simulate(O1)\n",
-    "### noise models are fed to tequila functions with the noise keyword.\n",
-    "E_noisy=tq.simulate(O1,samples=5000,noise=my_nm)\n",
-    "print('Without noise, E =',E)\n",
-    "print('With noise, E =',E_noisy)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "**Because noise is stochastic, results may vary wildly if the number of samples is low.**"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 36,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "round 1 sampling with 5 samples, E =  0.8\n",
-      "round 2 sampling with 5 samples, E =  1.0\n",
-      "round 3 sampling with 5 samples, E =  0.6\n",
-      "round 4 sampling with 5 samples, E =  0.6\n",
-      "round 5 sampling with 5 samples, E =  0.4\n",
-      "round 6 sampling with 5 samples, E =  0.2\n",
-      "round 7 sampling with 5 samples, E =  0.8\n",
-      "round 8 sampling with 5 samples, E =  0.4\n",
-      "round 9 sampling with 5 samples, E =  0.8\n",
-      "round 10 sampling with 5 samples, E =  0.6\n"
-     ]
-    }
-   ],
-   "source": [
-    "for i in range(1,11):\n",
-    "    print('round',i,'sampling with 5 samples, E = ', tq.simulate(O1,samples=5,noise=my_nm))\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Note that the *BitFlip* functions returned applicable `NoiseModel`s in their own right:\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "With 1-qubit noise only, E = 0.9139999999999999\n",
-      "With 2-qubit noise only, E = 0.69\n"
-     ]
-    }
-   ],
-   "source": [
-    "E_1_only=tq.simulate(O1,samples=1000,noise=bf_1)\n",
-    "print('With 1-qubit noise only, E =',E_1_only)\n",
-    "E_2_only=tq.simulate(O1,samples=1000,noise=bf_2)\n",
-    "print('With 2-qubit noise only, E =',E_2_only)\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Below, we demonstrate the effects of the ordering of the noise operations applied. \n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 26,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "WARNING - WARNING: all-qubit error already exists for instruction \"x\", composing with additional error.\n",
-      "WARNING - WARNING: all-qubit error already exists for instruction \"y\", composing with additional error.\n",
-      "WARNING - WARNING: all-qubit error already exists for instruction \"z\", composing with additional error.\n",
-      "WARNING - WARNING: all-qubit error already exists for instruction \"u3\", composing with additional error.\n",
-      "WARNING - WARNING: all-qubit error already exists for instruction \"u1\", composing with additional error.\n",
-      "WARNING - WARNING: all-qubit error already exists for instruction \"u2\", composing with additional error.\n",
-      "WARNING - WARNING: all-qubit error already exists for instruction \"h\", composing with additional error.\n",
-      "WARNING - WARNING: all-qubit error already exists for instruction \"x\", composing with additional error.\n",
-      "WARNING - WARNING: all-qubit error already exists for instruction \"y\", composing with additional error.\n",
-      "WARNING - WARNING: all-qubit error already exists for instruction \"z\", composing with additional error.\n",
-      "WARNING - WARNING: all-qubit error already exists for instruction \"u3\", composing with additional error.\n",
-      "WARNING - WARNING: all-qubit error already exists for instruction \"u1\", composing with additional error.\n",
-      "WARNING - WARNING: all-qubit error already exists for instruction \"u2\", composing with additional error.\n",
-      "WARNING - WARNING: all-qubit error already exists for instruction \"h\", composing with additional error.\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "amplitude damping before bit flip leads to E =  -0.08186\n",
-      "amplitude damping after bit flip leads to E =  0.15744\n"
-     ]
-    }
-   ],
-   "source": [
-    "amp=AmplitudeDamp(0.3,1)\n",
-    "bit=BitFlip(0.4,1)\n",
-    "forward=amp+bit\n",
-    "backward=bit+amp\n",
-    "\n",
-    "H = tq.paulis.Z(0)\n",
-    "U = tq.gates.X(target=0)\n",
-    "O = tq.ExpectationValue(U=U, H=H)\n",
-    "\n",
-    "E_1 = tq.simulate(O,samples=100000,noise=forward)\n",
-    "E_2 = tq.simulate(O,samples=100000,noise=backward)\n",
-    "print('amplitude damping before bit flip leads to E = ',E_1)\n",
-    "print('amplitude damping after bit flip leads to E = ',E_2)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Tequila will *always* attempt to apply noise to the circuit *in the order each noise was added to the noise model*. Some backends have behavior which is harder to control than others, but in general, this order will be preserved."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Below, we will optimize a noisy circuit."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 37,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "\n",
-    "import numpy as np"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Consider the 1-qubit expectation value, $<0|U^{\\dagger}\\hat{Y}U|0>$, with $U=H Rz(\\theta) H $. In the absence of noise, this expectation value just yields $Sin(\\theta)$. This circuit therefore has a minimum at $\\theta = -\\pi$. We can minimize this circuit under phase flip noise -- which is probabilistic application of pauli Z -- and see what happens!"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 42,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "optimizing expectation value with phase flip probability 0.08991331275688234.\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "U=tq.gates.H(0) +tq.gates.Rz('a',0)+tq.gates.H(0)\n",
-    "H=tq.paulis.Y(0)\n",
-    "O=tq.ExpectationValue(U=U,H=H)\n",
-    "\n",
-    "### we pick a random, small probability to apply noise\n",
-    "p=np.random.uniform(0,.1)\n",
-    "NM=PhaseFlip(p,1)\n",
-    "\n",
-    "print('optimizing expectation value with phase flip probability {}.'.format(str(p)))\n",
-    "result=tq.minimize(objective=O,lr=0.5,maxiter=60,initial_values={'a':np.pi},method='adam',samples=5000,noise=NM,silent=True)\n",
-    "\n",
-    "result.history.plot()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The final energy is not -1.0, because the application of noise leads the expected output to be $(-1+2*p)^{3} Sin(\\theta)$. One sees that this is approximately the value reached by minimizing $\\theta$. Because the number of samples is not infinite, the 'expected' best energy may be exceeded:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 43,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "best energy:  -0.5688\n",
-      "expected best  -0.5517178049632779\n"
-     ]
-    }
-   ],
-   "source": [
-    "out=result.energy\n",
-    "best=((-1+2*p)**3)*np.sin(np.pi/2)\n",
-    "print('best energy: ',out)\n",
-    "print('expected best ',best)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## This concludes our brief tutorial on Noise. Stay tuned (and up to date) for more exciting noise features in the future!"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.7.7"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}
diff --git a/tutorials/OptimizeDistributions.ipynb b/tutorials/OptimizeDistributions.ipynb
deleted file mode 100644
index 34546252..00000000
--- a/tutorials/OptimizeDistributions.ipynb
+++ /dev/null
@@ -1,531 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Training Distributions with KM Divergence"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Short tutorial on how to form objectives like in this paper  \n",
-    "https://arxiv.org/pdf/1801.07686.pdf\n",
-    "\n",
-    "First some imports and the advice to use `tq.numpy` for functions in objectives (avoid issues in automatic differentiations and use the regular `numpy` for everything else (avoid issues with jax where you don't want them)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import tequila as tq\n",
-    "import numpy"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "First we define the $\\max(x,\\epsilon)$ function we will need further down the road and some global variables for this example"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# global variables, change here if you want\n",
-    "eps = 1.e-8\n",
-    "n_qubits = 5\n",
-    "n_layers = 1\n",
-    "\n",
-    "def my_max(x):\n",
-    "    if x<eps:\n",
-    "        return eps\n",
-    "    else:\n",
-    "        return x"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In this example we will train for the generation of GHZ state (as in the paper above).  \n",
-    "The ansatz template consists of `Rx` gates and Mølmer-Sørensen gates which are just rotations around XX.  \n",
-    "We give here the option of using multiple layers, but one layer actually suffices for this example"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# create ansatz\n",
-    "U = tq.QCircuit()\n",
-    "for layer in range(n_layers):\n",
-    "    for q in range(n_qubits):\n",
-    "        # name can be any non-numeric hashable type\n",
-    "        # scaling variables with pi in this example\n",
-    "        variable = tq.Variable(name=(layer, q))\n",
-    "        U += tq.gates.Rx(angle=variable*tq.numpy.pi, target=q)\n",
-    "    for q in range(n_qubits):\n",
-    "        for p in range(q+1, n_qubits):\n",
-    "            U += tq.gates.ExpPauli(angle=tq.numpy.pi / 2.0, paulistring=\"X({})X({})\".format(q, p))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Here are some demonstrations on how to extract informations from your template circuit U"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "circuit: \n",
-      "Rx(target=(0,), parameter=Objective with 0 unique expectation values\n",
-      "variables = [(0, 0)]\n",
-      "types     = [])\n",
-      "Rx(target=(1,), parameter=Objective with 0 unique expectation values\n",
-      "variables = [(0, 1)]\n",
-      "types     = [])\n",
-      "Rx(target=(2,), parameter=Objective with 0 unique expectation values\n",
-      "variables = [(0, 2)]\n",
-      "types     = [])\n",
-      "Rx(target=(3,), parameter=Objective with 0 unique expectation values\n",
-      "variables = [(0, 3)]\n",
-      "types     = [])\n",
-      "Rx(target=(4,), parameter=Objective with 0 unique expectation values\n",
-      "variables = [(0, 4)]\n",
-      "types     = [])\n",
-      "Exp-Pauli(target=(0, 1), control=(), parameter=1.5707963267948966, paulistring=X(0)X(1))\n",
-      "Exp-Pauli(target=(0, 2), control=(), parameter=1.5707963267948966, paulistring=X(0)X(2))\n",
-      "Exp-Pauli(target=(0, 3), control=(), parameter=1.5707963267948966, paulistring=X(0)X(3))\n",
-      "Exp-Pauli(target=(0, 4), control=(), parameter=1.5707963267948966, paulistring=X(0)X(4))\n",
-      "Exp-Pauli(target=(1, 2), control=(), parameter=1.5707963267948966, paulistring=X(1)X(2))\n",
-      "Exp-Pauli(target=(1, 3), control=(), parameter=1.5707963267948966, paulistring=X(1)X(3))\n",
-      "Exp-Pauli(target=(1, 4), control=(), parameter=1.5707963267948966, paulistring=X(1)X(4))\n",
-      "Exp-Pauli(target=(2, 3), control=(), parameter=1.5707963267948966, paulistring=X(2)X(3))\n",
-      "Exp-Pauli(target=(2, 4), control=(), parameter=1.5707963267948966, paulistring=X(2)X(4))\n",
-      "Exp-Pauli(target=(3, 4), control=(), parameter=1.5707963267948966, paulistring=X(3)X(4))\n",
-      "\n",
-      "Circuit depends on variables:  [(0, 0), (0, 1), (0, 2), (0, 3), (0, 4)]\n"
-     ]
-    }
-   ],
-   "source": [
-    "print(U)\n",
-    "print(\"Circuit depends on variables: \", U.extract_variables())"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The circuit is parametrized by variables, so if we want to simulate it we will have to choose for which values we want to simulate the wavefunction. Here is an example where we set all variables to $\\pi$.  \n",
-    "Variables are passed down to the simulator as a dictionary holding the variable names and values"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "wfn with variables =  {(0, 0): 1.0, (0, 1): 1.0, (0, 2): 1.0, (0, 3): 1.0, (0, 4): 1.0}\n",
-      "+0.2500|10000> +0.2500|01000> +0.2500|00100> -0.2500|11100> +0.2500|00010> -0.2500|11010> -0.2500|10110> -0.2500|01110> +0.2500|00001> -0.2500|11001> -0.2500|10101> -0.2500|01101> -0.2500|10011> -0.2500|01011> -0.2500|00111> +0.2500|11111> \n"
-     ]
-    }
-   ],
-   "source": [
-    "variables = {k : 1.0 for k in U.extract_variables()}\n",
-    "wfn = tq.simulate(U, variables=variables)\n",
-    "print(\"wfn with variables = \", variables)\n",
-    "print(wfn)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Instead of simulating directly the circuit can also be compiled and afterwards be used like a function"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "+0.2500|10000> +0.2500|01000> +0.2500|00100> -0.2500|11100> +0.2500|00010> -0.2500|11010> -0.2500|10110> -0.2500|01110> +0.2500|00001> -0.2500|11001> -0.2500|10101> -0.2500|01101> -0.2500|10011> -0.2500|01011> -0.2500|00111> +0.2500|11111> \n"
-     ]
-    }
-   ],
-   "source": [
-    "compiledU = tq.compile(U)\n",
-    "wfn = compiledU(variables=variables)\n",
-    "print(wfn)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Next we will define the target distribution which we want to optimize for. It is the distribution of a GHZ state, i.e. $P(00..0) = 0.5$ and $P(11..1)=0.5$ where in the following we will use binary notation for easier coding i.e $00...0=0$ and $11..1=2^{n-1}+2^{n-2}+..+1$"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "one = sum([2**i for i in range(n_qubits)])\n",
-    "target_distribution = {0:0.5, one:0.5}"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "For the tequila objective Born's rule will be used. In order to make this work we need to reformulate this as an expectation value. This can be achieved as \n",
-    "$$\\displaystyle \\lvert\\langle ijk..l \\rvert \\Psi \\rangle\\rvert^2 = \\langle \\Psi \\rvert H \\lvert \\Psi \\rangle$$\n",
-    "where $i,j,k..,l \\in \\left\\{0,1 \\right\\}$ and the Hamiltonian is\n",
-    "$$ \\displaystyle H = \\lvert ijk..l \\rangle \\langle ijk..l \\rvert = \\otimes_{m \\in (ijk..l)} \\frac{1}{n}\\left( 1 + (-1)^{m}\\sigma_Z \\right)$$\n",
-    "\n",
-    "Tequila has a convenience shortcut for the operator $$Q_{\\pm} = \\frac{1}{2}\\left( 1 \\pm \\sigma_Z \\right) $$\n",
-    "\n",
-    "Lets build the Kullback–Leibler divergence of the distribution P generated by our template U and the target distribution Q\n",
-    "\n",
-    "$$ \\displaystyle D(P,Q) = -\\frac{1}{2^n} \\sum_{x} P(x) \\ln\\left(\\frac{P(x)}{Q(x)}\\right) $$\n",
-    "\n",
-    "where we use the same safety barrier as in the paper to prevent taking logarithms of zero (this is where the mymax function fron above is needed). In the end we will square the objective to avoid negative values and assure that zero is the minimum."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "objective = tq.Objective()\n",
-    "\n",
-    "for k, Q in target_distribution.items():\n",
-    "    Q = my_max(Q) # here we apply the mymax function to avoid having zeros\n",
-    "    wfn = tq.QubitWaveFunction.from_int(k, n_qubits=n_qubits)\n",
-    "    H = tq.paulis.Projector(wfn=wfn)\n",
-    "    P = tq.ExpectationValue(H=H, U=U)  # this is the born rule expectation value from above\n",
-    "    P = P.apply(my_max) # here we apply the mymax function to avoid having zeros\n",
-    "    objective += Q*(Q / P).apply(tq.numpy.log) # here we take the logarithm and sum up\n",
-    "    \n",
-    "objective = 1.0/2.0**n_qubits *objective\n",
-    "objective = objective**2 # here we take the square"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Lets see what we created here.\n",
-    "Tequila created an objective with 4 expectationvalues (we had 2 values in the target_distribution, and P entered twice each) but only 2 unique expectationvalues (meaning the simulator will only evaluate those two)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Objective with 2 unique expectation values\n",
-      "variables = [(0, 0), (0, 1), (0, 2), (0, 3), (0, 4)]\n",
-      "types     = not compiled\n"
-     ]
-    }
-   ],
-   "source": [
-    "print(objective)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Objectives can be compiled and simulated in the same way as the circuits above. \n",
-    "Here is a small demonstration.  \n",
-    "Since our objective is parametrized we need to pass the variables down again. We will use the same as in the example above.\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "value1 =  0.09578033\n",
-      "value2 =  0.09578033\n",
-      "value3 =  0.004561313\n"
-     ]
-    }
-   ],
-   "source": [
-    "value1 = tq.simulate(objective, variables=variables)\n",
-    "compiled = tq.compile(objective)\n",
-    "value2 = compiled(variables=variables)\n",
-    "variables2 = {k:1.1 for k in objective.extract_variables()}\n",
-    "value3 = compiled(variables=variables2)\n",
-    "print(\"value1 = \", value1)\n",
-    "print(\"value2 = \", value2)\n",
-    "print(\"value3 = \", value3)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Lets optimize our objective with one of the inbuildt optimizers in tequila.  \n",
-    "If no initial_values are passed down, random initialization will be used.  \n",
-    "Check the OptimizerSciPy Tutorial for more information"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Optimizer: <class 'tequila.optimizers.optimizer_scipy.OptimizerSciPy'> \n",
-      "backend         : qulacs\n",
-      "device          : None\n",
-      "samples         : None\n",
-      "save_history    : True\n",
-      "noise           : None\n",
-      "\n",
-      "Method          : COBYLA\n",
-      "Objective       : 2 expectationvalues\n",
-      "\n",
-      "active variables : 5\n",
-      "\n",
-      "E=+0.02747765  angles= {(0, 0): 1.196973294671848, (0, 1): 3.487261445909955, (0, 2): 1.2546004948085328, (0, 3): 4.323339379115283, (0, 4): 4.297460215759149}  samples= None\n",
-      "E=+0.04326624  angles= {(0, 0): 2.196973294671848, (0, 1): 3.487261445909955, (0, 2): 1.2546004948085328, (0, 3): 4.323339379115283, (0, 4): 4.297460215759149}  samples= None\n",
-      "E=+0.01335919  angles= {(0, 0): 1.196973294671848, (0, 1): 4.4872614459099545, (0, 2): 1.2546004948085328, (0, 3): 4.323339379115283, (0, 4): 4.297460215759149}  samples= None\n",
-      "E=+0.00350544  angles= {(0, 0): 1.196973294671848, (0, 1): 4.4872614459099545, (0, 2): 2.2546004948085328, (0, 3): 4.323339379115283, (0, 4): 4.297460215759149}  samples= None\n",
-      "E=+0.01896261  angles= {(0, 0): 1.196973294671848, (0, 1): 4.4872614459099545, (0, 2): 2.2546004948085328, (0, 3): 5.323339379115283, (0, 4): 4.297460215759149}  samples= None\n",
-      "E=+0.01654562  angles= {(0, 0): 1.196973294671848, (0, 1): 4.4872614459099545, (0, 2): 2.2546004948085328, (0, 3): 4.323339379115283, (0, 4): 5.297460215759149}  samples= None\n",
-      "E=+0.01034847  angles= {(0, 0): 0.685979841439285, (0, 1): 4.944201361642773, (0, 2): 2.573514021010323, (0, 3): 3.823072690958975, (0, 4): 3.875418739491467}  samples= None\n",
-      "E=+0.01162174  angles= {(0, 0): 1.651670921989714, (0, 1): 4.597812748750098, (0, 2): 2.3317579166074354, (0, 3): 4.20230566715666, (0, 4): 4.195352184817832}  samples= None\n",
-      "E=+0.00508079  angles= {(0, 0): 1.1149671676348478, (0, 1): 4.022498117220029, (0, 2): 2.326934146654208, (0, 3): 4.209872519048047, (0, 4): 4.2017358306182535}  samples= None\n",
-      "E=+0.00512684  angles= {(0, 0): 1.1634208877002723, (0, 1): 4.485383631676708, (0, 2): 2.0144306100441, (0, 3): 4.2769149666437, (0, 4): 4.258295050381908}  samples= None\n",
-      "E=+0.00376778  angles= {(0, 0): 1.196973294671848, (0, 1): 4.4872614459099545, (0, 2): 2.2546004948085328, (0, 3): 4.403941715367235, (0, 4): 4.201918270045619}  samples= None\n",
-      "E=+0.00116350  angles= {(0, 0): 1.0780493007238203, (0, 1): 4.48060567397981, (0, 2): 2.2885035613418996, (0, 3): 4.474044450349771, (0, 4): 4.453829483671055}  samples= None\n",
-      "E=+0.00017348  angles= {(0, 0): 0.8699840955232891, (0, 1): 4.572790893282165, (0, 2): 2.3848653520405336, (0, 3): 4.436950182559852, (0, 4): 4.446816900871537}  samples= None\n",
-      "E=+0.00009692  angles= {(0, 0): 0.8055200929315092, (0, 1): 4.619292958946304, (0, 2): 2.5031750271015456, (0, 3): 4.5571752667279055, (0, 4): 4.613342274861681}  samples= None\n",
-      "E=+0.00019319  angles= {(0, 0): 0.8164684670910927, (0, 1): 4.721878819459653, (0, 2): 2.4354367831154837, (0, 3): 4.5723238621269875, (0, 4): 4.626122129521147}  samples= None\n",
-      "E=+0.00003109  angles= {(0, 0): 0.634151845128931, (0, 1): 4.522137670542379, (0, 2): 2.3599390854610816, (0, 3): 4.579886606200957, (0, 4): 4.664931359578641}  samples= None\n",
-      "E=+0.00003188  angles= {(0, 0): 0.6208976455692607, (0, 1): 4.521395878020473, (0, 2): 2.3637176165598133, (0, 3): 4.676879253218375, (0, 4): 4.587298086652804}  samples= None\n",
-      "E=+0.00000198  angles= {(0, 0): 0.45154420387279026, (0, 1): 4.581848929569584, (0, 2): 2.4700800093744517, (0, 3): 4.490977398508964, (0, 4): 4.590411935484344}  samples= None\n",
-      "E=+0.00000310  angles= {(0, 0): 0.4133452137548334, (0, 1): 4.483007553848742, (0, 2): 2.528528788960446, (0, 3): 4.504241522559719, (0, 4): 4.618767230891968}  samples= None\n",
-      "E=+0.00000060  angles= {(0, 0): 0.46449680275183974, (0, 1): 4.5520927290127196, (0, 2): 2.455111064181742, (0, 3): 4.460249548201935, (0, 4): 4.549365880789348}  samples= None\n",
-      "E=+0.00000960  angles= {(0, 0): 0.3641970260110508, (0, 1): 4.5492602200774455, (0, 2): 2.382763975953847, (0, 3): 4.44274253343372, (0, 4): 4.545324230417266}  samples= None\n",
-      "E=+0.00000269  angles= {(0, 0): 0.47214839390618013, (0, 1): 4.553045421003813, (0, 2): 2.4540802386928084, (0, 3): 4.411631116972945, (0, 4): 4.587862388090924}  samples= None\n",
-      "E=+0.00000167  angles= {(0, 0): 0.4645626506745066, (0, 1): 4.592461390035946, (0, 2): 2.548790652977351, (0, 3): 4.435075601401865, (0, 4): 4.481647538245871}  samples= None\n",
-      "E=+0.00000018  angles= {(0, 0): 0.5181716041993695, (0, 1): 4.537191377732638, (0, 2): 2.4528745216579866, (0, 3): 4.485998751404, (0, 4): 4.537738678563787}  samples= None\n",
-      "E=+0.00000056  angles= {(0, 0): 0.5245353706849274, (0, 1): 4.56167978051848, (0, 2): 2.4363047352941503, (0, 3): 4.4823263309619685, (0, 4): 4.530786080986661}  samples= None\n",
-      "E=+0.00000012  angles= {(0, 0): 0.49818500717094444, (0, 1): 4.502231423735846, (0, 2): 2.4333119900939852, (0, 3): 4.510369016782503, (0, 4): 4.501572602194428}  samples= None\n",
-      "E=+0.00000004  angles= {(0, 0): 0.49632111804785545, (0, 1): 4.512847616661284, (0, 2): 2.455467554700634, (0, 3): 4.513780035209803, (0, 4): 4.482654865137477}  samples= None\n",
-      "E=+0.00000006  angles= {(0, 0): 0.5182014754216003, (0, 1): 4.476513061786526, (0, 2): 2.474398777313323, (0, 3): 4.47538264986223, (0, 4): 4.466085324042166}  samples= None\n",
-      "E=+0.00000006  angles= {(0, 0): 0.5050017983420092, (0, 1): 4.488857851451768, (0, 2): 2.491875113314596, (0, 3): 4.5532843951611, (0, 4): 4.501871581179305}  samples= None\n",
-      "E=+0.00000003  angles= {(0, 0): 0.4688996976913859, (0, 1): 4.5089760859588655, (0, 2): 2.465526151442391, (0, 3): 4.505029251280438, (0, 4): 4.488301799514845}  samples= None\n",
-      "E=+0.00000007  angles= {(0, 0): 0.46406939287955223, (0, 1): 4.501057186321916, (0, 2): 2.4598934921923568, (0, 3): 4.511081200539074, (0, 4): 4.478828317108222}  samples= None\n",
-      "E=+0.00000003  angles= {(0, 0): 0.4714479395429383, (0, 1): 4.5327729413049616, (0, 2): 2.4846840624229762, (0, 3): 4.499501551546495, (0, 4): 4.485812297232392}  samples= None\n",
-      "E=+0.00000007  angles= {(0, 0): 0.4662188530848333, (0, 1): 4.5409500871447435, (0, 2): 2.4785597989911414, (0, 3): 4.5086685347603295, (0, 4): 4.491140653630323}  samples= None\n",
-      "E=+0.00000001  angles= {(0, 0): 0.4828606984382382, (0, 1): 4.523969633207974, (0, 2): 2.4902514009755663, (0, 3): 4.476637706688408, (0, 4): 4.5004773079958875}  samples= None\n",
-      "E=+0.00000003  angles= {(0, 0): 0.48575608081819605, (0, 1): 4.509969854600638, (0, 2): 2.5018347737522344, (0, 3): 4.463177170608753, (0, 4): 4.479103845398909}  samples= None\n",
-      "E=+0.00000004  angles= {(0, 0): 0.48021226459622424, (0, 1): 4.529979283053911, (0, 2): 2.4800305136581473, (0, 3): 4.46778228902862, (0, 4): 4.496219894176555}  samples= None\n",
-      "E=+0.00000001  angles= {(0, 0): 0.48756842274314555, (0, 1): 4.5139317949398485, (0, 2): 2.5093696998754766, (0, 3): 4.487943282137166, (0, 4): 4.519459305933884}  samples= None\n",
-      "E=+0.00000001  angles= {(0, 0): 0.491670615898347, (0, 1): 4.497862413901057, (0, 2): 2.525185554644173, (0, 3): 4.4831373652547875, (0, 4): 4.498764586675032}  samples= None\n",
-      "E=+0.00000000  angles= {(0, 0): 0.5020834658658918, (0, 1): 4.515810317274042, (0, 2): 2.5058926274574302, (0, 3): 4.491612543796369, (0, 4): 4.51736842376104}  samples= None\n",
-      "E=+0.00000002  angles= {(0, 0): 0.5110192782411185, (0, 1): 4.510471172324929, (0, 2): 2.5225701308558586, (0, 3): 4.510823840069483, (0, 4): 4.532234299594948}  samples= None\n",
-      "E=+0.00000001  angles= {(0, 0): 0.5077644587451166, (0, 1): 4.515301547348465, (0, 2): 2.503340331011883, (0, 3): 4.477616859868862, (0, 4): 4.520403998224697}  samples= None\n",
-      "E=+0.00000001  angles= {(0, 0): 0.5024086468089339, (0, 1): 4.5220976962257975, (0, 2): 2.5101895037205124, (0, 3): 4.490457876148, (0, 4): 4.5161027711535375}  samples= None\n",
-      "E=+0.00000000  angles= {(0, 0): 0.49951388087611553, (0, 1): 4.51620822689089, (0, 2): 2.495156476772887, (0, 3): 4.496516610281995, (0, 4): 4.507465660192193}  samples= None\n",
-      "E=+0.00000000  angles= {(0, 0): 0.5020781816194445, (0, 1): 4.50900384905753, (0, 2): 2.493797717568015, (0, 3): 4.509852770989498, (0, 4): 4.509907486913885}  samples= None\n",
-      "E=+0.00000000  angles= {(0, 0): 0.5011082246509242, (0, 1): 4.513007258249391, (0, 2): 2.489815845774154, (0, 3): 4.510840728965155, (0, 4): 4.515126269399038}  samples= None\n",
-      "E=+0.00000000  angles= {(0, 0): 0.5086052742522993, (0, 1): 4.498742708380191, (0, 2): 2.4874129667703864, (0, 3): 4.50337563133552, (0, 4): 4.506229403456834}  samples= None\n",
-      "E=+0.00000000  angles= {(0, 0): 0.5019235130316978, (0, 1): 4.494809833655521, (0, 2): 2.487727164715163, (0, 3): 4.502786192605719, (0, 4): 4.505539793946878}  samples= None\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "E=+0.00000000  angles= {(0, 0): 0.5013061597176728, (0, 1): 4.4960270840878, (0, 2): 2.48566776555843, (0, 3): 4.503869897155823, (0, 4): 4.502714829363983}  samples= None\n",
-      "E=+0.00000000  angles= {(0, 0): 0.5029198512608419, (0, 1): 4.492672827965057, (0, 2): 2.493668010701275, (0, 3): 4.503215745083131, (0, 4): 4.501067936759923}  samples= None\n",
-      "E=+0.00000000  angles= {(0, 0): 0.5010813367874862, (0, 1): 4.486658600996661, (0, 2): 2.4982437752170585, (0, 3): 4.502987542012001, (0, 4): 4.500364802911858}  samples= None\n",
-      "E=+0.00000000  angles= {(0, 0): 0.5050821929857228, (0, 1): 4.4913470678686, (0, 2): 2.493017039272258, (0, 3): 4.506066486124667, (0, 4): 4.501592283216655}  samples= None\n",
-      "E=+0.00000000  angles= {(0, 0): 0.5077514527347123, (0, 1): 4.494003301783319, (0, 2): 2.494760747894221, (0, 3): 4.497595579045114, (0, 4): 4.499295852676457}  samples= None\n",
-      "E=+0.00000000  angles= {(0, 0): 0.5018493108267006, (0, 1): 4.4982290636498865, (0, 2): 2.49878720103826, (0, 3): 4.504549996864767, (0, 4): 4.502083321869336}  samples= None\n",
-      "E=+0.00000000  angles= {(0, 0): 0.5005249133046364, (0, 1): 4.499506414630132, (0, 2): 2.498249627588381, (0, 3): 4.504836006709628, (0, 4): 4.498691810717365}  samples= None\n",
-      "E=+0.00000000  angles= {(0, 0): 0.5007158035310001, (0, 1): 4.500719695272272, (0, 2): 2.4968556934942825, (0, 3): 4.504826323187917, (0, 4): 4.4992943571813235}  samples= None\n",
-      "E=+0.00000000  angles= {(0, 0): 0.49757043741954216, (0, 1): 4.499971825001763, (0, 2): 2.4988572241771903, (0, 3): 4.502611804222587, (0, 4): 4.499690311681204}  samples= None\n",
-      "E=+0.00000000  angles= {(0, 0): 0.49865506396009296, (0, 1): 4.50035037475882, (0, 2): 2.4991499263432067, (0, 3): 4.5011270559366405, (0, 4): 4.499237729551664}  samples= None\n",
-      "E=+0.00000000  angles= {(0, 0): 0.4986323051581947, (0, 1): 4.502780651059029, (0, 2): 2.502089667980496, (0, 3): 4.501905823886104, (0, 4): 4.499559393648119}  samples= None\n",
-      "E=+0.00000000  angles= {(0, 0): 0.4971725668684522, (0, 1): 4.498464068163066, (0, 2): 2.5002086734531486, (0, 3): 4.49867644934646, (0, 4): 4.497696165164443}  samples= None\n",
-      "E=+0.00000000  angles= {(0, 0): 0.4983265071934182, (0, 1): 4.50150275326537, (0, 2): 2.497907404314546, (0, 3): 4.500265580376056, (0, 4): 4.499542311824862}  samples= None\n",
-      "E=+0.00000000  angles= {(0, 0): 0.4986634557901244, (0, 1): 4.5001031961219855, (0, 2): 2.4993345249803203, (0, 3): 4.500838211533058, (0, 4): 4.500118069752259}  samples= None\n",
-      "E=+0.00000000  angles= {(0, 0): 0.5004906881768819, (0, 1): 4.499595239620232, (0, 2): 2.4988754502180437, (0, 3): 4.500886758937621, (0, 4): 4.500187299622162}  samples= None\n",
-      "E=+0.00000000  angles= {(0, 0): 0.5008384869266571, (0, 1): 4.500204797427772, (0, 2): 2.4995815791111857, (0, 3): 4.500924159611765, (0, 4): 4.500273662141612}  samples= None\n",
-      "E=+0.00000000  angles= {(0, 0): 0.5008595001177585, (0, 1): 4.500091588799973, (0, 2): 2.499715711072797, (0, 3): 4.500500893315355, (0, 4): 4.500074673419346}  samples= None\n",
-      "E=+0.00000000  angles= {(0, 0): 0.5008591025053959, (0, 1): 4.499395788451458, (0, 2): 2.500391866649934, (0, 3): 4.5007317589041325, (0, 4): 4.50014799757864}  samples= None\n",
-      "E=+0.00000000  angles= {(0, 0): 0.5008376553544984, (0, 1): 4.500062152389838, (0, 2): 2.499707552584497, (0, 3): 4.500292215317942, (0, 4): 4.500527490420508}  samples= None\n",
-      "E=+0.00000000  angles= {(0, 0): 0.5012520661509299, (0, 1): 4.500475995882607, (0, 2): 2.499896472382163, (0, 3): 4.499756860506933, (0, 4): 4.499740213207289}  samples= None\n",
-      "E=+0.00000000  angles= {(0, 0): 0.5012182219360312, (0, 1): 4.499849353299078, (0, 2): 2.4994654623482226, (0, 3): 4.500504741677361, (0, 4): 4.500073496490982}  samples= None\n",
-      "E=+0.00000000  angles= {(0, 0): 0.500000019905168, (0, 1): 4.4998915963773305, (0, 2): 2.4994430906135046, (0, 3): 4.500186509021493, (0, 4): 4.499855271058377}  samples= None\n"
-     ]
-    }
-   ],
-   "source": [
-    "result = tq.optimizer_scipy.minimize(objective=objective, method=\"Cobyla\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Lets compute our wavefunction with the optimized angles"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "-0.7071i|00000> +0.0001|01000> +0.0006|00100> -0.0002|00010> -0.0002i|11110> +0.0002|00001> +0.0002i|11101> -0.0006i|11011> -0.0001i|10111> -0.7071|11111> \n"
-     ]
-    }
-   ],
-   "source": [
-    "final_wfn = tq.simulate(U, variables=result.angles)\n",
-    "print(final_wfn)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "And plot some information about the optimization "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "result.history.plot(\"energies\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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MjOK1gWEVqOeFa8ANgDJi2yHCJXWzUEIJfurhLRRljq9/o2oukRKmFghjcDipVTF0VKM3yNQj31CUMR6vJaZBG6M8TjKKVnEkdVjDsXiTxWXNHjdu7xh1zaBjJDh5hHrSQ7D4lto0LB/uKkOArXEeiLKCUsRSSVaMIYQ6FlAal0+oZ6Y/Tuy0+0MfI3Ok8bNwU6BQT3oIFv8SPLVee/HmRL9IAw2KXChinU3caWtCMQ2QBHDKuNoc5NREElIOUV4Q7c+E0J4oPM7miV6ocEmUx8mg7xc2KvjKZiPrVPimchiOmO5Euw2R86o6GRTaDVrXE5pYVYVTJfgzL7ZWTMTTSMaEwojhe3Xgtmi3A5fFjs1VSvfDWzjS/fTGbyT1BjvzyDy8Fl3ncxWl5wZmpezPY/C5fSj/7Fl/7nfC0CzKv3qrNkvlzFzKVn5Dxuo65ys6Gsvhj2rDW3fewZ4CL+vWlPozLzJjDlLo6BmQNdBnpIfilx7y9310xGS+cZ3d+gwF1wYKrbUZJmMsCyB1AOuKR0nWRwdmfTSGaQYTgyc/JJw7gfLPVgZMhuDr5yleutUQo5rUrU0HcFdqLHZFzzmXknTOCPYsfgdVUULvnocoO346B9/YbMxcDJEmFoCrCv4nG865CyY+EPjeC1Mg/z+GcCTlsPXvgbMBi9Jz2Tr42iAhcvvuvIFe2WnFSzl38V+adX6aJGhAtCwmlNfdNPXEafe/yaz+HktcXKN/m+Dc51A5wJUfLQi4uMekb2Bkxr8bzWXuPTSVvd8cCcxThkbzi0NdS9tW7mNXr2l1BnrzyHZsDxBPoMlrMJwJORGbyNNWyAQhU2L6rI+yJUtYP+/dgC9SvUfKvXlGWtap0xtuc+B9Ui6/jFXf2PG6NfF2L6dufo2MglX+Yx1LH4blsp8x9vZpoY1ZfAv0Ggujrwvc/uQwyB4FV8xHu1xsGzUa3O6AJkXpuewecAkOa7K/POmxtxYGCsSB9xl9xyXt8sVt6uanKyvxlJY22oey2cj83aPmEpoWYHrxFLo8phfqz2bexnfpFzaaoRDWIE2INsETSHb0v4yizPHc9PyF4X+gqmOU3XWmMXB4tJzozEysp/TCsX4DuroajSI/+1wyyrZw6m/vCRAAMwtE8OxAwHhMT0gI8DTNYq8gdGZMn563M2VC/YGocNKywmjjtcQGlAi1uspxW2x43F4s0Q2U43Y5jEkp0cZgT9nHX7B+x3h2DQj0jAf/6FLKP1tJkTOFnQMuJ33kDJJmBN4AkmbMMK3Q1dhl1huJIAgGphDq5mRMtLb/GFc5YKwAE58cIkvh4Eb4xyS46jUYOAWAjf9Yxra+lwfkSG/rezlR65dy7qef8N28DcQXVTLshvPa9HO0BWa+kQiCYGAKoY6P01RUtV2+aN0sCytG1khVHaHe+OxS1q1x1NY+0OfCK2tZd7ACR3QS9Ly4XmEkryWWrakXsPueL6gsqybGHs2utcVSNEcQhIhjiqW4zrxqKBZLcNAi8LXCS5R2Nd5GaaIsgYJvsWgGHFtpvB8bS8Z1xui2o9wQ7I3PLmXVuigc1mRQCoc1mS+jb+KrQ2f4t9WrXufDY02gsszop7rKzfJXt7Hj66JwP7YgCEJYmEKoB47NYOJ1p5PQ3fBwE7rHMnRCdsDrCy6OYVLSX0hI1A23mX06k64bErBt4nWnc+7iv5D0o0uJstnod/VUrn/ibLIGpgCwbo0jcOIBGLHucGpJBMXIa4r1C4IgRBJThD7AEOvgsMG5dV9sfgviPmfgLX+CtEGh29TpK5i4UaMoe/sdPPn7sfft49/uiG687GjDhC4jWrMorSAIQqQwhUcdFn3PhR+/Ccmntmh3+0hj1mHlho18/e/d7N1yGACbuyz8TrQxySWheyy2+NBV4Gq8eUEQhEhhGo+6SRLSYdDUFu8e07cvvZ77O/ZRo9jy2w04KzPoPawHY86wsWpddWD4I+SMwmrGj/Ey8hc/BIyZd8tf3Ya72utvEx0T5Z85JwiCEClOHo/6+49h36qm2zWAiooiYcIELN26YYu3+gcTR9w0jezsKGLcJ0BrbK5Szhrt5syhJ7BVl/q3GSJdmyM9cGwG518zOCAefv41gyXrQxCEiHPyeNSfPArx6XDqwhZ3UZ2fz/H38rDFjaSq3MggObzrMAeKojnnqhEMv6B3bePnzmfkKRuM35Ny4MyH6vUXKq4uCIIQacL2qJVSFqXUBqXUe21pUIOUFUBSdqu6cO3fT8m8eVjdVTgqDKH+dslmlNdDdnSdkoSbF0DRFowBQ22UOF1yu7FdEAShnWlO6GMusLWtDGkUlwMqD0Ni64TaNnw4REURXXEUZ6Ub7dXs3umk+/EddD9zTG3DTx71L7FVa0OVsV0QBKGdCUuolVI5wHTgH21rTgOcOGj8bKVQWxISiB0wgNNLPuAn/z2ewu+PUeW1cWpaFSqmzmBiQ6vJNLLKjCAIQlsRrkc9D/gvwNtQA6XUjUqptUqptSUlJRExzk9ZgfGzlaEPAPuokTg3bQCtObJ5NzHOMvqf2z+wUVJO6J0b2i4IgtCGNCnUSqmLgGKt9brG2mmtn9Na52qtc9PS0iJmIAA5ufCLLyB7TNNtm8A+ciRl1p58/Ox6kg9t5qzVD5AycUJgo0kPgdUeuM1qN7YLgiC0M+FkfZwFXKyUuhCwAYlKqX9pra9tW9PqYLVDxrCIdJU4bRrVzsHsWH6QHfQm4aK/Er2zmoFj6zQKtW6hrIIhCEIH0ayFA5RS5wG/1lpf1Fi7lizF1SjbloKjDEb+uNVd7fi6iE9f2YrHXfu5o2OiJAdaEIQOpbGFA06OCS/rX4ZV/xeRrlYt3hUg0iDFlARBMDfNmvCitV4BrGgTSxojAjnUNZQfdRC6mFLzFoEVBEFoL04Oj/p4PiRmRaQrmyt0EaaGtguCIHQ05hfq6kqoOtbqHOoa+u5cRJQnsBRplMdJ352LItK/IAhCpDG/UB+vyaGOTA5zTnQBg7e/RqzjCGhNrOMIg7e/Rk50QUT6FwRBiDTmL8qU2h/+aw9ER6bOc/qdd+B58CEyVtdmpSibjfTfyfRwQRDMifmFWimIi9wq5TUrbhc/OQ93YSHRmZmk33mHrMQtCIJpMb9Qb1sKB9fD+ffXW6OwpSTNmCHCLAjCSYP5Y9Q7P4S1L0VMpAVBEE42zC/UEcyhFgRBOBkxv1AfL4BEqVonCELXxfxCXVYQsckugiAIJyPmFurqSvBUS+hDEIQujXmyPjYvCCwrOmAy7FwGbges+YcxM1HKjAqC0AUxh1BvXmAsHuuqMl6XHYC1L9S+X5ZvvA8i1oIgdDnMEfr45NFakW4IWVxWEIQuijmEOtxFY2VxWUEQuiDmEOpwCy7J4rKCIHRBzCHUoRaTDUYWlxUEoYtiDqEefgXMeBqSegHK+Jn788DXM56WgURBELok5sj6AEOERYgFQRDqYQ6PWhAEQWgQEWpBEASTI0ItCIJgckSoBUEQTI4ItSAIgskRoRYEQTA5ItSCIAgmR4RaEATB5IhQC4IgmBwRakEQBJMjQi0IgmByRKgFQRBMTpNCrZSyKaX+o5TapJT6Vin1SHsYJgiCIBiEUz3PCUzUWpcrpazAF0qp97XWq9vYNkEQBIEwhFprrYFy30ur759uS6MEQRCEWsKKUSulLEqpjUAx8JHW+usQbW5USq1VSq0tKSmJtJ2CIAhdlrCEWmvt0VqPBHKAHyilhoZo85zWOldrnZuWlhZpOwVBELoszcr60FqXAsuBqW1jjiAIghBMOFkfaUqpZN/vduCHwLa2NkwQBEEwCCfrIxN4WSllwRD2BVrr99rWLEEQBKGGcLI+NgOj2sEWQRAEIQQyM1EQBMHkiFALgiCYHBFqQRAEkyNCLQiCYHJEqAVBEEyOCLUgCILJEaEWBEEwOSLUgiAIJqdLCnXe7jwmL5zM8JeHM3nhZPJ253W0SYIgCA0SzhTyTkXe7jwe/uphHB4HAIUVhTz81cMATO87vQMtMwd5u/N4av1TFFUUkRGfwdzRc+W8CEIH0+WE+qn1T/lFugaHx8FT6586qQUpEgLb1W9iwedwQs4EVuavbPSchnPe5eYntBZlLOASWXJzc/XatWsj3m8kGP7ycHSIBWoUis0/3dzmx2+LL22wwALYLDYePvPhZvU9eeFkCisK623PjM9k2WXLWmVjKFp6LpraL9T7QJP7BJ/DYGwWGzP7z/SLd2JMIpXuSlxeV6vaNHRTCLbZ7G3Mbl97t2nu91optU5rnRvyva4m1O0tRnWJlKDW9FVzoSil8GpvvTbN/UxtfROra3NLBWxCzgQWf7844BxGq2gSYhIoc5aF7DdaRaOUqretZp+M+Ayq3FWUOktb/RkjRSibzd7G7Pa1Z5uWfK9FqOvwxrY3eOzrxwK2tVQsm0tDN4koFYXWOuw7cTjeXw2Z8ZlhP5YDIYXabrGTbEtutbcVLLCC0JlprqMkQl2Hf333L/53zf+SZk+jpMpY23Hu6LnMGTanzY/dkMdal3BuGg0JflME990cwW+MlnhbgtDZae6TaGNC3eUGE5fuWcqQ7kNYMGMBZc4yJi+cTLRqu9NQ12NtSqQhvIHNGu+3uTg8Dn7zxW+47/P7yIjPoNJdGVKk63r44YQE3Not69ILQhAZ8RkR66tLCfX+4/vZcngLvxrzKwCSYpNYeulSUu2pbXK8lnqshRWFTF44OWQYIT0unSgVhUd76u1XV2Ab8rhrYtmNeeRaa78nMPzl4c2y3YyE6/EnxSQRZ41rcXy8NW1aYrPZ2pjdvvaOUdeEBCNBlxLqpXuWolBM7VO7Nm+qPZW83XnMWzePQ5WHIpo+FSoVEGoFtaFBQKgV0sKKQt7c/qZ/+6HKQwBYlCVArIPDGi0Nj0CgJ9CY6LeWlghYOFkVwf0Gx9AbGsi8b+x9Tf7dR6WPajJTpSVtOjpDIRJtzG6f2bM+GqNLxaiLKopYU7SGGf1m+Lfl7c7jwS8fbDL7oCUnvqksitbEiIO9v5akm4WiJXHscD2McM5pW+UyByO5zYLZkMHERgjX8wxnkC/4y1/prqTMWVavXd3R4OB9wvVewxmoCCeFrynBD2WjGTwMQehsiFADi75fhD3azpTeUwK2h5OJUUNj6TahPM9QnmZTgh/ujaO5qT+RzOEWBCHydNqsj3BmoNV4doUVhcRaYnF73QHC1BwvNjjboimP1a3dJFmb9ljrMnf03LBmyDV3oKLmmPK4LwgnHyetRx3KQ7QoCwplpIs1QGtyiYNDFuHs15JZfS2J0wqCcHJzUnrUizYU8MSH2zlYWkVWsp27pwxi1qhs//uhMipCpawFE5ynHMrTDJV9EOzFNpTREUxLcimn950uQiwIgh9TCvWiDQXc984WqlyG8BaUVnHfO1sA/GLd0kkfofYNJYw16VOFFYVYo6z1YrnhHD/SuZSCIHRNTLlwwBMfbveLdA1VLg9PfLjd/7o1s37C2Xd63+ksu2wZc0fPxeV1MTwtcOJHQ5NkolQUCkVmfKYM1AmCEBFM6VEfLK1qcnuoQbe2mDE0vc90Ptr3EUcdR+nVrZd/e1Z8FoerDtfrW8RZMDMul4v8/HwcDimO1VHYbDZycnKwWq1h72NKoc5KtlMQQqyzku3+36f3nY5Xe3lk1SM4PU4y4zPbJJ83MyGTNy96M2DbgRMH+ObIN0zInsDO0p0yyCecNOTn59OtWzd69+6NUqqjzelyaK05cuQI+fn59OnTJ+z9TCnUd08ZFBCjBrBbLdw9ZVBAu/FZ43F6nNz3g/u4esjV/u1tIZYVrgocbgep9lRe/vZlLMrCb8/8Lelx6RE/liC0FQ6HQ0S6A1FKkZqaSklJSbP2M2WMetaobH5/6TD/6yR7NL+/dFhA1gfAoQqj7kUkq1SFotpTzeSFk3l+y/O4vC6+LPiSi/tdLCItnJSISHcsLTn/phRqgAuHZfp/v3rsqfVEGmozL9paqGMsMZzS7RRe3/o6Y14Zg1u7OT319DY9piAIQg1NCrVSqpdSarlS6jul1LdKqXbJNys+YQx2PHjRadwzdXDINkWV7SPUebvz2H5sO168aDRFFUX8Yc0fyNud16bHFYSOZtGGAs56/FP63BvM4VgAACAASURBVJvHWY9/yqINBR1tkp+9e/cydOjQiPR12WWXsXv3bgDWrVvHsGHD6N+/P7fffjtNTQrUWnP77bfTv39/hg8fzvr16wEoKSlh6tSpje4bLuF41G7gV1rr04BxwC1KqdMicvRGKCwzhLp/ekKDbaxRVvol9SMlNqVNbXlq/VP1MklqJs4IQmelZj5DQWkVmtr5DGYS60jw7bff4vF46Nu3LwA333wzzz//PDt37mTnzp188MEHje7//vvv+9s+99xz3HzzzQCkpaWRmZnJl19+2WobmxRqrXWh1nq97/cTwFagfhwiwtQI9Yb9x3j439+GbHPFoCtYNGtRm8fcGprc0ppJN4JgBq78+6p6/15ZtReAP3ywLeR8hoeXGN/HoxXV9fYNh1mzZjFmzBhOP/10nnvuOf/2hIQE7r//fkaMGMG4ceM4dMgYg9q1axfjxo1j2LBhPPDAAyQk1HfePB4Pd999N2eccQbDhw/n73//OwCFhYVMmDCBkSNHMnToUD7//PN6+7766qvMnDnT3/748eOMGzcOpRTXXXcdixYtavTzLF68mOuuuw6lFOPGjaO0tJTCwkL/Z3311VfDOi+N0awYtVKqNzAK+DrEezcqpdYqpdY2d0QzFFNPz+Czu8+jqtrDK6v34fF23FpPDYVW2jrkIggdSY2zFExpZevWxnzxxRdZt24da9eu5emnn+bIkSMAVFRUMG7cODZt2sSECRN4/vnnAZg7dy5z585ly5Yt5OTkhOzzhRdeICkpiTVr1rBmzRqef/559uzZw2uvvcaUKVPYuHEjmzZtYuTIkfX2/fLLLxkzZgwABQUFAcfIycmhoKDxJ4iCggJ69aqdY1F3n9zc3JA3h+YSdnqeUioBeBu4Q2t9PPh9rfVzwHM+41qtqjHRUZyaGk+v7nF4vJqSE04ykmwBbX7+4c8ZnzW+zRemDTW5RqaHC52BN28a3+B7Dc1nyPbNZ+geH9Po/g3x9NNP8+677wJw4MABdu7cSWpqKjExMVx00UUAjBkzho8++giAVatW+b3aq6++ml//+tf1+ly2bBmbN29m4cKFAJSVlbFz507OOOMMrr/+elwuF7NmzQop1IWFhaSlpTX7c4RDeno6Bw8ebHU/YQm1UsqKIdKvaq3fafVRw2DBmgNYohSZPnE+WFYVINQer4f1h9bXm9rdFkiJUKErEu58huawYsUKPv74Y1atWkVcXBznnXeef5ak1Wr1hzEtFgtud8NVMIPRWvOXv/yFKVOm1Htv5cqV5OXlMXv2bO666y6uu+66gPftdrvfhuzsbPLz8/3v5efnk53deKQ3OzubAwcOhNzH4XBgt9sb2jVswsn6UMALwFat9Z9bfcQweWX1PhZvOkhmkvEhi4Iew444juDWbjLi2if8UFP7Y/NPN7PssmUi0kKnp2Y+Q3ayHYXhSYeaz9AcysrKSElJIS4ujm3btrF69eom9xk3bhxvv/02AG+88UbINlOmTOFvf/sbLpcRltmxYwcVFRXs27ePnj17csMNNzBnzhx/RkZdhgwZwvfffw9AZmYmiYmJrF69Gq018+fP98evn3nmGZ555pl6+1988cXMnz8frTWrV68mKSmJzMxMvx2RyEwJx6M+C/gJsEUptdG37Tda66WtPnojFJY5OD0rkaxkGwmx0VQ4A++u7ZVDLQhdmVmjslslzMFMnTqVZ599liFDhjBo0CDGjRvX5D7z5s3j2muv5bHHHmPq1KkkJSXVazNnzhz27t3L6NGj0VqTlpbGokWLWLFiBU888QRWq5WEhATmz59fb9/p06ezYsUKLrjgAgD++te/Mnv2bKqqqpg2bRrTpk0DYNu2bZx11ln19r/wwgtZunQp/fv3Jy4ujpdeesn/3vLly5k+PQJOndY64v/GjBmjW4PD5dan3vOenvfRDu31ekO2WbZ3mR76z6F665GtrTqWIHQlvvvuu442odlUVFT4deD111/XF198cUT7r6ys1GPHjtVut7vRdtOnT9dOp7NZfZ9zzjn66NGj9baH+jsAa3UDmmrKWh+HypwAZCbbGky9i4uO4wcZPyAzPjPk+4IgdA7WrVvHrbfeitaa5ORkXnzxxYj2b7fbeeSRRygoKOCUU05psN17773XrH5LSkq46667SElp/TwPUwp1zazELF98+q8rvqfgWBWPXVJb/+Os7LM4K7v+Y4ggCJ2Lc845h02bNrXpMUINQraWtLQ0Zs2aFZG+TFnrI7d3d7b9bipj+3YHYHdJBR9vPdTBVgmCIHQMphRqAJvVgtVimJeVZKP4hBOXp3aV7znL5nD/F/d3lHmCIAjthimF+o3/7OePdZbdyky2ozUUn3D6t+0t29sBlgmCILQ/phTqj7ceCgh11Ex6KSozZkm5vW5Kqkoilppn5gphgiAIphTqg6UOvzgD5KTEMSA9AZfHmJl+uOowXu2NiFB3lQphgtAiNi+AJ4fCw8nGz80LOtoiP2Ypc7pt2zbGjx9PbGwsf/zjH/3bq6urmTBhQrNmWDaEKYW6sKyKzDrrI/ZPT+Cju85lXF9j5e+ayS4943q2+ljhrHguCF2SzQtgye1QdgDQxs8lt5tKrCNBa8ucdu/enaeffrpeDZKYmBgmTZrEm2++2cCe4WM6oXa4PByrdJEVVICpLvHWeC7udzF9EsNfHLIhwlnxXBA6LS9Nr//vP0bVOj5+BFxB3wNXFbx/j/F7xZH6+4ZBZytzmp6ezhlnnBFyVfEOKXPaHhytqCY1PiZgxXGAXy3YxIOLvgFgQMoAHjv7MXol9grVRbMIPk5T2wWhy3C8gfBf1dFWddvZypw2xtChQ1mzZk2L96/BdBNespLtrHvwh/XiQsUnHByvMgquOD1OYqJiIrJgQFtUCBOEk4afNbKcXFKOL+wRvN3nIMWnNr5/A3SlMqcWi4WYmBhOnDhBt27dWtyP6TzqGoJFOCvJzkFfBb17V97Lle9dGZHjtEWFMEHoFEx6CKxBT5ZWu7G9hdQtc7pp0yZGjRoV0TKnGzduZOPGjezZs4fJkyczYcIEVq5cSXZ2NrNnzw5ZlKm1ZU6bwul0YrM1HMoNB9MJ9cJ1+dz8r3X1VnTJTLZxuNxJtdvLocpDJMcmR+yY/dMTsFmjWHjzmXx570QRaUEAGH4FzHja50Er4+eMp43tLaQzljltjCNHjtCjR4+Q8evmYLrQx/r9x1i9+wiWqECPOjPJhtZw6LiDoooizs4+O2LHzD9Wya6SCjbsP8Zv3tnCP36aS6/ucRHrXxBOWoZf0SphDqYzljktKioiNzeX48ePExUVxbx58/juu+9ITEzsvGVOZ7/4tZ42b2W97Wv3HtHX/mO13n7omB72z2H6mQ3PtPgYwbzw+W596j3v6c+2F+tT73lPv7fpYMT6FgQzIWVO69OWZU4vueQSvX379nrbT/oyp4VlDnJS6mdcjDm1O6/8fCwF5QVodERXdjlYWoXdamFc31RiLFFsyi9l+nApnyoIZuBkLXNaXV3NrFmzGDhwYGtNNKdQn9G7e4Pvx1piuWHYDQztEZkZSWCsx5iVbCMmOorTshLZeKA0Yn0LgtA6TtYypzExMfXWZ2wpphLqareXXt3t9E+vn9AOMP3pzxnXN5UHL7o9oscd1DORnBQjJj0iJ4m31uXj8ep6cXJBEISOwFRCHRMdxXu3ndPg+26PZteRQ5Q5s0mKrT+g0FLmXjDA//s5A9Ioq3JR7nCTFNe6kVpBEIRIYLr0vMbITLaxw/kO096eFrE+a4L1NVxwWk/mXTVKRFoQBNNgGo86b3cej6/+M6XVxfSMy+C8U85lZf5KiiqKyIjPYO7ouXjs+znBl+ByMXnhZOaOnsv0vq1LfTlwtIqpT63kT5ePYNowYwBRa80Jp5tEm4i1IAgdjyk86rzdeTz81cOUuopBwaGqIt7c/iaFFYVoNIUVhTzwxQNsdj4HUUZCe2FFIQ9/9TB5u5s/hbUuBaVVVFZ7SLTXivLN/1rP1c83nYgvCJ2dvN15TF44meEvD2fywsmt/r5FErOUOX311VcZPnw4w4YN48wzz/QPfHa6MqdPrX8Kh8fRaBu3duMl8AM7PA6eWv9Uq45dUyWvbhGmPmnxbCs8gSOo/KkgdCVqHKi6DlMknCOz0doyp3369OGzzz5jy5YtPPjgg9x4441AZMucmiL0UVNfuiUUlhfS5948spLt/kJKT3y4nYOlVWQl2zl/cBrLt5X4X989ZVDAFPFC36oxdRcqGJGTjNur+a7wOKNPaXip90UbCgKOFdy3IJidn33ws3rbpvSewlWDr2Leunn1HCiHx8Hv//N7pvedzjHHMe5acVfA+y9NfanJY86aNYsDBw7gcDiYO3euX9gSEhKYO3cu7733Hna7ncWLF9OzZ0927drFNddcQ0VFBTNnzmTevHmUl5cH9OnxeLj33ntZsWIFTqeTW265hZtuuonCwkKuvPJKjh8/jtvt5m9/+xvnnBOYsNBQmVPAX+a0ZnZiKM4880z/7+PGjQuoFTJr1izuu+8+rrnmmibPS2OYwqNOtLa8cpXXlexfmeXutzZy98JNAau1/Gv1/kZXbykoddAjIQab1eLfNrKXUUdkc5186uDluh5YtEVWhhE6NYcqD4XcXuYsa1W/nbnM6QsvvBAg6p2qzKmzeAo66Q2UL/4MoDUEFNDzRqFRqKjacIT2WnGW1Caqu7wAjceTalZvqfF8x5yaQo+EmIA2GUk20rvFsinfuCBrluuqKYVacwNoqm9BMDuNecAZ8RkUVhTW254Zbwy6p9hSwvKgg+msZU6XL1/OCy+8wBdffOHfFqkyp6YQ6sNFp2OpvJTYtA9R1lK0Kxl3+WCiE7ZhiSkjIz6DPTsmoCGgjbNkCu7jo5p9vLqrt1w2JvQdeuLgdD767hB97s0jSik8TQwohOpbEE5m5o6ey8NfPRwQ/rBZbMwdPbfFfdYtcxoXF8d5550X0TKnoWYYrly5kry8PGbPns1dd91Vb7ZgJMqcbt68mTlz5vD++++Tmpoa8F4kypyaQqizku0UlI6qJ7o9nHa+vHciAGc9/ikFpVUtEuZQxwPjj3u8yk2iPTqg/vWiDQUs3njQ70GHK9IAUUoFxMzFuxZOVmpSX59a/1RAmmxrUmJbU+b0yiuvbLLM6cSJE7FarezYsYPs7GwOHz5MTk4ON9xwA06nk/Xr19cT6poyp7179w4oczp27Fjmz5/PbbfdBuAvcXrrrbcG7L9//34uvfRSXnnllXp1PSJV5tQUMeq7pwzCXidGDPVXWQnVJhhrlMJqaXzad91+jzvcjHh0GS9+uTegTagFb0MR6kgerSVmLXQapvedzrLLlrH5p5tZdtmyVs9bmDp1Km63myFDhnDvvfeGXeb0z3/+M8OHD+f7779vsMzpaaedxujRoxk6dCg33XQTbrebFStWMGLECEaNGsWbb77J3Ln1nwZqypzW8Ne//pU5c+bQv39/+vXrF1DmNNhbBnj00Uc5cuQIv/zlLxk5ciS5ubn+9yJV5lQ1lSPYEnJzc/XatWubtU84GRTBbUJldEDorI+C0ipiLFH84bLh/n63Fh5n2lOf839Xjw6oltfn3rwmIt2G4P9oTLb/+A2FR7KTa58KBKGj2bp1K0OGDOloM5pFZWUldrsdpRRvvPEGr7/+OosXL45Y/1VVVZx//vl8+eWXWCwNO4MXXXQR77zzDjExMQ22CebSSy/l8ccfr+dph/o7KKXWaa1zCUGToQ+l1IvARUCx1jpyJeuCmDUqu8kwQThtatoF81jed7y8ah8XDqsV5Noc6sD4kRGKqR9rtiiFV+uQN5I+94bOLZWYtSC0DilzGl6M+p/AM0D9pRFOIkadksLzn+/hu8Lj/vS7mjUYs4NWHG9owdvG1lJsSNxlNXNBaB1S5jSMGLXWeiXQuvXhTcDoU1LokRDL4RNO/7aDpVVYLYoeCbEBbVuy4G2oGLrNGiWrmQuC0GpMkfXRHmQk2Vhz/6SA7I6z+/cgyW4lKkTd6XDDLHXbQ218XAPn9O8hWR+CILSaiAm1UupG4Eag0ThPR6JUoCCf1b8HZ/XvEbH+64r77a9v4Os9R3C6PcRGN56tIgiC0BgRS8/TWj+ntc7VWudGYpZPW7B8WzHnPrGc4hNGbPr74hOUO1tf2SoUD0wfwod3TBCRFgSh1Zgij7q9SLRHs+9IJRv3l+LxaqbM+5xnV+xqk2OlJ9pIjovh3XX5jP/9J/4aIZJXLZxMlC1Zws6Jk9g65DR2TpxE2ZIlHW2SH7OUOV28eDHDhw/351DXTCEvKSlh6tSpEbGvSaFWSr0OrAIGKaXylVI/j8iRO4DTs5KwWhQbDpRSfMKBx6vbNCvj3fX5/GrhJgrLHDIJRjjpKFuyhMIHH8J98CBojfvgQQoffMhUYh0JWlvmdNKkSWzatImNGzfy4osvMmfOHADS0tLIzMzkyy+/bLWNTcaotdY/bvVRTILNauG0zETW7zvGBUPSAWN5r7bij8t24A26GVe5PPxqwSbufHNjWGVYBaEt2feT+ulj3aZNpfvVV1P85yfRjsAyp9rhoOix/yFpxgzcx45RcHvgTL9TX2k6i7ezlTlNSKhdjLuioiJgLGzWrFm8+uqrnHXWWU2el8boUqEPMPKpN+eXceCokfMcnEMdSRqa7FJ3mnlTZVgFoaNwF4WuE+8tLQ25PVw6Y5nTd999l8GDBzN9+vSACTm5ubl8/vnn4Z+cBugy6Xk1nDcoDYfLw87iE0DgggGRpqFJMI0hpVKF9qQxDzg6M9MIewRvz8oyfqakhOVBB9MZy5xecsklXHLJJaxcuZIHH3yQjz/+GID09HQOhjiHzaXLedTnDUrn8R8N5+IRxqSWbm24gG04haRCIdPOBTOQfucdqKDynMpmI/3OO1rcZ90yp5s2bWLUqFERLXO6ceNGNm7cyJ49e5g8eTITJkxg5cqVZGdnM3v2bObPr39jiUSZ0xomTJjA7t27OXz4MAAOhwO7vfVP7V1OqAG8Xk1KvJUf/6Bt872DZzhaVOOV/WqQaeeCGUiaMYPM3z1qeNBKEZ2VRebvHiVpxowW99maMqdAk2VOXS5j8ZEdO3ZQUVHBvn376NmzJzfccANz5sxh/fr19fatKXMKBJQ51Vozf/58f/z6mWee8Zc6rcv333/vzwxZv349TqfTX2Vvx44dEclM6XKhD4Af/e0rNhwoRUGbD+DVnQQTvFJMKILLuwpCR5I0Y0arhDmYqVOn8uyzzzJkyBAGDRoUdpnTa6+9lscee4ypU6c2WOZ07969jB49Gq01aWlpLFq0iBUrVvDEE09gtVpJSEgI6VHXlDm94IILAKPM6ezZs6mqqmLatGkBZU5DDQq+/fbbzJ8/H6vVit1u58033/Q/GXS6MqftxaINBfz6rU2466RjNFVwKdLHb6xU62Vjcki0W/n52X3a3Bah6yFlTuvTlmVOJ0yYwOLFi0lJCVwkO+JlTjsbT3y4PUCkoX0H8JqqIfLAoi089clOnv1sF4dPOCVlT+jynKxlTktKSrjrrrvqiXRL6HJC3dBAnVkG8E7LSgSgxFflz1hdfROPLPmW0kqXCLfQ5ThZy5ympaUxa9asiPTV5QYTGxqoM8sA3v99Wn9Ku8urOVbpklxrQeiidDmhDmd9xo4kHM++JlQjCELXoMsJdUsWBWhPwvXszRKqEQSh7elyMWpo/qIA7UmoZcBC0Z6hmnAWFQ7nfEaqn46kNQssN2fh5nD7aW6bF2dlkXiskhMON9UeLzGWKHr6ZuceKnP4t3WzRTe7Tah9UuLCz5BoLccqq1v9GVrapq0/a5dLzzsZqPulTbJbqah24/IE/p1+NXkgt00c0C62hJP7XXdF9lCCcf7gNN5eV9BkP5F4umkr0QvnM1ijFCjq/b2CP2fd8xXqbxxOPy1p8/zFmfQ8pW9AG4XRJpQWFH9zhL3LD+IscxGbFEPv8zNJH5ra4PHqEqUUKXHWJsUcWiae23bu4qafXMF7K76mmy2aY5UuvI3oWWOf81c3/ZQ7f/MIvU7tw3dbNvLAnTfjdDg4e+IPueeRxwMKLYXqR6H4bvN6rrn4h/zpby9y3TVX4a4o4yc/+UnI6nvNTc8ToT4JqCs8GUk2nG4PFw7LbJGX1lSbYHGqrHZzrNLVbp812W4lPja6xYLalqLXGQgl1A1R/M0Rdubtx+uqPSdRVsWA6aeELdZNoXz/G2XKmtem4MB+bpt9Je98sqpVNny/fSvPPPEY8/7xLwCuvmgS9z76OMNG5XLLdZdz9fU3cfb5P2y0D4/Hw01XX0JsbCyzrryWKRfNIjvFzl233MScOXPqTZSRPOpOSHCoZuHaAzy4+Fu/Z1eTCVLTFup7wuG2+dfq/f7jNLegVCQorXJRWuVq0J6739oISvkFNbhNzb51cQXXmg1BOG06I5vn76i3rcdpKWTlprH304MBIg3gdWl2fZhP+tBUXJVuti7cHfD+8OsGNnnMO35+DUWFBTidTq65/iYuu2Y2AOMG5XDN9Tex8pMPibXZeeqFV0lNS2f/3j3cd/uNVFVWcP7kC/nXC8+yent+QJ8ej4enfv8wa1d9SXW1kyt/OofLr/0ZJYeK+K9fXk9F+QncbjcP/M+fGD32zIB9l777FudPvhCAkkNFVJSfYPjoMwCY8aOr+PTDvCaF+vWXnuOCaTP4dtMG4zxpzaEyh5Q57co8+fHOeo/fNXWua1aSeWTJtyHb1M0WeeLD7U3Gws2Gy9v5vV6z4Dwe+knKXdW6a+aRPz7DG0tX8Pp7n/Lai3+n9NhRAKoqKxg2Ope3ln3BmLHjefs1Y7r3/z58L9dcfxNvf/wV6ZlZIft8941XSOiWxGt5n/Lae5/yzmvzyd+/j6WLFnLmuRNZ8OHnvLXsCwadPqzevhvXfs1pw0YAUFxUSM86x+iZmUVxUWGjn+dQ4UE+/eA9rrgucE2Vao9Xypx2ZRqrcw2Ne8J1942Ux6ygkQfX5rczM019hnBCKOGch7aKUQcz/LqBDcZuY5OsOMvqi3VsklFx0hoXHZYHHcxrL/2dTz8wZvkdKixg/55dJKd0xxoTw7kXGEtXDRk2ktWfrwBg87o1zPvHqwBcOOsy/vzfD9Xrc9XK5ezY+i0fLzWmlp84cZz9e3YxdMQofvvr23C73UycMp3BQ4fX+5wlxYdISTUWuVY0XTgt+Hw98chvuOM3DxMVFej3xliiSO8RmTKnItQnIS2pc11DlFL0uTeP7vHhj1A3FTcOd6CwqQHHtoqHR0r0wvkMLR2UtEYpEmzRAbNPm+qnJW2ioxSp8TFhDdb1m5TDtiV7g2LUUfQ+PyusrI9QA3xrVn3B6i9WMH/xMuz2OH5++UVUO41ZuNHRgWVOPXXKnKqmKk9qzf/84U+MOev8eva8uDCPr1Z8xKN338ovb5vL+RddFtDGbrfjdDqJsUQxYnAfjhYXEmOJotrj5cihIk7JyfG/DnW+vtu8gXtuMbzpY0eP8vnyj4iOjua6H18esTKnItQnIeGm8IWixus+UlENgNWimhSnhy8+vclMjNxTu7c69S6cDJNwRbetRC/cjJTmnq+G+g7neM1ps3XrVrJT4kK2CU4vy57ch+wkO6sW76L8qJOE7rGMn9mPgWMzmjxeDXGxgSlzqrqS5KQU7PY48nd/z5YNa0nrFkuMxfBGa8QzOkr5X/9g7FjWf/YBZ/1wBh/8+x0UkBofQ4mlts2FF07lrX+9xBUzL8RqtbJjxw6SE7NxHz/G+aMGckHuELrbotj+7WZuvuH6ABtHDjsda0UxgzOHA4kkJyVRuu87xo4dyz1L3uK2225jcGaiv8TprbfeGnC+8vfv86cG3nP7L5g4eSrX/fhyUuJiWLdui5Q57arUfOlqvuhRSvkFuC51PeGG2sTHRDeZZRGuELQ2rS74c0VaUCMlepHAzLn8dRk4NqNZwhxMSlxMwA2gz2UzeetfL3HlD8f7y5x2s1kZnJlIlILBmUatm+yUOFLiYxicmcj//eVprr32Wp764/8ydepUkpOTyE6Jw5XeDZvVwuDMRAb+8heUHMzvkDKndT9nSnyMYbvvM0uZU8FPKE80OCe5z715IeOiCtjzeOsvJOHkQMqc1kfKnArtQihPNNirbCiubZZiVILQEFLmVDzqLkM4XrfQ+TkZPerOiHjUQkjC8bqFroHWuuksCqHNaIlzLELdhThZBrCEtsNms3HkyBFSU1NFrDsArTVHjhzBFrS6e1OIUAtCFyInJ4f8/HxKSko62pQui81mIycnp1n7iFALQhfCarXSp48snHyyIbU+BEEQTI4ItSAIgskRoRYEQTA5bZJHrZQqAfa1cPcewOEImtNazGSPmWwBsacpxJ6GMZMtYA57TtVap4V6o02EujUopdY2lPTdEZjJHjPZAmJPU4g9DWMmW8B89gQjoQ9BEASTI0ItCIJgcswo1M91tAFBmMkeM9kCYk9TiD0NYyZbwHz2BGC6GLUgCIIQiBk9akEQBKEOItSCIAgmxzRCrZSaqpTarpT6Xil1rwnsuVMp9a1S6hul1OtKqeaVu2r98V9UShUrpb4J2n6bUmqbz7Y/tKM9vZRSy5VS3/mOPTfo/V8ppbRSqkc72GJTSv1HKbXJZ8sjvu2v+q6hb3znz9rWtgTZZVFKbVBKved73Ucp9bXvmn5TKRX+0iBtY88kpdR6pdRGpdQXSqn+7WjLXqXUFt+x19bZ3lHXc7JSaqHv2FuVUuPrvNdu13LYaK07/B9gAXYBfYEYYBNwWgfakw3sAey+1wuA2e1swwRgNPBNnW3nAx8Dsb7X6e1oTyYw2vd7N2BHzd8I6AV8iDHJqUc72KKABN/vVuBrYBxwoe89BbwO3NzOf7O7gNeA9+pcN1f5fn/WBPbsAIb4fv8l8M92tGVv8LXRwdfzy8Ac3+8xQLLvJbgemgAAA91JREFU93a9lsP9ZxaP+gfA91rr3VrrauANYGYH2xQN2JVS0UAccLA9D661XgkcDdp8M/C41trpa1PcjvYUaq3X+34/AWzFuKEBPAn8F4RclrEtbNFa63LfS6vvn9ZaL/W9p4H/AM2rJdkKlFI5wHTgH77XCpgILPQ1eRmY1VH2+NBAou/3JNr5mg5Bh1zPSqkkDEfoBd9xq7XWpb632/VaDhezCHU2cKDO63xqRaDd0VoXAH8E9gOFQJnWellH2VOHgcA5vsfpz5RSZ3SEEUqp3sAo4Gul1EygQGu9qZ1tsCilNgLFwEda66/rvGcFfgJ80I4mzcP4gnt9r1OBUq212/e6va/pYHsA5gBLlVL5GOfn8Xa0RwPLlFLrlFI3+rZ11PXcBygBXvKFhv6hlIrvqGs5HMwi1KZCKZWC4dH3AbKAeKXUtR1rFWB4+d0xHvPvBhaodl6mQymVALwN3AG4gd8AD7WnDQBaa4/WeiSG1/wDpdTQOm//FViptf68PWxRSl0EFGut17XH8ZqiEXvuBC7UWucALwF/bkezztZajwamAbcopSbQcddzNEZY8W9a61FABfAwHXQth4NZhLoAIzZUQ45vW0dxAbBHa12itXYB7wBndqA9NeQD7/ie7v+D4S2124CHz1N9G3hVa/0O0A/jZrZJKbUX4++2XimV0V42+R5ZlwNTfTb+FkjDiM+2F2cBF/vOwRsYIY+ngGRf6Aza95quZ49SKg8YUefJ403a8Zr2PaXWhDfexQh3dtT1nA/k1zkXCzGEu0Ov5cYwi1CvAQb4RsljgKuAf3egPfuBcUqpON8dfhJGTLajWYQxAINSaiDGIEi7VPzynYcXgK1a6z8DaK23aK3Ttda9tda9Mb4Ao7XWRW1sS5pSKtn3ux34IbBNKTUHmAL8WGvtbayPSKK1vk9rneM7B1cBn2qtr8G4gVzma/ZTYHFH2YPxhJjku27AOGftck37wgrdan4HJgPf0EHXs+/6PKCUGuTbNAlY3xHXcriYYikurbVbKXUrxmirBXhRa/1tB9rztVJqIbAe4/F+A+08xVQp9TpwHtDDF1P8LfAi8KIvZa8a+Klv4Kw9OAsjrrnFFxsG+I3Wemk7Hb8umcDLSikLhrOxQGv9nlLKjTFav8r3BP2O1vrRDrCvhnuAN5RS/41xDb3QUYb4vmM3AG8rpbzAMeD6djp8T+Bd398kGnhNa/2BzynrqOv5NuBVnw27gZ+103FbhEwhFwRBMDlmCX0IgiAIDSBCLQiCYHJEqAVBEEyOCLUgCILJEaEWBEEwOSLUgiAIJkeEWhAEweT8P7w6eHJq+dX9AAAAAElFTkSuQmCC\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "result.history.plot(\"angles\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "tequila-chemistry",
-   "language": "python",
-   "name": "tequila-chemistry"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.7.7"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}
diff --git a/tutorials/Optimizer_Tutorial.ipynb b/tutorials/Optimizer_Tutorial.ipynb
deleted file mode 100644
index ccd8f7bc..00000000
--- a/tutorials/Optimizer_Tutorial.ipynb
+++ /dev/null
@@ -1,2295 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Optimization"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Hello, and welcome to our tutorial on optimization. Here, we will explore the four different optimizers which already have `Tequila` interfaces: a native GD optimizer, alongside interfaces for `SciPy`, `GPyOpt`, and `Phoenics`."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "### start at the start: import statements!\n",
-    "import tequila as tq\n",
-    "import numpy as np\n",
-    "import matplotlib.pyplot as plt"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Overview\n",
-    "\n",
-    "**How to optimize an `Objective`:**\n",
-    "\n",
-    " In `tequila`, optimizers are accessed in several ways. They may be instantiated as objects directly, which can then be called; they are also accessible through `tq.minimize`. Either of these methods have an obligatory argument: an `Objective`. `tq.minimize` also requires you supply a `method`, which must be a string; the call methods of the GD, `SciPy`, and `GPyOpt` optimizers accept this key as well.\n",
-    " \n",
-    "As keywords to any optimization call, you can pass down the usual compilation kwargs for quantum simulation in `Tequila`:\n",
-    "* `backend`, a string indicating which quantum simulator to use\n",
-    "* `samples`, an int indicating how many shots of the circuit to measure (None means full wf simulation)\n",
-    "* `device`, (generally) a string indicating which (real or emulated) quantum computer to sample from (requires samples be specified),\n",
-    "* `noise`, the NoiseModel object to apply to the circuits simulated (see the tutorial on noise). \n",
-    "\n",
-    "additional keywords you might use include:\n",
-    "* `variables`,  a `list` of the `Variable`s you want to optimize (the default is all of them).\n",
-    "* `initial_values`, which gives a start point to optimization. If you supply arguments to `variables`, you also need to supply arguments to `initial_values` so that all non-optimized parameters have a value to use. The default is random initialization (not recomended) \n",
-    "* `gradient`, which specifies which type of gradient will be used : analytical gradients (Default): gradient=None, numerical gradients: gradient={'method':'2-point', \"stepsize\":1.e-4}, custom gradient objectives: gradient={tq.Variable:tq.Objective}, module specific gradients: gradient=\"2-point\" (to use for example `SciPy` finite difference stencils).\n",
-    "* `silent`, silence outputs\n",
-    "\n",
-    "Some of the optimizers take more, or different, keywords from the others, so check the documentation for each one. \n",
-    "In case the optimizer has some degree of verbosity (currently, they all do), you can deactivate this with `silent=True`. \n",
-    "\n",
-    "The following optimization methods are available on your system in `Tequila`:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "available methods for optimizer modules found on your system:\n",
-      "method               | optimizer module\n",
-      "--------------------------\n",
-      "NELDER-MEAD          | scipy\n",
-      "COBYLA               | scipy\n",
-      "POWELL               | scipy\n",
-      "SLSQP                | scipy\n",
-      "L-BFGS-B             | scipy\n",
-      "BFGS                 | scipy\n",
-      "CG                   | scipy\n",
-      "TNC                  | scipy\n",
-      "TRUST-KRYLOV         | scipy\n",
-      "NEWTON-CG            | scipy\n",
-      "DOGLEG               | scipy\n",
-      "TRUST-NCG            | scipy\n",
-      "TRUST-EXACT          | scipy\n",
-      "TRUST-CONSTR         | scipy\n",
-      "adam                 | gd\n",
-      "adagrad              | gd\n",
-      "adamax               | gd\n",
-      "nadam                | gd\n",
-      "sgd                  | gd\n",
-      "momentum             | gd\n",
-      "nesterov             | gd\n",
-      "rmsprop              | gd\n",
-      "rmsprop-nesterov     | gd\n",
-      "Supported optimizer modules:  ['scipy', 'phoenics', 'gpyopt', 'gd']\n",
-      "Installed optimizer modules:  ['scipy', 'gd']\n"
-     ]
-    }
-   ],
-   "source": [
-    "tq.optimizers.show_available_optimizers()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We will use two different `Objective`s for optimization in this tutorial. The first of these is a two qubit expectation value with the tractable but non trivial hamiltonian $[Y(0)+Qm(0)]\\otimes X(1)$, where $Qm=\\frac{1}{2} (I - Z)$, the projector onto the |1> state. "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "We will optimize the following objective: \n",
-      "\n",
-      "Objective with 1 unique expectation values\n",
-      "variables = [a, b, c, d]\n",
-      "types     = not compiled\n",
-      "\n",
-      "Expectation Value 0\n",
-      "Hamiltonian :  (+1.0000Y(0)X(1)+0.5000X(1)-0.5000Z(0)X(1),)\n",
-      "variables :  [a, b, c, d]\n",
-      "circuit:\n",
-      "\n",
-      "     ┌───┐┌───────────────┐   ┌───────────────┐   \n",
-      "q_0: ┤ H ├┤ RY(f((a,))_0) ├─■─┤ RX(f((c,))_2) ├─■─\n",
-      "     ├───┤├───────────────┤ │ ├───────────────┤ │ \n",
-      "q_1: ┤ H ├┤ RZ(f((b,))_1) ├─■─┤ RX(f((d,))_3) ├─■─\n",
-      "     └───┘└───────────────┘   └───────────────┘   \n",
-      "c: 2/═════════════════════════════════════════════\n",
-      "                                                  \n"
-     ]
-    }
-   ],
-   "source": [
-    "### optimizing the circuit in terms of pi makes the result of the optimization easier to interpret.\n",
-    "\n",
-    "a = tq.Variable(name=\"a\")*tq.numpy.pi\n",
-    "b = tq.Variable(name=\"b\")*tq.numpy.pi\n",
-    "c = tq.Variable(name=\"c\")*tq.numpy.pi\n",
-    "d = tq.Variable(name='d')*tq.numpy.pi\n",
-    "\n",
-    "U1 = tq.gates.H(target=[0])\n",
-    "U1 += tq.gates.H(target=1)\n",
-    "U1 += tq.gates.Ry(target=0, angle=a)\n",
-    "U1 += tq.gates.Rz(target=1, angle=b)\n",
-    "U1 += tq.gates.Z(target=1,control=0)\n",
-    "U1 += tq.gates.Rx(target=0, angle=c)\n",
-    "U1 += tq.gates.Rx(target=1,angle=d)\n",
-    "U1 += tq.gates.Z(target=1,control=0)\n",
-    "\n",
-    "\n",
-    "### once we have a circuit, we pick a hamiltonian to optimize over\n",
-    "H1=(tq.paulis.Y(0)+tq.paulis.Qm(0))*tq.paulis.X(1)\n",
-    "O1=tq.ExpectationValue(U=U1,H=H1)\n",
-    "\n",
-    "### we use the .draw function to pretty-print circuits via backend printers.\n",
-    "print('We will optimize the following objective: \\n')\n",
-    "tq.draw(O1,backend='qiskit')"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Our second `Objective`, O2, will measure a 3-qubit circuit with respect to the Hamiltonian $Y(0)\\otimes X(1) \\otimes Y(2)$"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "We will optimize the following objective: \n",
-      "\n",
-      "Objective with 1 unique expectation values\n",
-      "variables = [a, b, c, d]\n",
-      "types     = not compiled\n",
-      "\n",
-      "Expectation Value 0\n",
-      "Hamiltonian :  (+1.0000Y(0)X(1)Y(2),)\n",
-      "variables :  [a, b, c, d]\n",
-      "circuit:\n",
-      "\n",
-      "     ┌──────────┐┌───────────────┐                                     \n",
-      "q_0: ┤ RY(pi/2) ├┤ RZ(f((a,))_0) ├──■──────────────────────────■───────\n",
-      "     ├──────────┤├───────────────┤┌─┴─┐     ┌───────────────┐┌─┴─┐     \n",
-      "q_1: ┤ RY(pi/3) ├┤ RZ(f((b,))_1) ├┤ X ├──■──┤ RY(f((c,))_2) ├┤ X ├──■──\n",
-      "     ├──────────┤└───────────────┘└───┘┌─┴─┐├───────────────┤└───┘┌─┴─┐\n",
-      "q_2: ┤ RY(pi/4) ├──────────────────────┤ X ├┤ RX(f((d,))_3) ├─────┤ X ├\n",
-      "     └──────────┘                      └───┘└───────────────┘     └───┘\n",
-      "c: 3/══════════════════════════════════════════════════════════════════\n",
-      "                                                                       \n"
-     ]
-    }
-   ],
-   "source": [
-    "### this time, don't scale by pi\n",
-    "\n",
-    "H2 = tq.paulis.Y(0)*tq.paulis.X(1)*tq.paulis.Y(2)\n",
-    "U2 = tq.gates.Ry(tq.numpy.pi/2,0) +tq.gates.Ry(tq.numpy.pi/3,1)+tq.gates.Ry(tq.numpy.pi/4,2)\n",
-    "U2 += tq.gates.Rz('a',0)+tq.gates.Rz('b',1)\n",
-    "U2 += tq.gates.CNOT(control=0,target=1)+tq.gates.CNOT(control=1,target=2)\n",
-    "U2 += tq.gates.Ry('c',1) +tq.gates.Rx('d',2)\n",
-    "U2 += tq.gates.CNOT(control=0,target=1)+tq.gates.CNOT(control=1,target=2)\n",
-    "O2 = tq.ExpectationValue(H=H2, U=U2)\n",
-    "\n",
-    "print('We will optimize the following objective: \\n')\n",
-    "tq.draw(O2, backend=\"qiskit\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Local Optimizers\n",
-    "\n",
-    "We will begin this tutorial by focusing on local optimizers. By local optimization, we mean the any optimization schema where the suggested parameters at step t are always a transformation of the parameters suggested at step t-1. This includes a large number of the standard optimization techniques in use today, like gradient descent.     `Tequila` comes with two local optimizers: a native gradient descent optimizer, implementing a number of the most popular gradient descent algorithms used in classical machine learning, as well as a plugin for the `SciPy` package (which is installed alongside `Tequila`), which allows the use of a number of gradient-free, gradient-based, and hessian-based optimization methods.\n",
-    "\n",
-    "### The GD Optimizer\n",
-    "we will start this tutorial by looking at the GD optimizer. Here is an overview over the available optimization methods.\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "available methods for optimizer module gd\n",
-      "method               | optimizer module\n",
-      "--------------------------\n",
-      "adam                 | gd\n",
-      "adagrad              | gd\n",
-      "adamax               | gd\n",
-      "nadam                | gd\n",
-      "sgd                  | gd\n",
-      "momentum             | gd\n",
-      "nesterov             | gd\n",
-      "rmsprop              | gd\n",
-      "rmsprop-nesterov     | gd\n"
-     ]
-    }
-   ],
-   "source": [
-    "tq.show_available_optimizers(module=\"gd\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "As one sees, a variety of methods are available for optimization. Here, 'sgd' refers to the standard gradient descent algorithm, without momentum. like all tequila optimizers, the GD optimizer has a minimize function and most of the arguments are the same. However, there is one important difference: the GD optimizer takes a learning rate, lr. This parameter mediates step size in all of the GD optimizer methods; it is a positive float which scales the step in the direction of the gradient. \n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We will now optimize O1, our two-qubit expectation value, choosing starting angles equivalent to $\\frac{1}{4}\\pi$ for all four variables, and optimizing via the ['Adam'](https://towardsdatascience.com/_adam-latest-trends-in-deep-learning-optimization-6be9a291375c) method."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "init={'a':0.25,'b':0.25,'c':0.25,'d':0.25}\n",
-    "lr=0.1\n",
-    "\n",
-    "### For even more fun, try using sampling with the samples keyword, \n",
-    "### or pick your favorite backend with the 'backend' keyword!\n",
-    "\n",
-    "adam_result=tq.minimize(objective=O1,lr=lr,\n",
-    "              method='adam',\n",
-    "              maxiter=80,\n",
-    "              initial_values=init,\n",
-    "              silent=True)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The plots below show the trajectory of both the value of the objective and the values of the angles as a function of time."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "best energy:  -1.6179942172570136\n",
-      "optimal angles:  a : 0.14749682605178346\n",
-      "b : 1.0037044962376886\n",
-      "c : -0.0020942074899867142\n",
-      "d : -0.498209057390019\n",
-      "\n"
-     ]
-    }
-   ],
-   "source": [
-    "adam_result.history.plot('energies')\n",
-    "adam_result.history.plot('angles')\n",
-    "print('best energy: ',adam_result.energy)\n",
-    "print('optimal angles: ',adam_result.angles)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "**We see that, minus a few hiccups, all the angles converge to optimimum values.**"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "**Let's repeat what we did above, but with a few of the other methods! Here's RMSprop:**"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "RMSprop optimization results:\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "best energy:  -1.6180339887498905\n",
-      "optimal angles:  a : 0.14758363531643576\n",
-      "b : 1.0000000183809166\n",
-      "c : -1.625339216876925e-08\n",
-      "d : -0.5000000021961905\n",
-      "\n"
-     ]
-    }
-   ],
-   "source": [
-    "init={'a':0.25,'b':0.25,'c':0.25,'d':0.25}\n",
-    "lr=0.01\n",
-    "rms_result=tq.minimize(objective=O1,lr=lr,\n",
-    "              method='rmsprop',\n",
-    "              maxiter=80,\n",
-    "              initial_values=init,\n",
-    "              silent=True)\n",
-    "print('RMSprop optimization results:')\n",
-    "rms_result.history.plot('energies')\n",
-    "rms_result.history.plot('angles')\n",
-    "print('best energy: ',rms_result.energy)\n",
-    "print('optimal angles: ',rms_result.angles)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "**... And here's Momentum:**"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "momentum optimization results:\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "best energy:  -1.6178164176706864\n",
-      "optimal angles:  a : 0.153130292696303\n",
-      "b : 0.9975386964199592\n",
-      "c : -0.0008949959645234715\n",
-      "d : -0.5018114831041253\n",
-      "\n"
-     ]
-    }
-   ],
-   "source": [
-    "init={'a':0.25,'b':0.25,'c':0.25,'d':0.25}\n",
-    "lr=0.1\n",
-    "mom_result=tq.minimize(objective=O1,lr=lr,\n",
-    "              method='momentum',\n",
-    "              maxiter=80,\n",
-    "              initial_values=init,\n",
-    "              silent=True)\n",
-    "\n",
-    "print('momentum optimization results:')\n",
-    "mom_result.history.plot('energies')\n",
-    "mom_result.history.plot('angles')\n",
-    "print('best energy: ',mom_result.energy)\n",
-    "print('optimal angles: ',mom_result.angles)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Note that when using the [RMSprop](https://towardsdatascience.com/understanding-rmsprop-faster-neural-network-learning-62e116fcf29a) method, we reduced the learning rate from 0.1 to 0.01. Different methods may be more or less sensitive to choices of initial learning rate. Try going back to the previous examples, and choosing different learning rates, or different initial parameters, to gain a feel for how sensitive different methods are."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "**Accelerated gradient descent to achieve numerical accuracy:**\n",
-    "\n",
-    "One issue with gradient descent is that they are slow when it comes to converging to machine precision. Indeed, as one approaches an optimum, the gradient goes to zero, which means that each successive step is smaller and smaller, and convergence slows down. This is not really a problem in machine learning, where convergence to many digits is not needed, but it is an issue in chemistry.\n",
-    "\n",
-    "The standard method used to converge quantum chemical calculations is an accelerated form of gradient descent alternatively called Direct Inversion of the Iterative Subspace (DIIS) or Pulay mixing (for its inventor Peter Pulay). Basically, DIIS extrapolates from the error on past function evaluation to where the error is zero using a subspace approach. It is closely related to other subpsace and Krylov methods, such as GMRES.\n",
-    "\n",
-    "DIIS works best once we are pretty close to our solution. In this case, we start from a significantly better initial guess, and try to achieve a tolerance of 1e-9 with just standard gradient descent,\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Optimizer: <class 'tequila.optimizers.optimizer_gd.OptimizerGD'> \n",
-      "backend         : qulacs\n",
-      "device          : None\n",
-      "samples         : None\n",
-      "save_history    : True\n",
-      "noise           : None\n",
-      "\n",
-      "Objective       : 1 expectationvalues\n",
-      "Gradient        : 8 expectationvalues\n",
-      "gradient instr  : None\n",
-      "active variables : 4\n",
-      "iter.        <O>          Δ<O>      max(d<O>)   rms(d<O>)\n",
-      "  1       -1.61467625   -2.87e-01   1.603e-01   1.169e-01    \n",
-      "  2       -1.61755894   -2.88e-03   3.376e-02   2.077e-02    \n",
-      "  3       -1.61770417   -1.45e-04   2.436e-02   1.566e-02    \n",
-      "  4       -1.61779488   -9.07e-05   2.099e-02   1.332e-02    \n",
-      "  5       -1.61786059   -6.57e-05   1.788e-02   1.135e-02    \n",
-      "  6       -1.61790828   -4.77e-05   1.523e-02   9.665e-03    \n",
-      "  7       -1.61794287   -3.46e-05   1.297e-02   8.230e-03    \n",
-      "  8       -1.61796795   -2.51e-05   1.104e-02   7.008e-03    \n",
-      "  9       -1.61798613   -1.82e-05   9.403e-03   5.966e-03    \n",
-      " 10       -1.61799931   -1.32e-05   8.006e-03   5.079e-03    \n",
-      " 11       -1.61800886   -9.55e-06   6.815e-03   4.324e-03    \n",
-      " 12       -1.61801579   -6.92e-06   5.801e-03   3.680e-03    \n",
-      " 13       -1.61802080   -5.02e-06   4.939e-03   3.133e-03    \n",
-      " 14       -1.61802443   -3.63e-06   4.203e-03   2.667e-03    \n",
-      " 15       -1.61802707   -2.63e-06   3.578e-03   2.270e-03    \n",
-      " 16       -1.61802897   -1.91e-06   3.046e-03   1.932e-03    \n",
-      " 17       -1.61803036   -1.38e-06   2.592e-03   1.644e-03    \n",
-      " 18       -1.61803136   -1.00e-06   2.206e-03   1.400e-03    \n",
-      " 19       -1.61803208   -7.25e-07   1.878e-03   1.191e-03    \n",
-      " 20       -1.61803261   -5.25e-07   1.598e-03   1.014e-03    \n",
-      " 21       -1.61803299   -3.81e-07   1.360e-03   8.629e-04    \n",
-      " 22       -1.61803326   -2.76e-07   1.158e-03   7.345e-04    \n",
-      " 23       -1.61803346   -2.00e-07   9.851e-04   6.252e-04    \n",
-      " 24       -1.61803361   -1.45e-07   8.390e-04   5.322e-04    \n",
-      " 25       -1.61803371   -1.05e-07   7.139e-04   4.528e-04    \n",
-      " 26       -1.61803379   -7.60e-08   6.078e-04   3.855e-04    \n",
-      " 27       -1.61803384   -5.50e-08   5.168e-04   3.281e-04    \n",
-      " 28       -1.61803388   -3.99e-08   4.406e-04   2.792e-04    \n",
-      " 29       -1.61803391   -2.89e-08   3.747e-04   2.377e-04    \n",
-      " 30       -1.61803393   -2.09e-08   3.189e-04   2.023e-04    \n",
-      " 31       -1.61803395   -1.52e-08   2.713e-04   1.721e-04    \n",
-      " 32       -1.61803396   -1.10e-08   2.313e-04   1.465e-04    \n",
-      " 33       -1.61803397   -7.94e-09   1.962e-04   1.248e-04    \n",
-      " 34       -1.61803397   -5.76e-09   1.674e-04   1.062e-04    \n",
-      " 35       -1.61803398   -4.18e-09   1.428e-04   9.036e-05    \n",
-      " 36       -1.61803398   -3.02e-09   1.209e-04   7.702e-05    \n",
-      " 37       -1.61803398   -2.20e-09   1.037e-04   6.542e-05    \n",
-      " 38       -1.61803398   -1.58e-09   8.750e-05   5.576e-05    \n",
-      " 39       -1.61803399   -1.15e-09   7.463e-05   4.749e-05    \n",
-      " 40       -1.61803399   -8.37e-10   6.390e-05   4.041e-05    \n",
-      " 41       -1.61803399   -6.04e-10   5.436e-05   3.437e-05    \n",
-      " 42       -1.61803399   -4.39e-10   4.625e-05   2.923e-05    \n",
-      " 43       -1.61803399   -3.16e-10   3.910e-05   2.491e-05    \n",
-      " 44       -1.61803399   -2.28e-10   3.314e-05   2.124e-05    \n",
-      " 45       -1.61803399   -1.69e-10   2.909e-05   1.818e-05    \n",
-      " 46       -1.61803399   -1.22e-10   2.432e-05   1.527e-05    \n",
-      "delta f smaller than tolerance 1e-10. Stopping optimization.\n"
-     ]
-    }
-   ],
-   "source": [
-    "init={'a':0.18,'b':0.8,'c':-0.1,'d':-0.4}\n",
-    "lr=0.1\n",
-    "no_diis_result=tq.minimize(objective=O1,lr=lr,\n",
-    "              method='sgd',\n",
-    "              tol=1e-10,\n",
-    "              maxiter=80,\n",
-    "              initial_values=init,\n",
-    "              silent=False)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We run out of iterations. Looking at the printout (obtained with `silent=False`), we see that convergence is achieved after 46 steps. We note that specifically convergence slows down significantly after 5 steps, as the gradients (and thus step sizes) become smaller the closer we get to the minima. This is the problem DIIS solves.\n",
-    "\n",
-    "Let's try again with acceleration."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Optimizer: <class 'tequila.optimizers.optimizer_gd.OptimizerGD'> \n",
-      "backend         : qulacs\n",
-      "device          : None\n",
-      "samples         : None\n",
-      "save_history    : True\n",
-      "noise           : None\n",
-      "\n",
-      "Objective       : 1 expectationvalues\n",
-      "Gradient        : 8 expectationvalues\n",
-      "gradient instr  : None\n",
-      "active variables : 4\n",
-      "iter.        <O>          Δ<O>      max(d<O>)   rms(d<O>)\n",
-      "  1       -1.61467625   -2.87e-01   1.603e-01   1.169e-01    \n",
-      "  2       -1.61755894   -2.88e-03   3.376e-02   2.077e-02    \n",
-      "  3       -1.61770417   -1.45e-04   2.436e-02   1.566e-02    DIIS\n",
-      "  4       -1.61783934   -1.35e-04   1.908e-02   1.203e-02    DIIS\n",
-      "  5       -1.61803383   -1.94e-04   1.855e-03   9.289e-04    DIIS\n",
-      "  6       -1.61802839   +5.45e-06   1.098e-02   5.504e-03    DIIS\n",
-      "  7       -1.61803399   -5.60e-06   7.242e-05   3.631e-05    DIIS\n",
-      "  8       -1.61803399   -2.04e-10   2.974e-05   1.492e-05    DIIS\n",
-      "delta f smaller than tolerance 1e-10. Stopping optimization.\n"
-     ]
-    }
-   ],
-   "source": [
-    "diis_result=tq.minimize(objective=O1,lr=lr,\n",
-    "              method='sgd',\n",
-    "              diis={'tol':1e-1},\n",
-    "              tol=1e-10,\n",
-    "              maxiter=80,\n",
-    "              initial_values=init,\n",
-    "              silent=False)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Convergence is obtained in just 8 steps. We can see here that DIIS kicks in at step 3, that is, when max(gradient) is below 1e-1 (the `tol=` argument in the DIIS dictionary) and we have accumulated at least 3 vectors. Once DIIS starts, convergence is very rapid, with a four orders of magnitude drop in the error in only three steps.\n",
-    "\n",
-    "We can see this most clearly in a log plot of the error,"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "SGD + DIIS optimization results:\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "<matplotlib.legend.Legend at 0x7f19ac4ee7c0>"
-      ]
-     },
-     "execution_count": 18,
-     "metadata": {},
-     "output_type": "execute_result"
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "print('SGD + DIIS optimization results:')\n",
-    "Emin = diis_result.history.energies[-1]\n",
-    "plt.semilogy(no_diis_result.history.energies[:-1] - Emin)\n",
-    "plt.semilogy(diis_result.history.energies[:-1] - Emin)\n",
-    "plt.ylabel('Error on energy')\n",
-    "plt.legend(['without DIIS', 'with DIIS'])"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We clearly see here that when DIIS kicks in, convergence rapidly accelerates. In comparison, the convergence rate of standard gradient descent actually gets slower the closer we are to a solution. However, it should be noted that DIIS is not entirely stable and only really works close to an optima. Furthermore, the implementation here is somewhat experimental. Use at your own risk!"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "**The GD optimizer, with the Quantum Natural Gradient:**\n",
-    "\n",
-    "The Quantum Natural Gradient, or QNG, is a novel method of calculating gradients for quantum systems, inspired by the natural gradient sometimes employed in classical machine learning. The usual gradient we employ is with respect to a euclidean manifold, but this is not the only geometry -- nor even, the optimal geometry -- of quantum space. The QNG is, in essence, a method of taking gradients with respect to (an approximation to) the Fubini-Study metric. For information on how (and why) the QNG is used, see [Stokes et.al](https://arxiv.org/abs/1909.02108). \n",
-    "\n",
-    "Using the qng in Tequila is as simple as passing in the keyword gradient='qng' to optimizers which support it, such as the GD optimizer.  We will use it to optimize O2, our 3 qubit `Objective`, and then compare the results to optimizing the same circuit with the regular gradient."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "### the keyword stop_count, below, stops optimization if no improvement occurs after 50 epochs.\n",
-    "### let's use a random initial starting point:\n",
-    "init={k:np.random.uniform(-2,2) for k in ['a','b','c','d']}\n",
-    "\n",
-    "lr=0.01\n",
-    "qng_result = tq.minimize(objective=O2,\n",
-    "                     gradient='qng',\n",
-    "                     method='sgd', maxiter=200,lr=lr,\n",
-    "                     initial_values=init, silent=True)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "best energy with qng:  -0.3094659562236847\n",
-      "optimal angles with qng:  a : -1.949589374320652\n",
-      "b : -2.5183083763768193\n",
-      "c : 1.1753365433636513\n",
-      "d : 1.2325405724983405\n",
-      "\n"
-     ]
-    }
-   ],
-   "source": [
-    "qng_result.history.plot('energies')\n",
-    "qng_result.history.plot('angles')\n",
-    "print('best energy with qng: ',qng_result.energy)\n",
-    "print('optimal angles with qng: ',qng_result.angles)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "To gain appreciation for why one might use the QNG, let's optimize the same circuit with the same learning rate and the same method, but without QNG."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "plotting what happens without QNG\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "best energy without qng:  -0.1101990865736325\n",
-      "optimal angles without qng:  a : -1.9977162739218457\n",
-      "b : -2.0000101558168653\n",
-      "c : 0.7197529470316536\n",
-      "d : 0.15019291645695712\n",
-      "\n"
-     ]
-    }
-   ],
-   "source": [
-    "lr=0.01\n",
-    "sgd_noqng_result = tq.minimize(objective=O2,\n",
-    "                     gradient=None,\n",
-    "                     method='sgd', maxiter=200,lr=lr,\n",
-    "                     initial_values=init, silent=True)\n",
-    "print('plotting what happens without QNG')\n",
-    "sgd_noqng_result.history.plot('energies')\n",
-    "sgd_noqng_result.history.plot('angles')\n",
-    "print('best energy without qng: ',sgd_noqng_result.energy)\n",
-    "print('optimal angles without qng: ',sgd_noqng_result.angles)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Though the starting point was random you will most likely see that the QNG run achieved a greater degree of improvement -- it will not perform worse --, and that the trajectories followed by angles there were different from those followed by angles in the sgd-only optimization. Feel free to play around with other methods, learning rates, or circuits in the space below!\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "### Use this space to optimize your own circuits!"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### The SciPy Optimizer\n",
-    "\n",
-    "`SciPy` is one of the most popular optimization packages in `Python`. It offers a wide variety of optimization strategies. We will not cover them here; for a full exploration of all the `SciPy` methods, see [their docs](https://docs.scipy.org/doc/scipy/reference/tutorial/optimize.html). Here, we will exhibit a few of the more powerful options available. Most `SciPy` keywords like `method_options` can just be passed to `minimize` directly in the same way as when using `SciPy` directly.  "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "available methods for optimizer module scipy\n",
-      "method               | optimizer module\n",
-      "--------------------------\n",
-      "NELDER-MEAD          | scipy\n",
-      "COBYLA               | scipy\n",
-      "POWELL               | scipy\n",
-      "SLSQP                | scipy\n",
-      "L-BFGS-B             | scipy\n",
-      "BFGS                 | scipy\n",
-      "CG                   | scipy\n",
-      "TNC                  | scipy\n",
-      "TRUST-KRYLOV         | scipy\n",
-      "NEWTON-CG            | scipy\n",
-      "DOGLEG               | scipy\n",
-      "TRUST-NCG            | scipy\n",
-      "TRUST-EXACT          | scipy\n",
-      "TRUST-CONSTR         | scipy\n"
-     ]
-    }
-   ],
-   "source": [
-    "tq.show_available_optimizers(module=\"scipy\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We will try three different optimizers: `COBYLA`, which is gradient-free, `L-BFGS-B`, which employs gradients, and `NEWTON-CG`, which employs the Hessian."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "As a reminder: we will optimize:\n",
-      "Objective with 1 unique expectation values\n",
-      "variables = [a, b, c, d]\n",
-      "types     = not compiled\n",
-      "\n",
-      "Expectation Value 0\n",
-      "Hamiltonian :  (+1.0000Y(0)X(1)+0.5000X(1)-0.5000Z(0)X(1),)\n",
-      "variables :  [a, b, c, d]\n",
-      "circuit:\n",
-      "\n",
-      "     ┌───┐┌───────────────┐   ┌───────────────┐   \n",
-      "q_0: ┤ H ├┤ RY(f((a,))_0) ├─■─┤ RX(f((c,))_2) ├─■─\n",
-      "     ├───┤├───────────────┤ │ ├───────────────┤ │ \n",
-      "q_1: ┤ H ├┤ RZ(f((b,))_1) ├─■─┤ RX(f((d,))_3) ├─■─\n",
-      "     └───┘└───────────────┘   └───────────────┘   \n",
-      "c_0: ═════════════════════════════════════════════\n",
-      "                                                  \n",
-      "c_1: ═════════════════════════════════════════════\n",
-      "                                                  \n"
-     ]
-    }
-   ],
-   "source": [
-    "print('As a reminder: we will optimize:')\n",
-    "tq.draw(O1, backend=\"qiskit\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "best energy with cobyla:  -1.6180095801270247\n",
-      "optimal angles with cobyla:  a : 2.1466459827493174\n",
-      "b : 1.002273376125911\n",
-      "c : -0.003983388162904869\n",
-      "d : -0.5006752029196884\n",
-      "\n"
-     ]
-    }
-   ],
-   "source": [
-    "init={'a':0.25,'b':0.25,'c':0.25,'d':0.25}\n",
-    "\n",
-    "cobyla_result = tq.minimize(objective=O1,\n",
-    "                            method=\"cobyla\", \n",
-    "                            initial_values=init, \n",
-    "                            tol=1.e-3, method_options={\"gtol\":1.e-3},\n",
-    "                            silent=True)\n",
-    "\n",
-    "cobyla_result.history.plot('energies')\n",
-    "cobyla_result.history.plot('angles')\n",
-    "print('best energy with cobyla: ',cobyla_result.energy)\n",
-    "print('optimal angles with cobyla: ',cobyla_result.angles)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "best energy with L-BFGS-B:  -1.6178070201838934\n",
-      "optimal angles with L-BFGS-B:  a : 0.14354383870194684\n",
-      "b : 1.0061131726451131\n",
-      "c : -0.00825692744088291\n",
-      "d : -0.5036909480382052\n",
-      "\n"
-     ]
-    }
-   ],
-   "source": [
-    "lb_result = tq.minimize(objective=O1,\n",
-    "                            method=\"l-bfgs-b\", \n",
-    "                            initial_values=init, \n",
-    "                            tol=1.e-3, method_options={\"gtol\":1.e-3},\n",
-    "                            silent=True)\n",
-    "\n",
-    "lb_result.history.plot('energies')\n",
-    "lb_result.history.plot('angles')\n",
-    "print('best energy with L-BFGS-B: ',lb_result.energy)\n",
-    "print('optimal angles with L-BFGS-B: ',lb_result.angles)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "best energy with NEWTON-CG:  -1.6180323934132854\n",
-      "optimal angles with NEWTON-CG:  a : 0.14753463639545006\n",
-      "b : 1.0008716211744726\n",
-      "c : -0.0011067836511529652\n",
-      "d : -0.4998455957582174\n",
-      "\n"
-     ]
-    }
-   ],
-   "source": [
-    "newton_result = tq.minimize(objective=O1,\n",
-    "                            method=\"newton-cg\", \n",
-    "                            initial_values=init, \n",
-    "                            tol=1.e-3, method_options={\"gtol\":1.e-3},\n",
-    "                            silent=True)\n",
-    "\n",
-    "newton_result.history.plot('energies')\n",
-    "newton_result.history.plot('angles')\n",
-    "print('best energy with NEWTON-CG: ',newton_result.energy)\n",
-    "print('optimal angles with NEWTON-CG: ',newton_result.angles)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "All three of the methods converged to the same minimum, but not necessarily to the same angles; the gradient and hessian based methods converged to approximately the same angles in similar time. "
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "**Scipy Extras: numerical gradients and Hessians**\n",
-    "Scipy allows for the use of numerical gradients. To use them, pass down keywords to the `gradient` argument, like `'2-point'`. When using the numerical gradients of `SciPy` it is often crucial to determine a feasible stepsize for the procedure. This can be done with the `method_options` entry `finite_diff_rel_step` (for `SciPy` version 1.5 or higher) or `eps` (for `SciPy` version < 1.5).\n",
-    "\n",
-    "Here is one example. **Please check your SciPy version!**"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "best energy with L-BFGS-B:  -1.6180322764615407\n",
-      "optimal angles with L-BFGS-B:  a : 0.14737921020398723\n",
-      "b : 0.9991028633007109\n",
-      "c : 0.0010812477825766602\n",
-      "d : -0.5000405396241386\n",
-      "\n"
-     ]
-    }
-   ],
-   "source": [
-    "lb_result = tq.minimize(objective=O1,\n",
-    "                            method=\"l-bfgs-b\", \n",
-    "                            initial_values=init,\n",
-    "                            gradient=\"2-point\",\n",
-    "                            tol=1.e-3, method_options={\"gtol\":1.e-3, \"finite_diff_rel_step\":1.e-4}, # eps for scipy version < 1.5\n",
-    "                            silent=True)\n",
-    "\n",
-    "lb_result.history.plot('energies')\n",
-    "lb_result.history.plot('angles')\n",
-    "print('best energy with L-BFGS-B: ',lb_result.energy)\n",
-    "print('optimal angles with L-BFGS-B: ',lb_result.angles)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "**Scipy Extras: the QNG in SciPy**\n",
-    "Scipy is also configured to use the qng, just as the gd optimizer is. All one needs to do is set `gradient=qng`. Let's See how QNG interacts with the `BFGS` optimizer. We will use 02, our 3-qubit expectationvalue, that we used previously."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "plotting what happens with QNG\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "best energy with qng:  -0.3535533676156721\n",
-      "optimal angles with qng:  a : -1.570884542409681\n",
-      "b : 0.754829536265003\n",
-      "c : -1.5708867115312135\n",
-      "d : -1.5704585913166933\n",
-      "\n"
-     ]
-    }
-   ],
-   "source": [
-    "init={k:np.random.uniform(-2,2) for k in ['a','b','c','d']}\n",
-    "lr=0.01\n",
-    "bfgs_qng_result = tq.minimize(objective=O2,\n",
-    "                     gradient='qng',\n",
-    "                     method='bfgs', maxiter=200,lr=lr,\n",
-    "                     initial_values=init, silent=True)\n",
-    "print('plotting what happens with QNG')\n",
-    "bfgs_qng_result.history.plot('energies')\n",
-    "bfgs_qng_result.history.plot('angles')\n",
-    "print('best energy with qng: ',bfgs_qng_result.energy)\n",
-    "print('optimal angles with qng: ',bfgs_qng_result.angles)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "plotting what happens without QNG\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "best energy without qng:  -0.35355296837705463\n",
-      "optimal angles without qng:  a : -1.5699318047491537\n",
-      "b : 0.6835176416172444\n",
-      "c : -1.5699495726072827\n",
-      "d : -1.5717565421037312\n",
-      "\n"
-     ]
-    }
-   ],
-   "source": [
-    "bfgs_noqng_result = tq.minimize(objective=O2,\n",
-    "                     gradient=None,\n",
-    "                     method='bfgs', maxiter=200,lr=lr,\n",
-    "                     initial_values=init, silent=True)\n",
-    "print('plotting what happens without QNG')\n",
-    "bfgs_noqng_result.history.plot('energies')\n",
-    "bfgs_noqng_result.history.plot('angles')\n",
-    "print('best energy without qng: ',bfgs_noqng_result.energy)\n",
-    "print('optimal angles without qng: ',bfgs_noqng_result.angles)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Numerical and Customized Gradients\n",
-    "\n",
-    "By default `tequila` compiles analytical gradients of the objectives using `jax`, internal recompilation and the parameter shift rule. The default is not setting the `gradient` keyword or setting it to `None`. The keyword can also be set to a dictionary (keys are the variables, values are the `tequila` objectives which are assumed to evaluate to the corresponding gradients of the objective).  \n",
-    "For example `gradient=tq.grad(objective)` will results have the same results as `gradient=None` or simply not setting it.\n",
-    "\n",
-    "`tequila` offers its own way of compiling numerical gradients which can then be used troughout all gradient based optimizers. It can be activated by setting `gradient` to a dictionary holding the finite difference stencil as `method` as well as the `stepsize`.   \n",
-    "\n",
-    "Numerical gradients of that type come with the cost of 2*`len(variables)` and can lead to significantly cheaper gradients, especially if many expectation values are involved in the objective and/or if heavy recompilation of parametrized gates is necessary. \n",
-    "Here is a small example using our `O2` objective, here the numerical 2-point procedure leads to 4 expectation values in the gradients (while anayltial gradients would lead to 8, set silent to False in the upper example or remove the gradient statement here)."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 32,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Optimizer: <class 'tequila.optimizers.optimizer_gd.OptimizerGD'> \n",
-      "backend         : qulacs\n",
-      "device          : None\n",
-      "samples         : None\n",
-      "save_history    : True\n",
-      "noise           : None\n",
-      "\n",
-      "Objective       : 1 expectationvalues\n",
-      "Gradient        : 4 expectationvalues\n",
-      "gradient instr  : {'method': '2-point', 'stepsize': 0.0001}\n",
-      "active variables : 4\n",
-      "Iteration: 1 , Energy: -0.60003241, angles: {a: 0.09936269222059471, b: 0.09939775441865076, c: 0.09936269222059471, d: 0.09936269222060581}\n",
-      "Iteration: 2 , Energy: -0.60018803, angles: {a: 0.09872953938259146, b: 0.09879900936485822, c: 0.09872953938259146, d: 0.09872953938264697}\n",
-      "Iteration: 3 , Energy: -0.60034166, angles: {a: 0.0981005608850504, b: 0.09820379122594805, c: 0.09810056088502819, d: 0.0981005608850948}\n",
-      "Iteration: 4 , Energy: -0.60049334, angles: {a: 0.09747568193347869, b: 0.09761199308737636, c: 0.09747568193347869, d: 0.09747568193355641}\n",
-      "Iteration: 5 , Energy: -0.60064311, angles: {a: 0.09685487540521667, b: 0.09702364170889313, c: 0.09685487540521667, d: 0.09685487540527218}\n",
-      "Iteration: 6 , Energy: -0.60079098, angles: {a: 0.09623806839960106, b: 0.09643871923710182, c: 0.09623806839960106, d: 0.09623806839964547}\n",
-      "Iteration: 7 , Energy: -0.60093698, angles: {a: 0.0956252806498358, b: 0.0958572078908814, c: 0.0956252806498358, d: 0.09562528064989131}\n",
-      "Iteration: 8 , Energy: -0.60108113, angles: {a: 0.0950164855547663, b: 0.09527908992764669, c: 0.0950164855547441, d: 0.09501648555481071}\n",
-      "Iteration: 9 , Energy: -0.60122346, angles: {a: 0.09441165665331477, b: 0.09470434768407135, c: 0.09441165665330367, d: 0.09441165665333698}\n",
-      "Iteration: 10 , Energy: -0.60136397, angles: {a: 0.09381076767438482, b: 0.0941329635311349, c: 0.09381076767435151, d: 0.09381076767439592}\n",
-      "Iteration: 11 , Energy: -0.60150271, angles: {a: 0.0932137924882114, b: 0.09356496217552959, c: 0.0932137924881892, d: 0.09321379248824471}\n",
-      "Iteration: 12 , Energy: -0.60163968, angles: {a: 0.09262074932341316, b: 0.09300024119288644, c: 0.09262074932337985, d: 0.09262074932344647}\n",
-      "Iteration: 13 , Energy: -0.60177491, angles: {a: 0.09203156762944689, b: 0.09243882573122245, c: 0.09203156762939138, d: 0.0920315676294691}\n",
-      "Iteration: 14 , Energy: -0.60190844, angles: {a: 0.09144617816974057, b: 0.09188069835390769, c: 0.09144617816967396, d: 0.09144617816976278}\n",
-      "Iteration: 15 , Energy: -0.60204027, angles: {a: 0.09086459969669383, b: 0.09132588302063196, c: 0.09086459969666053, d: 0.09086459969673824}\n",
-      "Iteration: 16 , Energy: -0.60217043, angles: {a: 0.0902868068917039, b: 0.09077432059370052, c: 0.0902868068916706, d: 0.09028680689175941}\n",
-      "Iteration: 17 , Energy: -0.60229894, angles: {a: 0.08971277462606056, b: 0.09022595297237804, c: 0.08971277462603836, d: 0.08971277462612717}\n",
-      "Iteration: 18 , Energy: -0.60242582, angles: {a: 0.0891424779130067, b: 0.08968084491347553, c: 0.08914247791298449, d: 0.08914247791307331}\n",
-      "Iteration: 19 , Energy: -0.60255110, angles: {a: 0.08857589196267215, b: 0.0891388978221496, c: 0.08857589196266105, d: 0.08857589196272767}\n",
-      "Iteration: 20 , Energy: -0.60267478, angles: {a: 0.08801299212510819, b: 0.08860013546788661, c: 0.08801299212508598, d: 0.0880129921251859}\n",
-      "Iteration: 21 , Energy: -0.60279690, angles: {a: 0.08745375389718194, b: 0.08806454080229056, c: 0.08745375389714863, d: 0.08745375389724855}\n",
-      "Iteration: 22 , Energy: -0.60291747, angles: {a: 0.08689815296898376, b: 0.08753213655906525, c: 0.08689815296895045, d: 0.08689815296908368}\n",
-      "Iteration: 23 , Energy: -0.60303651, angles: {a: 0.08634616512834806, b: 0.08700286567778762, c: 0.08634616512832585, d: 0.08634616512843687}\n",
-      "Iteration: 24 , Energy: -0.60315405, angles: {a: 0.085797766404938, b: 0.08647667211360002, c: 0.08579776640486028, d: 0.08579776640499351}\n",
-      "Iteration: 25 , Energy: -0.60327009, angles: {a: 0.08525293292241934, b: 0.08595361772982804, c: 0.08525293292236383, d: 0.08525293292250816}\n",
-      "Iteration: 26 , Energy: -0.60338466, angles: {a: 0.08471164095450448, b: 0.08543360763502142, c: 0.08471164095444897, d: 0.0847116409546155}\n",
-      "Iteration: 27 , Energy: -0.60349778, angles: {a: 0.08417386696589749, b: 0.08491666433226844, c: 0.08417386696585308, d: 0.08417386696600851}\n",
-      "Iteration: 28 , Energy: -0.60360947, angles: {a: 0.08363958756893988, b: 0.0844027712452399, c: 0.08363958756887327, d: 0.08363958756907311}\n",
-      "Iteration: 29 , Energy: -0.60371973, angles: {a: 0.08310881904757253, b: 0.08389191184905434, c: 0.08310881904746151, d: 0.08310881904766135}\n",
-      "Iteration: 30 , Energy: -0.60382861, angles: {a: 0.08258145896503635, b: 0.08338406963162007, c: 0.08258145896493643, d: 0.08258145896513627}\n",
-      "Iteration: 31 , Energy: -0.60393610, angles: {a: 0.08205752419070392, b: 0.08287922821224028, c: 0.0820575241905818, d: 0.08205752419078163}\n",
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-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
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-     ]
-    }
-   ],
-   "source": [
-    "lr=0.01\n",
-    "num_result = tq.minimize(objective=O2,\n",
-    "                     gradient={\"method\":\"2-point\", \"stepsize\":1.e-4},\n",
-    "                     method='sgd', maxiter=200,lr=lr,\n",
-    "                     initial_values=0.1, silent=False)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 33,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "num_result.history.plot('energies')"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "`tequila` currently offers `2-point` as well as `2-point-forward` and `2-point-backward` stencils as `method`.\n",
-    "The method can also be set to a python function performing the task. Here is an example which implements the same as `2-point`. The function can be replaced by any function with the same signature."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 39,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "import copy\n",
-    "def my_finite_difference_stencil(obj, var_vals, key, step, *args, **kwargs):\n",
-    "        \"\"\"\n",
-    "        calculate objective gradient by symmetric shifts about a point.\n",
-    "        Parameters\n",
-    "        ----------\n",
-    "        obj: Objective:\n",
-    "            objective to call.\n",
-    "        var_vals:\n",
-    "            variables to feed to the objective.\n",
-    "        key:\n",
-    "            which variable to shift, i.e, which variable's gradient is being called.\n",
-    "        step:\n",
-    "            the size of the shift; a small float.\n",
-    "        args\n",
-    "        kwargs\n",
-    "\n",
-    "        Returns\n",
-    "        -------\n",
-    "        float:\n",
-    "            the approximated gradient of obj w.r.t variable key at point var_vals[key] as a float.\n",
-    "\n",
-    "        \"\"\"\n",
-    "        left = copy.deepcopy(var_vals)\n",
-    "        left[key] += step / 2\n",
-    "        right = copy.deepcopy(var_vals)\n",
-    "        right[key] -= step / 2\n",
-    "        return 1.0 / step * (obj(left, *args, **kwargs) - obj(right, *args, **kwargs))\n",
-    "\n",
-    "num_result = tq.minimize(objective=O2,\n",
-    "                     gradient={\"method\":my_finite_difference_stencil, \"stepsize\":1.e-4},\n",
-    "                     method='sgd', maxiter=200,lr=lr,\n",
-    "                     initial_values=0.1, silent=True)\n",
-    "num_result.history.plot('energies')"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The `gradient` keyword can also be replaced by a dictionary of `tequila` objectives which evaluate to gradients approximations of it."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Bayesian optimization\n",
-    "\n",
-    "\n",
-    "[Bayesian optimization](https://arxiv.org/abs/1807.02811) is a method of global optimization, often used to tune hyperparameters in classical learning. It has also seen use in the optimization of [quantum circuits](https://arxiv.org/pdf/1812.08862.pdf). Tequila currently supports 2 different bayesian optimization algorithms: [Phoenics](https://github.com/aspuru-guzik-group/phoenics) and [GPyOpt](https://github.com/SheffieldML/GPyOpt), optimizers originally developed for optimizing expensive experimental procedures in chemistry. Click the links to get to the respective github pages, and download the optimizers before continuing this tutorial."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### GPyOpt\n",
-    "\n",
-    "GPyOpt can be used like any of our other optimizers. Like the GD and SciPy optimizers, it also takes a 'method' keyword. 3 methods are supported: `'lbfgs'`,`'DIRECT'`, and `'CMA'`. See the `GPyOpt` github for more info."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "As a reminder, we will optimize\n",
-      "Objective with 1 unique expectation values\n",
-      "variables = [a, b, c, d]\n",
-      "types     = not compiled\n",
-      "\n",
-      "Expectation Value 0\n",
-      "Hamiltonian :  (+1.0000Y(0)X(1)+0.5000X(1)-0.5000Z(0)X(1),)\n",
-      "variables :  [a, b, c, d]\n",
-      "circuit:\n",
-      "\n",
-      "     ┌───┐┌───────────────┐   ┌───────────────┐   \n",
-      "q_0: ┤ H ├┤ RY(f((a,))_0) ├─■─┤ RX(f((c,))_2) ├─■─\n",
-      "     ├───┤├───────────────┤ │ ├───────────────┤ │ \n",
-      "q_1: ┤ H ├┤ RZ(f((b,))_1) ├─■─┤ RX(f((d,))_3) ├─■─\n",
-      "     └───┘└───────────────┘   └───────────────┘   \n",
-      "c_0: ═════════════════════════════════════════════\n",
-      "                                                  \n",
-      "c_1: ═════════════════════════════════════════════\n",
-      "                                                  \n"
-     ]
-    }
-   ],
-   "source": [
-    "print('As a reminder, we will optimize')\n",
-    "tq.draw(O1,backend='qiskit')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 40,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Optimizer: <class 'tequila.optimizers.optimizer_gpyopt.OptimizerGPyOpt'> \n",
-      "backend         : qulacs\n",
-      "device          : None\n",
-      "samples         : None\n",
-      "save_history    : True\n",
-      "noise           : None\n",
-      "\n",
-      "method          : lbfgs\n",
-      "Objective       : 1 expectationvalues\n",
-      "num acquisition: 1, time elapsed: 0.22s\n",
-      "num acquisition: 2, time elapsed: 0.47s\n",
-      "num acquisition: 3, time elapsed: 0.73s\n",
-      "num acquisition: 4, time elapsed: 1.46s\n",
-      "num acquisition: 5, time elapsed: 1.67s\n",
-      "num acquisition: 6, time elapsed: 1.96s\n",
-      "num acquisition: 7, time elapsed: 2.39s\n",
-      "num acquisition: 8, time elapsed: 2.78s\n",
-      "num acquisition: 9, time elapsed: 3.20s\n",
-      "num acquisition: 10, time elapsed: 3.68s\n",
-      "num acquisition: 11, time elapsed: 3.83s\n",
-      "num acquisition: 12, time elapsed: 4.06s\n",
-      "num acquisition: 13, time elapsed: 4.24s\n",
-      "num acquisition: 14, time elapsed: 4.41s\n",
-      "num acquisition: 15, time elapsed: 4.59s\n",
-      "num acquisition: 16, time elapsed: 5.07s\n",
-      "num acquisition: 17, time elapsed: 5.25s\n",
-      "num acquisition: 18, time elapsed: 5.50s\n",
-      "num acquisition: 19, time elapsed: 5.69s\n",
-      "num acquisition: 20, time elapsed: 5.89s\n",
-      "num acquisition: 21, time elapsed: 6.14s\n",
-      "num acquisition: 22, time elapsed: 6.35s\n",
-      "num acquisition: 23, time elapsed: 6.53s\n",
-      "num acquisition: 24, time elapsed: 7.06s\n",
-      "num acquisition: 25, time elapsed: 7.42s\n",
-      "num acquisition: 26, time elapsed: 7.70s\n",
-      "num acquisition: 27, time elapsed: 7.97s\n",
-      "num acquisition: 28, time elapsed: 8.65s\n",
-      "num acquisition: 29, time elapsed: 9.12s\n",
-      "num acquisition: 30, time elapsed: 9.43s\n",
-      "num acquisition: 31, time elapsed: 9.79s\n",
-      "num acquisition: 32, time elapsed: 10.20s\n",
-      "num acquisition: 33, time elapsed: 10.57s\n",
-      "num acquisition: 34, time elapsed: 10.91s\n",
-      "num acquisition: 35, time elapsed: 11.37s\n",
-      "num acquisition: 36, time elapsed: 11.55s\n",
-      "num acquisition: 37, time elapsed: 11.80s\n",
-      "num acquisition: 38, time elapsed: 11.99s\n",
-      "num acquisition: 39, time elapsed: 12.16s\n",
-      "num acquisition: 40, time elapsed: 12.66s\n",
-      "num acquisition: 41, time elapsed: 13.06s\n",
-      "num acquisition: 42, time elapsed: 13.91s\n",
-      "num acquisition: 43, time elapsed: 14.20s\n",
-      "num acquisition: 44, time elapsed: 14.66s\n",
-      "num acquisition: 45, time elapsed: 15.16s\n",
-      "num acquisition: 46, time elapsed: 15.58s\n",
-      "num acquisition: 47, time elapsed: 15.93s\n",
-      "num acquisition: 48, time elapsed: 16.30s\n",
-      "num acquisition: 49, time elapsed: 16.83s\n",
-      "num acquisition: 50, time elapsed: 17.29s\n",
-      "num acquisition: 51, time elapsed: 17.50s\n",
-      "num acquisition: 52, time elapsed: 17.81s\n",
-      "num acquisition: 53, time elapsed: 18.09s\n",
-      "num acquisition: 54, time elapsed: 18.38s\n",
-      "num acquisition: 55, time elapsed: 18.86s\n",
-      "num acquisition: 56, time elapsed: 19.08s\n",
-      "num acquisition: 57, time elapsed: 19.25s\n",
-      "num acquisition: 58, time elapsed: 19.64s\n",
-      "num acquisition: 59, time elapsed: 19.92s\n",
-      "num acquisition: 60, time elapsed: 20.11s\n",
-      "num acquisition: 61, time elapsed: 20.47s\n",
-      "num acquisition: 62, time elapsed: 20.78s\n",
-      "num acquisition: 63, time elapsed: 21.10s\n",
-      "num acquisition: 64, time elapsed: 21.48s\n",
-      "num acquisition: 65, time elapsed: 21.73s\n",
-      "num acquisition: 66, time elapsed: 21.94s\n",
-      "num acquisition: 67, time elapsed: 22.19s\n",
-      "num acquisition: 68, time elapsed: 22.39s\n",
-      "num acquisition: 69, time elapsed: 22.90s\n",
-      "num acquisition: 70, time elapsed: 23.60s\n",
-      "num acquisition: 71, time elapsed: 24.06s\n",
-      "num acquisition: 72, time elapsed: 24.64s\n",
-      "num acquisition: 73, time elapsed: 25.01s\n",
-      "num acquisition: 74, time elapsed: 25.46s\n",
-      "num acquisition: 75, time elapsed: 25.89s\n",
-      "num acquisition: 76, time elapsed: 26.31s\n",
-      "num acquisition: 77, time elapsed: 26.85s\n",
-      "num acquisition: 78, time elapsed: 27.29s\n",
-      "num acquisition: 79, time elapsed: 27.60s\n",
-      "num acquisition: 80, time elapsed: 27.97s\n",
-      "GPyOpt optimization results:\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "best energy:  -1.584212943157413\n",
-      "optimal angles:  {a: 1.870128626698086, b: 5.887193501069059, c: 5.18274634095629, d: 1.5011709655643113}\n"
-     ]
-    }
-   ],
-   "source": [
-    "### let's use the lbfgs method.\n",
-    "init={'a':0.25,'b':0.25,'c':0.25,'d':0.25}\n",
-    "### note: no lr is passed here! there are fewer tunable keywords for this optimizer.\n",
-    "result=tq.minimize(objective=O1,\n",
-    "              method='lbfgs',\n",
-    "              maxiter=80,\n",
-    "              initial_values=init)\n",
-    "\n",
-    "print('GPyOpt optimization results:')\n",
-    "result.history.plot('energies')\n",
-    "result.history.plot('angles')\n",
-    "print('best energy: ',result.energy)\n",
-    "print('optimal angles: ',result.angles)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "**Don't worry, the plot's not broken!**\n",
-    "Perhaps you are looking at the plots above in horror. But, do take note: bayesian optimization is a global, exploratory optimization method, designed to explore large portions of parameter space while still seeking out optimality. Look at the optimal energy again, and one sees that the best performance of this optimization method matched that of all the gradient descent methods. We will apply gpyopt, next, to the QNG example circuit above, and see how bayesian optimization compares to QNG and SGD."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 41,
-   "metadata": {
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Hey, remember me?\n",
-      "Objective with 1 unique expectation values\n",
-      "variables = [a, b, c, d]\n",
-      "types     = not compiled\n",
-      "\n",
-      "Expectation Value 0\n",
-      "Hamiltonian :  (+1.0000Y(0)X(1)Y(2),)\n",
-      "variables :  [a, b, c, d]\n",
-      "circuit:\n",
-      "\n",
-      "0: ───Ry(0.5π)─────Rz(0.318309886183791*pi*f((a,))_0)───@────────────────────────────────────────────@───────\n",
-      "                                                        │                                            │\n",
-      "1: ───Ry(0.333π)───Rz(0.318309886183791*pi*f((b,))_1)───X───@───Ry(0.318309886183791*pi*f((c,))_2)───X───@───\n",
-      "                                                            │                                            │\n",
-      "2: ───Ry(0.25π)─────────────────────────────────────────────X───Rx(0.318309886183791*pi*f((d,))_3)───────X───\n",
-      "Optimizer: <class 'tequila.optimizers.optimizer_gpyopt.OptimizerGPyOpt'> \n",
-      "backend         : qulacs\n",
-      "device          : None\n",
-      "samples         : None\n",
-      "save_history    : True\n",
-      "noise           : None\n",
-      "\n",
-      "method          : lbfgs\n",
-      "Objective       : 1 expectationvalues\n",
-      "num acquisition: 1, time elapsed: 0.14s\n",
-      "num acquisition: 2, time elapsed: 0.45s\n",
-      "num acquisition: 3, time elapsed: 0.76s\n",
-      "num acquisition: 4, time elapsed: 1.04s\n",
-      "num acquisition: 5, time elapsed: 1.37s\n",
-      "num acquisition: 6, time elapsed: 1.67s\n",
-      "num acquisition: 7, time elapsed: 2.02s\n",
-      "num acquisition: 8, time elapsed: 2.40s\n",
-      "num acquisition: 9, time elapsed: 2.71s\n",
-      "num acquisition: 10, time elapsed: 2.96s\n",
-      "num acquisition: 11, time elapsed: 3.20s\n",
-      "num acquisition: 12, time elapsed: 3.43s\n",
-      "num acquisition: 13, time elapsed: 3.73s\n",
-      "num acquisition: 14, time elapsed: 4.06s\n",
-      "num acquisition: 15, time elapsed: 4.42s\n",
-      "num acquisition: 16, time elapsed: 4.63s\n",
-      "num acquisition: 17, time elapsed: 4.95s\n",
-      "num acquisition: 18, time elapsed: 5.30s\n",
-      "num acquisition: 19, time elapsed: 5.55s\n",
-      "num acquisition: 20, time elapsed: 5.88s\n",
-      "num acquisition: 21, time elapsed: 6.10s\n",
-      "num acquisition: 22, time elapsed: 6.31s\n",
-      "num acquisition: 23, time elapsed: 6.71s\n",
-      "num acquisition: 24, time elapsed: 7.04s\n",
-      "num acquisition: 25, time elapsed: 7.36s\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "best energy:  -0.6123724356957851\n",
-      "optimal angles:  {a: 0.0, b: 0.0, c: 0.0, d: 6.283185307179586}\n"
-     ]
-    }
-   ],
-   "source": [
-    "print('Hey, remember me?')\n",
-    "tq.draw(O2)\n",
-    "### the keyword stop_count, below, stops optimization if no improvement occurs after 50 epochs.\n",
-    "### let's use a random initial starting point:\n",
-    "init={k:np.random.uniform(-2,2) for k in ['a','b','c','d']}\n",
-    "\n",
-    "gpy_result = tq.minimize(objective=O2,maxiter=25,method='lbfgs',\n",
-    "                     initial_values=init)\n",
-    "\n",
-    "gpy_result.history.plot('energies')\n",
-    "print('best energy: ',gpy_result.energy)\n",
-    "print('optimal angles: ',gpy_result.angles)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "**In a very, very small number of steps, GPyOpt is able to match the performance of SGD with the QNG.**"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "**There's a few extras you can access if you are well-familiar with GPyOpt.** We return as part of `result` an attribute `result.gpyopt_instance`, which is an instance of the native `GPyOpt` `BayesianOptimization` object -- the one built and run during your optimization. It has some plotting features you can use. "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 45,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 720x360 with 2 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "obj=gpy_result.gpyopt_instance\n",
-    "obj.plot_convergence()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "If your function has 1 or 2 parameters (but no more) you can also see a plot of its acquisition function! see [here](https://www.blopig.com/blog/2019/10/a-gentle-introduction-to-the-gpyopt-module/) for more info!\n",
-    "\n",
-    "You can also extract the acquisition function of the model itself, and play with it (it takes ones object, an np array, as input), using:\n",
-    "\n",
-    "`acq=result.gpyopt_instance.acquisition.acquisition_function`"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Phoenics\n",
-    "\n",
-    "Finally, we turn to [`Phoenics`](https://github.com/aspuru-guzik-group/phoenics). This algorithm, originally developed within the Aspuru-Guzik group, can be accessed in the usual fashion. It's performance on the two-qubit optimization circuit is shown below. Note that the number of datapoints exceeds the provided __maxiter__; __maxiter__ here controls the number of parameter __batches__ suggested by phoenics. phoenics suggests a number of parameter sets to try out, per batch, that scales with the number of parameters (in a nonlinear fashion), so you may want to set maxiter lower if you are only playing around."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 47,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "With phoenics we will optimize:\n",
-      "Objective with 1 unique expectation values\n",
-      "variables = [a, b, c, d]\n",
-      "types     = not compiled\n",
-      "Phoenics config:\n",
-      "\n",
-      "{'general': {'auto_desc_gen': 'False', 'batches': 5, 'boosted': 'False', 'parallel': 'False'}, 'parameters': [{'name': a, 'periodic': 'True', 'type': 'continuous', 'size': 1, 'low': 0, 'high': 6.283185307179586}, {'name': b, 'periodic': 'True', 'type': 'continuous', 'size': 1, 'low': 0, 'high': 6.283185307179586}, {'name': c, 'periodic': 'True', 'type': 'continuous', 'size': 1, 'low': 0, 'high': 6.283185307179586}, {'name': d, 'periodic': 'True', 'type': 'continuous', 'size': 1, 'low': 0, 'high': 6.283185307179586}], 'objectives': [{'name': 'Energy', 'goal': 'minimize'}]}\n",
-      "phoenics has recieved\n",
-      "objective: \n",
-      "\n",
-      "Objective with 1 unique expectation values\n",
-      "variables = [a, b, c, d]\n",
-      "types     = not compiled\n",
-      "noise model : None\n",
-      "samples     : None\n",
-      "maxiter     : 5\n",
-      "variables   : [a, b, c, d]\n",
-      "passive var : {}\n",
-      "now lets begin\n",
-      "[TIME]:   0:00:00.001013   (overall)\n",
-      "***********************************************\n",
-      "energy = -0.29609650 , angles= {a: 6.237680912017822, b: 4.117485046386719, c: 1.029970407485962, d: 1.9295929670333862}\n",
-      "energy = -0.59038616 , angles= {a: 2.3871936798095703, b: 4.896121978759766, c: 2.3418636322021484, d: 0.12066761404275894}\n",
-      "energy = -0.26690391 , angles= {a: 5.304489612579346, b: 3.034426689147949, c: 3.76320219039917, d: 0.8069871664047241}\n",
-      "energy = +0.43135729 , angles= {a: 3.035806179046631, b: 0.9094901084899902, c: 5.705395221710205, d: 5.713986873626709}\n",
-      "energy = -0.27043020 , angles= {a: 1.9153386354446411, b: 5.5784382820129395, c: 3.728203535079956, d: 4.011273384094238}\n",
-      "energy = -0.40218865 , angles= {a: 5.176544666290283, b: 5.341585636138916, c: 5.676353931427002, d: 4.678478717803955}\n",
-      "energy = +0.30506690 , angles= {a: 2.712526798248291, b: 4.21279239654541, c: 4.61173152923584, d: 6.0248637199401855}\n",
-      "energy = -0.08816349 , angles= {a: 5.385326385498047, b: 5.44980001449585, c: 2.605787992477417, d: 2.9794654846191406}\n",
-      "energy = +0.32159788 , angles= {a: 1.376722812652588, b: 2.962172269821167, c: 2.562309980392456, d: 2.237804412841797}\n",
-      "energy = +0.66997147 , angles= {a: 2.3023128509521484, b: 3.7119622230529785, c: 2.8415794372558594, d: 2.4819388389587402}\n",
-      "Quantum Objective evaluations: 0.022472858428955078s Wall-Time\n",
-      "==========\n",
-      "\u001b[0;37m[INFO] Acquisition ... starting process for 0 ...\n",
-      "\u001b[0m\u001b[0;37m[INFO] Acquisition ... starting process for 1 ...\n",
-      "\u001b[0m[TIME]:   82.91020917892456   (optimizing proposals)\n",
-      "[TIME]:   0:01:31.765821   (overall)\n",
-      "***********************************************\n",
-      "energy = +0.36786933 , angles= {a: 2.0853826999664307, b: 4.634885787963867, c: 2.061150550842285, d: 0.26250821352005005}\n",
-      "energy = +0.01851594 , angles= {a: 0.003306345082819462, b: 1.980368971824646, c: 0.30129608511924744, d: 1.9018864631652832}\n",
-      "energy = -0.73104112 , angles= {a: 2.4472453594207764, b: 5.115787029266357, c: 2.1066818237304688, d: 0.43426579236984253}\n",
-      "energy = -0.41926522 , angles= {a: 0.10517703741788864, b: 3.627812385559082, c: 0.04848513379693031, d: 1.2869781255722046}\n",
-      "energy = -0.87322996 , angles= {a: 2.5099880695343018, b: 5.172698497772217, c: 2.082657814025879, d: 0.38423633575439453}\n",
-      "energy = -1.49111438 , angles= {a: 0.00037171694566495717, b: 2.5451977252960205, c: 0.4486967623233795, d: 1.4575597047805786}\n",
-      "energy = -0.14131340 , angles= {a: 2.2483391761779785, b: 5.067838668823242, c: 2.0422258377075195, d: 0.401293009519577}\n",
-      "energy = -0.44592199 , angles= {a: 0.15016400814056396, b: 3.554527759552002, c: 0.04311426728963852, d: 1.2492430210113525}\n",
-      "energy = -0.28994584 , angles= {a: 2.499864339828491, b: 4.610923767089844, c: 2.253262996673584, d: 0.42330190539360046}\n",
-      "energy = -0.23522167 , angles= {a: 0.08437494933605194, b: 2.5218212604522705, c: 0.10680994391441345, d: 1.9883257150650024}\n",
-      "Quantum Objective evaluations: 0.02498912811279297s Wall-Time\n",
-      "==========\n",
-      "\u001b[0;37m[INFO] Acquisition ... starting process for 0 ...\n",
-      "\u001b[0m\u001b[0;37m[INFO] Acquisition ... starting process for 1 ...\n",
-      "\u001b[0m[TIME]:   29.99247694015503   (optimizing proposals)\n",
-      "[TIME]:   0:00:39.753281   (overall)\n",
-      "***********************************************\n",
-      "energy = -1.01252001 , angles= {a: 0.0462680421769619, b: 2.7883026599884033, c: 0.03881902992725372, d: 1.1791245937347412}\n",
-      "energy = -1.22907347 , angles= {a: 4.0027337074279785, b: 0.09763965010643005, c: 0.7208928465843201, d: 3.698227643966675}\n",
-      "energy = -1.01233697 , angles= {a: 0.029933353886008263, b: 2.7854623794555664, c: 0.06852176785469055, d: 1.1778004169464111}\n",
-      "energy = -1.22907347 , angles= {a: 4.0027337074279785, b: 0.09763965010643005, c: 0.7208928465843201, d: 3.698227643966675}\n",
-      "energy = -0.88516505 , angles= {a: 0.022830920293927193, b: 2.727048635482788, c: 0.16732501983642578, d: 1.1276936531066895}\n",
-      "energy = -0.55817715 , angles= {a: 4.064866542816162, b: 1.30270516872406, c: 4.971987247467041, d: 1.681876540184021}\n",
-      "energy = -1.19048299 , angles= {a: 0.11043459922075272, b: 2.793375253677368, c: 0.01577768288552761, d: 1.239717721939087}\n",
-      "energy = -0.55817715 , angles= {a: 4.064866542816162, b: 1.30270516872406, c: 4.971987247467041, d: 1.681876540184021}\n",
-      "energy = -1.41154797 , angles= {a: 0.15773962438106537, b: 2.832333564758301, c: 0.01315511018037796, d: 1.3356469869613647}\n",
-      "energy = +1.09178703 , angles= {a: 4.163552284240723, b: 0.2528429329395294, c: 1.9030687808990479, d: 6.191180229187012}\n",
-      "Quantum Objective evaluations: 0.025141477584838867s Wall-Time\n",
-      "==========\n",
-      "\u001b[0;37m[INFO] Acquisition ... starting process for 0 ...\n",
-      "\u001b[0m\u001b[0;37m[INFO] Acquisition ... starting process for 1 ...\n",
-      "\u001b[0m[TIME]:   48.34318137168884   (optimizing proposals)\n",
-      "[TIME]:   0:01:00.187099   (overall)\n",
-      "***********************************************\n",
-      "energy = -0.98060805 , angles= {a: 0.21618297696113586, b: 2.6016123294830322, c: 0.2853825092315674, d: 1.219753384590149}\n",
-      "energy = -0.25808323 , angles= {a: 3.4333252906799316, b: 6.278115749359131, c: 3.4610934257507324, d: 5.684024333953857}\n",
-      "energy = -1.05799937 , angles= {a: 0.11564324796199799, b: 2.6404154300689697, c: 0.3493330180644989, d: 1.1831600666046143}\n",
-      "energy = -0.25808323 , angles= {a: 3.4333252906799316, b: 6.278115749359131, c: 3.4610934257507324, d: 5.684024333953857}\n",
-      "energy = -0.98552410 , angles= {a: 0.007972335442900658, b: 2.642519950866699, c: 0.37203270196914673, d: 1.1596922874450684}\n",
-      "energy = -0.94007391 , angles= {a: 5.723466396331787, b: 6.273910999298096, c: 2.6695010662078857, d: 3.162034749984741}\n",
-      "energy = -0.98552410 , angles= {a: 0.007972335442900658, b: 2.642519950866699, c: 0.37203270196914673, d: 1.1596922874450684}\n",
-      "energy = -0.94007391 , angles= {a: 5.723466396331787, b: 6.273910999298096, c: 2.6695010662078857, d: 3.162034749984741}\n",
-      "energy = -1.03289837 , angles= {a: 0.08608753234148026, b: 2.6485812664031982, c: 0.37535393238067627, d: 1.1694862842559814}\n",
-      "energy = -0.31476750 , angles= {a: 1.627071499824524, b: 6.256295204162598, c: 3.108327627182007, d: 6.261186599731445}\n",
-      "Quantum Objective evaluations: 0.024885892868041992s Wall-Time\n",
-      "==========\n",
-      "\u001b[0;37m[INFO] Acquisition ... starting process for 0 ...\n",
-      "\u001b[0m\u001b[0;37m[INFO] Acquisition ... starting process for 1 ...\n",
-      "\u001b[0m[TIME]:   68.03577494621277   (optimizing proposals)\n",
-      "[TIME]:   0:01:20.377163   (overall)\n",
-      "***********************************************\n",
-      "energy = +0.00793908 , angles= {a: 0.05368649587035179, b: 2.886265516281128, c: 0.5431649684906006, d: 0.9369292855262756}\n",
-      "energy = -0.13862884 , angles= {a: 0.7798250913619995, b: 4.2954206466674805, c: 5.3001627922058105, d: 5.039661884307861}\n",
-      "energy = -1.47627820 , angles= {a: 0.0034380992874503136, b: 2.746985673904419, c: 0.3536768853664398, d: 1.4768966436386108}\n",
-      "energy = -0.13862884 , angles= {a: 0.7798250913619995, b: 4.2954206466674805, c: 5.3001627922058105, d: 5.039661884307861}\n",
-      "energy = -1.49312955 , angles= {a: 0.0, b: 2.70723295211792, c: 0.2528174817562103, d: 1.4755951166152954}\n",
-      "energy = -0.60500240 , angles= {a: 0.7093976736068726, b: 0.5523882508277893, c: 1.441382646560669, d: 2.139066696166992}\n",
-      "energy = -1.49312955 , angles= {a: 0.0, b: 2.70723295211792, c: 0.2528174817562103, d: 1.4755951166152954}\n",
-      "energy = +0.20032241 , angles= {a: 6.004479885101318, b: 4.0001044273376465, c: 6.148054599761963, d: 5.081597328186035}\n",
-      "energy = -1.48791277 , angles= {a: 0.0, b: 2.645176887512207, c: 0.2961067259311676, d: 1.5270349979400635}\n",
-      "energy = +0.20032241 , angles= {a: 6.004479885101318, b: 4.0001044273376465, c: 6.148054599761963, d: 5.081597328186035}\n",
-      "Quantum Objective evaluations: 0.02483844757080078s Wall-Time\n",
-      "best energy after 5 iterations : -1.49312955\n",
-      "Phoenics optimization results on 2 qubit circuit:\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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zAXBITsOAO6bm+/PLNimfz7/8Nwn2mGPkzNDqQ17+RES77g6Hx6W8kOILZXh8Ht7e+jbb67d3yXy6FVF7JZmFaw6y41DHSDHVEj62Hek4RJYo/Pj7ZwAwjBxJ3gP3kxRHGXICEfD6rLb/1ijyonz79/Dtnr78q/LaVtd2bBw4mjKno0aNar3x5k+7S0lJYfPmzdx4443MmxfKx/dWVbWpgg3IFURC9ZML2nZTiTKmotGBSXDgkLXc6vl/THE/ETweCWUWN095z2aFbwQAJhwxx0i2UOxbcvx+9eSdfo/as29+XPY2j41H1j7C68Xfdcl8ulXoI7CZ2Ozq2GZiY4qK9DCk3JjiT40Ks8SOJEW4Q1tP3gP3YxgzGk12dofmk0AcaIoQ83QcWcbA0ZQ5HTVqFJ6WJOUn7QsvvDD48+abbw6+fbgkagDeyraKbLHei3S8R6oBU7OTZgz4ULU6Hgkpqek82XguZmy84D2dPXKPmGMMB/9N1uQUhKQMkpL2R7Tr7shOUUGlisF58e2XBZy9Kks7KlHbgW5F1HqNiCh0PD3Pc+35uFrEqAFcGuV4pI7KuX36U+mxtDmXITuP1HPOAcC5dSuo1egHDuzQvP7n8ccoqWApBeGLNVJ6Kj+TMqKPD4OjLXN6yy23cOG0aaFxfqJumf3R6rVGE5aso8kVqHOy8R6qinvM7dMHcfeiq3jYdSHHiVuYI67iAeHqqEUZfz2lkEcW/8IhbxIPey8CYhdy6FM96E/Ig8yBsHFzRLvujpuOuZ5+aT1Ze2gxHt94NKrodR1uf99LfaS2akeIbhX6EASBJJ2a5g4S9ZSr7qFx3oVYDSADdWaBxnkXKhuJEToqz21oRK9qXSquV+n5i3EOLn8csfwvf6H2mX91aE4JxEBHWkTFwNGWOV2/fj2q1FRlE1EM3WLvv/9+8Oexx4aUgtU5OW2EmASdNqpcQfa8mxC0rckjmsTBnNH53H/2KKwY6StUcr76Pzx8Wu+o+b5npOxllfp6pprLSMbOgBSZh84eEXWMt8GC26bBVS/hqW9un9ZJN0J5vcS60iq+2v8VDl/sEI7NrdjoD29d1knoVh41QJbpyPIQp1x1D5f32MOMp9eSmdqDUwPZHhE6J8+qKYOZ7/D4usepcdSQa8xl3jHz6PeXN6gyF9PrtVdRJZvxWePMbU2gfQhkd3Ri1kd3kDkV9XpEvR51RkZwfENDA0VFReh0OhYuXBg8rk5NBY8TDilhOJXOR86fzoma9ZEy52xkQUXNE0/grapGbVaTPT+6xMEcxyJKDAepcykPxpkD226YtoJf9Omkon48W3INmpF/gNGnRx1St9ZG486tCIb9JA+dSJ7kBfH3V9H74rrFfFn2KSo9uLwuiPERmv1OoOF/hai/v23KEZ/j5F4n41WtRV/dIqQRcYldwOSCyUzIm0CGPgNBEJBlmZ0H/h780qvMZrwtFQH/C9PJjiqKzu/Uv59Op+PLL78M+15zc2iz69xzz+Xcc88FID8/n59//jkoc7pjh5LZUFhYyJYtSpsrURR58MEHefDB1oW5l19+OZdffnmrY5I/h1o0KtLt+/fvB+CRR8LLkaqzchHUOwHI++sNJJ95cfQP2VxD6lAjuscfhm/vw5Dhglg6NJveY6Y2mR/SpkM9sZsH+HOzn15ZxakmPZlx5GpLLjeCJhkxyYycNQLUvz+SBtjVvBKVXgktuXyumPZ9kgeirbibQQNHd8l8uh1RdwZO/9lH9W4Zh6FFHufUe+CzG8Hb4o+u0sHUe1i8azGPrXuMF099EY2oYbSmL5LVirawNwCi2Yxvzx5lTIRYN5Ag698xiouLufHGG5FlmdTUVF577bUjOp+3uhrZ40HQ6xFNJsVrjjrAheDXupFS+sdue1VejOeVi9i/JAd1ZioDXv5bdHsAVxMWKZNDTj95xiJe//vNGLALxri6wshpgxAbLQh6vVL84vOEekH+juCWQjzhjCOnOtNkpPjO+ISrOoJuFaMGeH75Hh76suOa1F7Ji3W70sHa4JDwNSu5oxSdD8fe6LcSlCownwu0SdQ4atCpdLyy+RUWFC/A7fd+tIWFgOJRB0MfEWLdfNfxCsgEjj46XeZUkkAUkaxWpUIxFhoPIAoKOci7f1LKvaPBZcVtVbI3vLWNMCQOVUeXlQqHhu0N4NUmK6XkMewBmtHjEIxxVT9KqQMRzGmIghvp1y+hvDj2vLohPJLyt5E8yTi9sbPQ9jbu5aWSl6hzdI20a7cj6o0HG1i+vWONBwAONB3g+12hZa/3UIt0paFnwqBZcMMauHU79BgDH19Ddf1OsgxZDEobxK7GXTj37QNA21vxqFPPP4/8f/4TADlCrDvS8QT+R+EnagQhmPURj72+qAhxy+uw5ePo9q4mJG+L27csBiHKMria6ZmbzVa5kHV/2AT9T4k+pt9J/NL/ZmREHIIhNlH7vEi2JkSdHsFgVPK8nb/PQjGv7MZr64tt9130NEXXNwH46WAJz2x4htX7S7tkPt2OqI8k6wOg2l6NzgOyTkvqHy5A0LXYnMwbCRe+C1kDlcyCCxeCPoWa/T+S3XCQQT8+hcProDHtAD1feQVNvrK7rR80CNPk4wGoIvySNNLxBP5HIckIoqiQdTxELfvw2byo09Iw99fGFZaQvC0yRV45Ofp1/CG/gb2VXGinJ45ahV4TWZd/CQD/SZoO466Obl+3m3TxczJmjiTz8j+QMbQ5/ia63QyZySI901Lom5mEL45GJvV2ZeXucHcNpXY7ojbp1HE1Dli8oZxJD39PnzuWMunhkFhMjaMGnUdGGDKA+j+fhzOn7e59EMm5MPZKagSZLJedwW5lubNz09OYzOUIaiWE76muxvrtt/iam3nIfR52ufUGiV3W8pC76+r8E/j9QZYlEESFrOPpWCRLIKOIgOmS20/U0LrV1uHQ6OGeWtbmX44KH4NWzIUti6Jfo7GUHkI9hRlGrv/TrTA6xgany4qphwvzicdiOnEKplwXONvWKLTE0r1LmfbRNIr+XcS0j6axdG/snPmOjGkv3pn1Js9Mv4shoz+k1BZbft/uLzk3HZ5q2knodkSdpFPHLHhZvKGcOxdtprzRgQyUNzq4c9FmFm8op9peTXWqgKdXDhd+dgEb968ODSx+Ax7rD/YWVW/r/821FgtnNdvo6/aglmWsu1Q43v170MRZUkLZjX/GU1rKOvOp3OG5mio5FVmGKjmVOzxXs858auf+IRL4XUOTn486MwNBowFVHLeZ5EMGrN98Q+0mTXTSBRhzKdKoqwAouNkv6h9HDHneByX4EMkpXwaHSqIbf34zZ+26g+W3n4TO2wx1e6Lbu5pwNqhxNzhxV1lw1GqietSRdHaiEW9HxnQEq3ZZWL23nh/LfqTK3raw6HAERJxMuq5Jz+t2RJ1l0pGbosftjbyMe+zrHTgOW7oFxGJq7DW8PSeV7P+bz9Mv+lA/+UYLowaw1YC6RTjEUsbsZjuTHE60wNvlVYz4UUvTttAXTEw2A4rU6e3TB/GTahwXuu+mv+stJrie4xvViZ3adieB7oOOypyqkpIQDQa0vXujjaAdEoQsK5WYfsfbY1PFDhmkFZI+9/8Y+PNqTMf5U8KiEXX9PuTF/49BQilmvQY5Tq8dXTIfF5ex5r0H4JkxIEUJmbislK1Mp+atz6h9/S3K1vaCnpFz2CPp7Dy1/qlOHdMRPLR6AQ/+oEgQlDZEXxVAiKiTtcZOnUcA3Y6orzy+Dyv+cjJadeSpResGPLlgMtePvJ4MQwYNJgGqWmxMBrI11KHliS2lgF+1Guz+yrCBFi+yT0CbHZI8V6WEiHrO6HyenWjle91tDBP2k52si1mtlUB0/BZL2d8Ssizjs1iQXLHzbwGlKjEpVBgjZY+G0yMLMgGw9z8IpSvxWa00rdmN5CW6F24pQ9j4LumCletO7IdKb46LqHdZBG79cBNrKrzBY9HsJZ+AaDQh6vVIaKH3sRHNI+nsRDre0TEdQY34PaJe2RhscsaWaz0l/3xSqh8iWfc/0DggXkTrBnx8/vGc+Oj3WF59A2uqFnVti6eh2wYaY6uy3q3jL+MP+Xls1ilx51K78of2TA7lRKrMClEHurxMMCti7e9p72fx0OXdn6RLPoAnh8O9qcrPI5QQ7Ux01VL2qMqc/vgj7oMH8Vma8NbU4i4rY+3atRx33HGMHDmS8ePHY21Z6Sr5wG1DNBr8v6oho1/0D7jyCZpeuJvSy6+g4rF/45v6BKT1iWzvJ1irbKC0zo5HY4qLqOs8yv3QFJD7jDYmrwgZPYIpFdGgV9ISrZEJNDcpt13HOzqmI5DxoCYJAJsndh71tCEFrLz9dPpld01Pm25H1OtLG7jklV/YV2uLaBPs+tsCAbGYfZZ9ODZvxldbhzPThLHeFkqP8tgVom6BL1yKiI3aq9wkh5qVG/RDc+hGEc0Bj9r/Ja3ZSYWcjh1dqMNGd0UX6T23B3/86o9t/r23XdHTWFC8IOxS9qE1DwHQ4GxoMzYeHFWZ0yJFw1wQBSSXC2dDAxdccAFPPfUUmzZt4ttvv8VgaOFseF1QuxOVUYdhzBikhipY/2b0D+iy0nzAp+hYA1KvKa288jbwe9vNGHh/3UEO+LKUTcuo12jCJijzbPDpg9eNiLyRSF4ZMSkZQadHdruRP7spovncMXPD6uzMHTO3U8e0F7IsIwsedKIJyZWJithx528OfMOLm17stDkcjm5H1DaXl5W7a6ltjrxsnDM6n4fOHhH8PSNJy0Nnj+DMUT04+9OzkBwOBKOBY0bMQOWV8flvUvKPgRHntjrXkl8Voe+r7crmYVV9b9xqeKM0VHQjJiXR6403MM/yayHX7iA5fyj1cjJCFyW4R0R7veNuXqATaaPG4oodF4yGp59+Oug1B2ROgTYyp4HS7tWrV3PeeUrmzkUXXRT2nMuWLePNN99k1KhRTJgwgbq6uqDM6euvv869997L5s2bQ964KCKIAjv37iUvL49x48YBYDabUatbFAXLErKshKoNo0ehT/eE9LgjwWVF8oWcFWnXKmiMksPrj3nfNltpffrxwEfg7Jci2wPMeIRV+ikANHj9HnWU8IrcWAFeL6JBj6BX7OXmyP+Ps/rO4t7j7sWoVpwns9bMvcfdy6y+kTXHZ/WdxT3HhgS78pLyYo5pLzySIrqlVyVh23sbY9LaqiUejndLvuaFDW9jjyNjrSPodiXkSUFN6ugfeM7ofG75YCOSDH87bQhzRufT4GxA8HgRZBlRb2DYidNpVmVB4KYYfUmb81g9dWh8WhqkLGrkFKRhem4+IQWrHNIFEQSBpIkTlF9kGWp3wZALaCirJfUIdZPbhY6Ur0cqxIlWoNPJWiavz3g94nu5SblU2tpqKOclKSudNH1a1PHhcLRlTuf9+c9cMGGCEmITxdgFL7IPWQJvbQO6AQNIHSfB8v+Az6v0UgwHlxXJF8rdlz67FVL+Dsf+KdLkQZ/C6WMHcufXVfHlUY+6kF9/WQ3Us0PqiXzGEwgB+dlw+OFB8k+W0J1yCoJGg658MYKnIeolZvWdxYbqDby/431uGHVDXIQ7tdfU4Otl5y6L/TnaCZfPxfG/Sly96lsMdZ8grcrB8pdbowpe9f5lL1d8Xc+BR4r8rdTmxWyl1h50O4860DwgHk1qtT/tqc6meN/V9mq0fllf0aCnsWcqm07rDyn+JZ7cNp/VaLQje5XQxjapF2lqG5WGAnRJrWNr1uXLsf30E8gS9tOf4y3HJHoW9CRT/A1V9TriHadEyDiIdPw3DpV0xVL2aMucbtiwASBY8DKwsJDKykrWrl0LgNVqbf2AkHwgKw8P0WAMhSSibQ66mpE9BAu6ZK8QPSwx/hqs8/awtsKJyycxqvIjeC9KXrTHCQfXMDpT4spJfVjxwMUI464Cc2SNbMFrwzzEhG7AALSFhSSP7IngiX5/WJYsYcatn/DeQ16GXvtU1PZjATQs+Yxnn/Xy/sNedp08Na4x7YH09XLmLtNirLMiAKqaqqhtzixLlnDWpzvItsbfSq29iIuoBUHYLwjCZkEQNgqCsK7Trh4GSe0g6rNG5SMK0DdTWWrWOGoQZZDGDENTUMB/Spdz36dzqT2oLHt5Y/0f3nkAACAASURBVBa8fU6rc1w54nKkOuXJd7XrFn5ZP5DBpUno9M14pdAcav/1LHVvvAGiiorcqTxaoqcq+wTEoWd0wqeOEx3xjqfe0yrLBYiu9/wbh0oCy9+8pDwEhE5Zys6YMQOv18uQIUO444474pY5feKJJygqKmL37t0RZU6HDh3KmDFjGD58ONdddx1er5fly5czcuRIRo8ezfvvv8/cefPQ9e2LaDQiqNXoTSbeW7iQP//5z4wcOZJTTz016OEDSujD/7LulVfYO98vgRqNeK/8CkmXiWHECAo/eB9DrhgzpW9rRRPnvbAat1ci2VUBu6O0jbIchFdP5Y4BFdwze6ji3VeWgDVyTrFktWCr0uKtq8NbU4N1tx2fNXLow7JkCZXz7yGpzo4I6Gqa4uoV2XTfw2Q1gSDTJaRY/eQCZGfrfZNobc6qn1yA1iPFbd8RtCf0cZIsy12+c5asVzMwx4RBG3tqj5xbxCPnFgV/r7HXYDUKpL70FMmmfDIPfMuCl3zU175G7t8fUzwUbevd/D9PmkpP42Ae/Xo7cnktZ+1ZwbiT5zL14tcRhdBzTGVORrI0waEt+PbuQwCeqJvAtcP6MrnTPn0MRJFqjYii82HnMtjyod+2Z/RQRkceBkeIWX1ndWqMMZbMaaOrkWpbNUOmDKHo5CIaXY0xZU4DYy6+5WKuuO0KspOySdUpinjhZE4DUKeno05PZzxE9ux1yZCUA9SBKOCu8ZNbNKLOHU7hx5+Az6dU0H6dHN0D/+lfFOzfDszk6uP7MNDXAzY4IqvbBUhfl8yaffV89ss27t9+Gkx7AI67sa094K5uoPSjRvKPX4egVlH26lr63P8nVGGtoxNipLBB9ZMLwOlq15j2or1tztp7vCPodjFqs17DsptPjGkn+8MYgiDg9kpo1SKjskcxf+J8sgxZAGQbczhkhswKf18+t71VNxFZlll+cDnDe/fjlcvGkbPBQvU3MGmA2IqkAURzCp5DVbDuVfqWfIzMc6zYVcuAdA2T+2W0SvnrMky9p3WMGuLrhmJMU35mDoQb10a37cjD4HeERlcjFc0Vwe+PR/JQ0VzB/o37ufOWO8PKnEYaAwTJuiUktxvJZkOVnByUIYgKtQ40SiqYOj0Dp8uDfON6hNQI8WCnBUo+QOh3MlJyTywffYTemoQ+GrGXrsZctROYyZzR+RQczFGOu6xgTG9r7z/X/K8O8J1dwyGLnfv1RH14yH69C9GgB1GhZ6lv5I24jhDcb0GKcnYGQlVbnzRSmzN1Xh5ef/ZNPPYdQbzsIgPLBEEoFgTh2nAGgiBcKwjCOkEQ1tXUdFz9Ll5srWxi0N1fMfDuLzn7+VUA9Enpw2z3EEpnzsa+fgNZxixqzQJSVbUyyGMHbVLwHFaPlZt+uImFW5Zy2tMrePKdXwDQUs4jax7hra1vBW1Vycn4mpqgZieWpEJAYLb4E/dsOgnq93b55wUUL3j206GHjdak/B5ro6/hgOJJX7s89jW6oDVWd0K1rTpIuAHIskz/0f0jypxGGlNtqw57Dclux1Nejuzz4Wu24dqzN3rxi8eBIHgRTclo+yi50LIxL7LoflMlfHEbh+6/n6YvvqDy7vnYkk+H42+JfA2XFbdKWU2W1tspd6iDxyPZA+xqBKdXQkJEUkeXOpWGKlkzgk6vkDUgV/yqxLvDIBrxRUJHxrQXzX88F/dhz9dobc6yb56HoNfHbd8RxEvUx8uyPAaYCdwgCMIJhxvIsvySLMtjZVkem5WVdUSTuuqNtTzznT+uHCEdzeLw4PZJ5Jh11DUrYkpb67ZSUbkLT2kpyBIZhgzqzaCq9u88Bwpe/KixKw8UnaB4nMkNtYhaUDn2UlJTwg8HfwjaiuZkpeCldgf1hj4IAqiS/J6q/TdM0Ss6H3pPUl73nhRfNkZjKeQWtXpIRT3/7KdB9H9TU3rG9zD4nSCQehXv8Q6NCWR5iCJIPiSHHXxRsiyaqxFtFajMyWgKlOIpaflTUPVreHs/WTZ+sxbXrl0gCEi6HMiNUurusuJWKf//D3+5ndc2OSB3BMgR5uW/Rr1XR4pBCY34tCZwR/Go88YDikct+DUvpE9vgYZ9Ye07QnC/BSk2TB7DJxOVzV0ZaEgxkPePyG3OUmbPpuTKSUj+cK26R4+o9h1BXEQty3K5/2c18AkwvtNmEAa7qpvZU9McNQOhyaHcJP2yTNQ1u5FlmX+s/gcfb34XANFgQCNqmDR6DrpGO5LbDWMuhT6hiHK1XfGI1CgbRyluG6p0A0L1NgamD2RH/Y6gJ5V+2eX0ee8N5OYaBg47ht0PnIYY6MJh/42LXhyNys+MOMTtZRkaDyhz/OpvcQn3UHS+EosEGH/Nfw1JA2jE8N1GIh3v0JiWXcf9IbHDPfJWkCVkVMg+H7q+fTFPOwlWPAplEfbtXU2K2J7Xp2xYGgxI1fuUvYhIcFlJSUvn+YvHUJBm4BfVKLh+JaRH0FouPB753Nc56DUHidqrjlLNKMtI5YrKnKA3hDzqKJrUKbNnk/eP+3DplL+Ry6COSXAps2dT///OCv4u5uV0Oila3Q52FihE7RVVLL3j3zHP/8/ULdSaNJhPO40B33/XqfOBOIhaEIQkQRCSA6+BaUCM9hNHBlNAkzpKBkKjXSHqvpkm3D6JJqeXakc16YLiNQh6Zfk+eM5l5D38kEJY0+5Xmgf4UeNQPGrRpxD1w+MuRXXdNKjfw+CUfjS5m4IaApqcbHQmt9IsOmsQKlHApz8KHjUoMcqhc2DGg7FtJR+c8nfIGgQ/PwvN4ZfrbTDxekjKgrrdRzbXbobspOxgHnUAgiCQnZTdaWOCpCz6ZU4hula07MPrBG9VFcaxY8l/9CHUOikyKbqbgxKnosGIaDAglW6EL26NfI2kLIyZvZk5Io9UowanJ0Zud2ov3IPPxCHrSE/SYtarOTD2TphwfXh7jwPDpr9RcNMMNPn5aPLz6fXoHRiz3VGzUVJmz2bdRCVGvnZar7gIrnF06OGS8vl7nU6K6UYNaV7lQSMKAr0zYgstuSUXOqcPMYz0QGcgHo86B1gpCMImYA2wVJblr7pkNn4EiTpKBoIl4FFnK8RcbbVT56gjTVYIOqCbsD3dyc8j9YgajbKZ2MKzCXjUsjdUSltpHgr5xzBIr2y27GhQdv/dZWXULSvBe85i/l2ey1Pf7uK+i6Yog35roj7pbzA2vlJqVGqYcC0M9nePdkQvQACUTID6vWDKVeLb/0VI1aXSw9Qj+LtG1NDD1CPspmDLMTnGnPjHBEi5hUcdlahb5FELanUoMylK/Fjy+Yna6CdqnwiuKFkfV37J3tF/5T87a9CrVaS4DsFLJ8Gub8LbV2+DfSs5ZUgO5x1TQMm90xl8wvnQK0Kqo8uKxiCRPG4YKpOiHJh07ETUeimmJrVDpYRfREd8IlaeFil/na3xAXBy75N4YPRdAGy4bRqbPbHT7CQ8GNzeo0fUsizvlWV5pP/fMFmWH+iSmbRAkk6FzeWLWqwxOM/MxRN6MbZ3Oted2BePbMUn+9DnFWA66aTgH2zxjo/5YNH9uHeVwIN5sO7V4Glm953Ny9NeZubw3jw0IY2/r3+bWmcvuPpbBvQ8jt7m3sEOxO59+6n+5xO4Pal8ucvOyt01pJhT4PibldL03xLDz1ayBB7tBwdWR7e1HoKaHaD35wXb46iktByEp0dD1WZo2H/E0+1uaEmwA9IGRCXpgMypWWumT0ofhmYMZWD6wKhj1BkZ6Pr3D4Y+RIMhmAUBSuVkoIwdUJoGAAgCjo0b2TF2PLa6lMhEPews5Es+RzSZFHmDV18h55xxin2UEMui9eVc+cZadBoVdi9QsR6aysMbr3kZ3SdX8srlY5k5wr9RV7Mz8vfNZcXVpMK6uQLZ60X2erH8Zy3ORnXM/O4tZ43AroPe6sirmpbw+gWtMp59Mi779uJgvZ1Xtf3Qf/QZ2/to2NW4K+YY0edG65VQJR89j/o3x7AeKQzMSY6agXDiwCweOGsEg3KTuXPmEFArXwb98cfS8/nnUPmJOkubzu0v19G45HP/+NCGWk5SDhPzJjI418zpZgfjSzdy6gBlGZakSeLzsz5neqGSXhSUOt32A412D6lGLd9tq+Jx6ULo02Zvtevg80LpL8omkL1WiT9Hw8Z34dnxob9jPCXvATLPHaGsanxdo18QgGXJEnadPJVtQ4Z2SaVZNMhEiR23gMVtYZ9lH5IcI2SA4hWL/g0vUatF169f9Bs4tReyyqB43xoNkt2OJBgjb9xpk9COmMSgdWtJmX062t69UWdlgeQJttxqBWcTvH4avaq/R68WuXhCL+48S9EdiZr14a+QrLe5+dM7xVR9+RAsuiaCfRPWgwbKHl1IQLik4u4HaDafD32ip9u+eOqLmNNyGZYUX0PhAFG/vOcddjbsjGtMe7B093e8vO9RKkpL0X2ynZrm6E0cvJIXjU/DloH5aPvFUD3sILolUd82fRCPnz9S2cQaMD1EMsl5wQwEu9uLT5KRZZkmp4cUTS7/OvlfjMwa2epcmSk9sBihudxPaC2EvZftX8b6qvX8WmHhYIkS4tD27g2LroP3W+uCiMnKl1ba9gMNdjdpRg1r9tXz9o9b44/7dgbsdfDaNChfDwixPd7GA2DMgNReyu/xNBsNhHIGn660X/LG0UW7gwhUp3krKjq1/DaWzOnZU87mkpmXUO1P3YwlcyrJEj6fj3m3zospc7r8q6/wNrQOMX311VcMHjyYMWPGsGjRYS2wtEmA0ghXNCjfT+mE/4OZj4b/cLu/hZ+fD/7a9M03WNb5c9/DEa/TAgdWoXE3otOoGJ6fwglDC4EoZecuKy6VkbH3f8PXvx7ii82HaPDqI3vHgdZgKhWCRqN0tlGrkVIHxpRsrXvlFVLOOIPc+/4e1S6APifPZvGVA+m/qJiayhhdZzqA0ua9jKvdSNr8v3Le1zuQvdFlTtWimknmV6i46XnM06Z1+nygGxa8tILPo8TQRl0Cs/7Z6q1r3yzG7vbywXXHUnTvMuZOHcDNp55I9YIF7P7iS/ov+xqATGMmtWYwHzoEKbTyqJ8ofoLR2aMxL85m5rJ/owU2zphN/1PSSUndwZf7vuTxdY/z6ZxP0RkVTQWfKp0Gu4c0oxajVs1TwuPI7z6DcO33v83fJBDvM2WDOT8Ooi5VSFqfCvPrIov8tESAqIsugPQoGsdx4sCll7U5ljxzBukXXUT1E0+GrU479MCDpMyejbehgfKbWut+9H4rhgQoisxpeno6DoeDcePGcc4555CRkRGUOb34lot59v5neeWVV7j77ruDMqcXXnghL7zwQpvzybLMoncWYUw2snbtWlwuF5MmTWLatGksWrSI6dOnc9ddd+Hz+WjcsQNfbS3qtDTFkdi6lWuuuorvly+nf//+XHDBBS1PDI4GVGYjKpMppEktqdquJgPYtgTHyi+oe38n2fPmYVn0CZ6yUlJe+D4U4mqJFlrUerVIaZ2dXdVWTtaaEKIQtUdtorbZjc7fxMMhGpU4uCwr8feWyBqE1OdUxNLNwUOiTodcVwrV2yF7cNjL+CQfP3/6Ij6HgyfyP2X5BcvDz6cFxudPxNxrFvL+J6lqiGPPpZ1wel2M2ykj2JQCHm0cingL/jC60+fREt3So37r5wOc+NgPSGXF4LG1SqkLwOLwYDZoUKtE0owa9jRtY0XZCnyNjUi2kJZ1tiGbWrOAr9pPPn6PWpZlqu3VFG2wcNrXb6DzuBAAY0MNlZ/uwbK5AYPko8pexc6GnajcSvaHWzaRatCQlawjSaeinmSkI9lMbK9saYCo9SmQVhibqBsOQGpv5caKh6QhRNTGDGUTLA7h9I7Ceyi8sLzU2HhE540lc9ovpR+jx4xm7z6lWCmWzKkkS/z0w0989O5HsWVOjaHmFIIgsG37dgp79mLAgAEIgsAll7RYrckSNB5ApfYGNwYB5N2r4Oe2DwwAXM14nEasX36F5HAgGo1Ibo+yVxKuSCZA1BjQa1R8saWSq/69Dl/h8crDPhzcVrxqxalJNSrpeXbBoITcDs/EAkjORU7qiWAMPVwEgwFp69ew8onw1wAcXgdeWzMDynxM/y4+0q3+8Vuk195Xptl0ZN+TcHB6XRhcoQdRmq131PTKemc9/3ztarYeOwH7+vWdPh/oph61w+3lQJ0dz5416AB6HQuvnwYjzgtmOzQ63PTLUr5IGSYd222fMX/VFt51TAjGB0HZLNKNPgPps6+Rj78VwR8CsLgseCQPQz4sRut1t7q+7PZSXZJMeaXyR7/sy8vI06RwywUWBl15FWt6jwHgvTWl1MtmBPtmOoSOyJa2JOqhZ0TfUZck5ZxD/BtX/3lUySiIJIUZQJ8TYMbDypL84Z4w4brYlYktpVFnfgz2nGBpcjQPOGL5bQ8lM0OdlhaXB90S8cicunwurB5rUAkvFiQkZFnmvn/ex8Vz2qrOtZQ5/fMll3DJOSHxLwEBIsXC/QUnkldG9il50annnYtW2gjr1yhpkofDZUVGB7gRDQZEowHZZoPif0P/qW034f1EPXvcICamFrG5TPnONJ35JulJEaofT3+SfWVW2G3DpNMgCmDHGDrf4b0BGw4g1Za2uvdEnQ5Z1kQNtzl9Tgz+22/cr0o9xOGpkIfj26XPMrpU+c54m+MI5bUTLp8LYwuizqg7L+qcLC4LJftWM6tBUkI+XYBu6VEHFPTYtwJyhivL/KotrSq1LHZPMBE/I0lLs7eebGM2ksOJYAh9WfRqPb0vvZqeL7wIU+cHv8TVDiU2qa0N/x/tsatYsPeT4O+VHgvzC9P40hXavDPq1NTLyYhuKxxG9nGhI0p1Tr8HoU9RCPTEv0S2lSU493XlAQeKWtrO8GJFrZA3Eib+PyVTwZgRO0Xv8MIkyau8jiPDpCsqzWLJnPr8KyUIbSbGkjlN16cz6eRJvPnKmzFlTjdu+TWUPw0M6t+PAwcPsmePEk9duHBh6MT+tD13VSM+iwVBoyHvH//ANKwgenqerITiBINB8VwdduX/4FAYp0GthdwieuUXcEzvdHT+7khRNanzj6EueQgAeo1IYUYSFdmT4ZKPQW9ua7/5Q7KMn5H/6MPBQwXPPUvWlOyoWR8OjwO9/9YxuMAtxb6PRFtohad1xKGr3U4U9cgiXQo9wI7JjPAw88PpdWL07+GKSf9DWR+KJrWM5HGEdozN+WBVhFd8kozV5Q0SdWayDpfUQJYxC8npQNS3ju19IW/m58xqBHtd8MYI5lBnZxIODWYRp9w6NnXsZljx+qNc9cZa9tQ0c9rwXG4509+8syPhj44o1fWaqJBvYMnqcUZ+SKjUijed6++GY0yPLz2vejvU+8t+03rHziwJ98CRpeD/VzQEqtPUPXqAIHRK+W0smVOf7MPtU/5mAaKOJXNqUBu44sorGDR4UEyZ0xsuuxRaiHrpDQaeffhhZs2axZgxY8jObpGGFijhlmUEIVTFKKuTom/cyQp5KOESI5LDpWTmhSP3PifA9Sv4sT6FX/bWodco1zEtuzWyJvXmj+jpO8CZo3qQYdLx/W1TuHzmZOh/SvjYucuKNlWNYXQoVVU/aBCa7IyoHrXda8fmf04b3ArpxYJoV2y0hYVMKDgupn17MfeYuQzS9SLpuGMpf/0uvsl/JSg3EQ7N7hZEbYpDpqED6JahD4WoBXbO+piRBf4bJjkPmpTljk+SmTt1ABP6KD3izh6dT3FxM1mGLJIm9EQ6bHPqw41vMv7XBiZbS9D+YzcY0xmXO45P53yKKWUDtXfOR2gRgxL0et6e0pb8TtwsIQkWbper+evMwUrjgt7HwvSHIm/8RENHlOpSCkLvl6+Hl0+Ciz6AgWFUyur2KCTb+3jFqzKkQ8XG2PP6fJ6i9XHF50p8e+fX0e0jPVh88a0yUmbP7tTqslgypwEymHbGNK66+CqAmDKndo+dHFMOT//zaWi9r91G5lQ+rGuMmJTEjOnTmX3ppW0nFEj3k0IbdLunTiWpt4EehdbwG3dXfoXwzkLUG99CNBjIuPoq0s+ZCa+Oj+q9Pvb1DjJMWi4Y61flczRAcxhBMa8bPr6KQSffzVN/uD103NGgrHILxrVtIOCyYq0yI65eTdKxivNiXb4cebcbszlyeE4janjnjmO4bLWOnh/+hBg7+xGVw019tp5JX8WxOuwAfthezarL7+GvpwxgU81yDu6sxBEl86nZ7QiGb1TJ/yPNbQHyUgxMHZyNQasKfUnNeUEPTasWmXfKQI7tpxD1CYPSsfssZBuzybjqKrJuuKH1+YRUpr9Xhe2QLihMpFPp6JvSl/TjT1RadyUnt/Lo9oxvu8li1wmYXcqyMdWooarJyZ2rfJT0vAgMkQsgImLqPW21gGMp1VVthf0rldeBtkiRNhQ3fwRvnRUiA2O6kkcdTXcClNWB0d8oNa032KoVQatIiPRgUUVfMh4ttMyFllBeFxcXM2rUKIqKinjuued4/PHHW405ZD9ElS2yaH5LCGp1K3lTbX4+muwIxRwaI2QOVDarRH+1oU6vdGyRJUXx8XDoTKRfeQ0DVvyIoFKhSk5GnddLuVXCedRrXoaXTsLl8aJXqxjXJ513r56AITk1vH1A11obIp07F21m4bKV8MGlUF7cdozLSm2JVmmu4UfDW29Tt94NZz4b/rMDfVP78vZpbzN2wBRUKSkYfZHUq0MQ3F48eg03/3AzC7cvjGnfXry85TneLn0JlUZN/XNf0K9CbtOAuSXcXonyFAPl48a2CeN1FrolUQ/tYeZV7eMMXH9/6GDeKMgZBrKM0+OjqsmJ16fcZC63zD+Pe4PTCs8Mez5TTgE+ETx2TZA8vi/9no93fkzNt4pCXvLzLzNk29agoMrc9GPQH1b26zQIpLqVTZRUgxa728cHa/ZRtbcEbB0IfRSdDwUt9K3iUapb8yJ86C8fT8pU0g0jEXVjqVIGrvF/eUzZShFDrOVlS6LuMwWm3KmUOUfC1HtAOOwGE0RlFdQNEdjB72HqQbJGIaPJkydHlDkNjLF5bJRZYzdQ8FRX44tRJBGEqEJWG1p5zqLBgGTMh3vq2yoeyjIsuxv2Lg8ecm7fTvW/XsTn0YQn3ob9ULsTp1dGrxHJNOk4rn8mGoM5vL3fK19x0MmQ+V/R5PSw8WAjJTX+B3zYMVZkn9gq7CgY9MiSKmpBmM9qpfSaa1H36knByu+RjbGJTvXI3/C+cD+THv8e+f3PY9q3F9WuHVz9y0Zsq1YxfulyhpXKONyR75ljcsahHvI82vlPxNwI7Si6JVHjccKe70NSm6CouF3yMQgCa/fXM+HB79hwUNlYW7m7nmtfraTZZmL3qdOonN/aI800ZVOXDG6XNngzfLr7U97e9jb1335PrT6FbcYcDtbbOfNfK1m+o5pZ/c7g3tp60vwpSpleLyPyhqF3eDHp1GjVIkk6Fak0c+r3s+HXw4oY4kUgZiyIMLcktlKd0xLKlRWE6Cl6jQcUjziA4/4Mt++OHqaRfMoSN0DUPcfBlDvCbyAFUHS+kqcdgKhCNheEF6TvBpBRMgv0Kj0qMbYHByEvPNoSGBRC91ZXt0oRdZeX4/J3O28Djx0c9ajz8oIZE4LRgORwtio7D8Lrgp+eofaV16i4S9GjcO3ZQ92LL+Kd8x4cG6b7iqsJdMk4PT70GhUWu4fPNlVgxRC+7NxPxM2yEYfHh04toteIWCRdq/dbYcpfkTRph2V96JHszbD104j7KKt2foNtxQrW/Po1E96dwJba2HpvZ/Y/k1P6TqNXpZek8i5oLu12MmuDBdfefUiCgMElY3VH/n/PNOl4+bKxnDDwyOSdo6FbEnXT7p/A5+JHd/gk+YAgU2Az0SNWoEn9hYONdcoNomr9sbIMWdSawWkPEX+No4ZcbSZC8S/8kjsEs1GLTi2yqczCwQYHZA9mls3O0zlTALivtp5+fcajddoZlqPs7CZp1TTi3+XtyGaiswlqtitSkz0nxFcB2JKoITpRB3Ko2zUni7LkDhC1LCuVl9GqL50WcPg/f95I9Nn9qHPI0aU9jyJMWhND0odg89qweaKEdFogQNQxS8gDEqctO/74JORIaYDOJmgsxSJJGPzxTdFgRLI2wJJ5bZtS+EnSebARx6ZNQXsASZ8buVtLC6Iua7Rz08IN7KGXstl8+F6C/xo2DAgCaFUierWKBl+AqMPEwXuMRvLSKuNKMOiRbU3wwWURpYCbGpRwkrHWxs2f+HDuiq2rseveO6n48F1celXcQk7tgcbf6kuVbMKnN6BrTkcrRt4kXFG2gi/+cCK7zz+v0+cSQLfcTDSUrcInC+wyjCC4aKrbA2+fDTMeptE+FAgRdal9M/q8T6iynksfp7NN1scZ/c6gpu8SPL+GJDur7dUMSB9L/XlX8N0+Fafr1aT5c0obbG4wpIE5n6wGRbSmNimNjKtvJPOGm3hfq9gZNCokQYVTbUZv64AmdeVGQIaZj8GAU+Ib47S09l5H/gGaw8ROfV5FcCdQOg7K33DZfDjhNsgfE/78GgOc9+9QpgjAU6NgzGUw8+HwYwJpk8l50FxNQUEBZWVl/Badfo4EFc0VmLQmzNooqwU/DtkOIckSoiAiVUUma1mS8FZVoXI4EWuV74SvoQHJ7UbjDVPh5mwERxMao0hBT2XPwTxjBtLBzVD8BAw7q7VmtJ8kJY8cJOhgNeOvX4K4SxnTEn6ifveaiaQYNLj9IcMDedMZNfPKtnPKLYJrfuBAsQ+dulZZfWhEal1qJXQYzqPe+TWy3YaoO8yjdvtDZs4mMPdoM8xjU85lUOk4drtMfYQCqJawLF7M7vpdaPVqVPbOJ2qtvxuPaDIhG03oGnpRkBS5DP7ngzvp3VhLs7HrPOpuSdTqg6sokfvQ4GtBuDqz4jk2lmJxDABCRO2QG5BlEadTh+xwBL+4ARg1RvLufji4xJNklSn7mwAAIABJREFUiVpHLRlpPSg7ZQ7bFm3GrNegUYkk69XU2/weRvZQMmv3ghFqzLmtlnUAoiiQbtRiV6eg74hHbcpRlqqRSDMcnJbWXnKkLuiCANd8p2R6BODzwI6livpeNKIeNqf1eWKl6BWMg+tXwYFVULEBjUZDnz5HXnreVVhVvoov9n3BZ3s+47Khl3H7yNtjjmk+1MxbW99iRfkKNly6IaKdu6ycPeecS94DD5B6ztkAHLrvPpq+/IqBq39qO2DprTiWf8L+JTo8z/4L/dSpyrjKfvDiE21J0f+75PYhmgKSvv5q281LwJXSlqizBoPkY3i+shIrb1RWbhHzqHUmyB+DZd0W9P6c694ZScrrMz+HlDDVjIv/ROGfTkacHZLfzfx/15N+Un/49rqI2SheP1Hrc5VzBgSXIsEn+TC4gCQDoimJJE/nx4RHmXsAFYhJJlTJyfQ3CGhUkYMPzS4HBpcMWV2TQw3dNPQh9J/KYuEURZM6AGMGiBpoqqDJ4fHHzZQvkcVVB95kGhsdSj7qYR613WPnX6WvstGjeH71znp8kpf+m2px1Cllq8l65ZmVkaQNEfXYK9EdewNmrZnqgafg2ruXdy++iVc/WBk8d/H8U0nP6tGx0EfWIJj+ANhq4F/jW20QRcRZL8LkFgLxPq/iKTsOK6UVVdBjdOsYdWBZHE2T2lIOe35QtLsDSO0dvehFpVHaQE24Ds6KUPbcjbCzYSef7fkMg9oQV94uwLjccUwumMzQjKH4omysyk6FBMWWIQC9oU3KaBAuK7Lg94z95eOS243PFXq/FfzZN7LbFyTo4DhZF97bnf4AnmkP8s4vB9h+qAm9X7sjtepneLSvX+CrBQ5tgeI3GFdgCKby3XvGMJ6/5BjoNSF8lo/Liq53HpqckG63OjMTbS//AztCLrWrbhflGZBU/AgA3oPRq3ydzRZEGYTqYoaynwFCbWzZhXbiryNuUgSyTEmkv/o4j5+9j5+rI3fPcfgLXlSmrknNg25K1JxwO1/pZ2BrSdSiP4vAWsnUITn87bQhwbdqHDUUmHM4bXguaZdeimFE695xGlHDoo0fUfXEfNxlZWQaMllx3Pv0eeRDplZu4r1rJ5Lk73c2sW9GqKPD4NNg1EVcMvQSxuWOw1dXx+jib3AePCz3efJtMKm1cFBcKF+vbA6JaqjdoTQtjYWCsa1749XvhWfGwK7DvkgVG2D9m611OgyBjjRRNmD2fAdvzWn94EkrVDzqSDHnlQuUqscAumlsOoDAhmCqLjXm5iCAx+fhq31fMTF3Iu+c9k7UDUht374MKl6H6ZRQKEs/ZAjJJ50UPmbvsiqSpoQ845qnnmLXGZcF32+Fwkkwvw51r/5oe/cKXXN9Mckj8yNWM9pcXu76ZAs/7a4LOjhOn6j8Px8uQ7DnO1gyl9nDc7izxX0GKO2+Dm/55XUhuVzUryzFuSMkO+rYvIXaj75REoZcYXKpSz4gybuaTy92k56hfE9zd/4clXgda5VWewJ2ckY30WN0ebA9X2fhNWsqPz73KcaxY9GmZ1AtNWIPlybph9PrwugGdRflUEN3JOr6veC2MWtEHiN7HpabbO4BTRWM75PO5ccVBg9XO6oZmJlPUf9ccu/6WzDhPgCNSkNPu0D/72w4NytPbN/KNQDkzTiFiX3/P3XnHSZFmYX7X3VOk/PAwJCjBEFQURFQDIBiXMOaVte8hlXMKGtA0TW7Zte4rgoqSlgFQQEJEiRIGHKcnEPn7qr7x1cdqtMMiPdy3+fhAWrq6zTVp853zvu+JwedymF95qJB3DO+j1i48XOYUcotXz/AWV/egVQlpMhZUZzKFxbu4NWD3YTHwuGguVyIVdZ9EJXpttPBDvjEBVkfZe0YqkHHNhTL5sOcO7XMAb1RlJBSPU+0IVMIWV0FtzbRriHohx+fEruB8l9hemfB2DmG4Ql4sOgt2Ay2lPzYEJp9zUxZOoUVFQlKFzGQdDp0djs6U4RDnjFpIp1eeD4xdWviS8gnCKaGFKo5W20oPh+KZBYe07HQGyh5/V8UPPigWKfXq7MTk9DtXj8J/XJhjGQx6rEa9cy+bRSnDlSz3bjyShsg4ddbwzeX95fv5fK3V8Hyl2D5y3HnB/06qj//Bff6SFnIvWEDtW//B/mSL6D7mPjXtehxLmhu4tWaOux6GYMtQFHQm9JCwbPiDVqsoDcrvJmZzt/yc9u3XThMfLjvfr7Z9zWSTseOz77jghUy22uSf2cMko0f+6VhPCHJ9JujgGMvUH91E3x8IY9M7M+fT4xhLPQeDyUj2VPbRlVz5Av27/H/5to+f2fdnjpkjydh5iI5xDF/RSWrK1ezbe7HGHv1ZLXLxMKtCZpxm74Qgc7dSACoc9agXyFmFKZHbZd/2VPP5u3bRaA6nEyyXB1c2mk4mDMEPa89eberXhi3R5dIjBax04gN1E37hcw8VlBTMCD1NHJXPRisWtOdHuPgvNfAYI4/v26HYA0UDhJsFF/r/11/7iOAK+DCYrDw/tnv8+SoJ9s9P1QeWVO9hgu+uYDKtuQ7H8+OHVQ/MwN/B5piAKQVIOtUtofaWwmXMu7ZAydpxVvs/hHm/l0zdksJBKh++mna9jjjg66iQG0ZQa/ICM0GHTqdxJCSTLKz1Ztxojq4OZ3rP1rH5H8tB6CqxcO6/Y2Chx9bb/a2CIFO1HsQ70MdcJt7XGI2SvMhmvda2bcoB0WG7Ml1GPq6UlooZMgVHPhzMz06teHYZmLypybxtUtlu3AYUBSFPvu3c/H3PyK7XNg3beLstTLuFCWyP/W6mqoJb5E94Zyj8hoS4dgK1N42MR6oq9DvxwXcU++BcVO5/dP1PDI7UsvKtGTy3xXNPPv6XLYPGUrb4viMLt2g4DGDv7KSjXtWkFFWieP00by/fB8vLIxs195dtodTZixGWfR4mC73SlYm47t0Qq8T/0+L2i47zAZGtC2Cj87v2ITvEMrXiQ564UBR1rFmtZ9Rh7aosSrIRBS9ZNS8v3yXWvnoatBm0wB5vcUEd3OCrV3IBKjwONEcBWjrYJD6fwSjzkieLY8sSxY2Y/uDS6Pr2LuadtHmTy5m8e3ZS8MHH7Dwl52MemYx3R6Yx903zmDz0GH4E7gEsuZd7IV+Or30IoZc4Tujs6t0O1eC7XblBlj7Hvuuvp7GL9Ttvl5Pw0cf4w72gbtiarx+FygyPr24OYfKHl/9eohfq9Rauy/m/UTR+UIGThaDHl9QRjalxV/naYXI54nhDNHKPEllgMibvkk8UT2jM9/LabhrzUg6OKekmLczM1JaKKSld+KSVifd/AGsXiiuU+1SUtkuHAa8QS/dq+CkDftAr8fgSFM9SJKzS0aUZvHS5L5k2f4Y5zw4lgL1pi/g5cHCeW39x3z01rOc+8rP8ecpCs0uH+kq46PeXc+r61/FYKnF0yoaLaGMJBp5AT9N6Tr8VZWwcSsGGdLHjKXF4yfdEiG/BGWFQ41uzR06LxjEL0m0miQknUJGlCGBzWygNngEXOpD60RwC2Wpvc+GnHZGEUVbnEYjqzS+2dd0QNtI7Chc9Ymzn4r1YmZeLKp+A71ZvHazQ9ioHuMZ9f0j7uer875i7p65/Gfbf9o9P7qmDamNg2S1mfjsT/spb3KjAA0uP3q3i4W/JmjI/jQDY/1y0s8+O3zdhj2pF06Hla9rz/e2osh63Bs3EawX15skScJBz68ItWrM+UBUoBZf+enzy/hqW4s6HKJ7zBohkPEG5HBgD/0dNNrjA7XRipLRU/Paxb/VjHrRDNj0efx7H/co/qAer1FBkuAv38t0X2NOmUjUFV7O1pV5tLj0SEaRyAWxtW/D20F4g14sPoWAXofObMaQnobFD3mGLknXvLfwGbYPPZ7mr2cfldeQCMdGoA7ZZIZI8c5aLqv6JyNbf9CeVzYfnswnz7OHTKuoAR5sPcjbm95Gb2pC7xd3vVjWB8C0kY/Qo3Qg/ooKNvYx8fJ9vbAOHkyrJ0CaJXInDHGpg2kRClJeUGQetQY9fW7QM+SRe8M/c5j1VAVCgbqDKik5KAJfp+GRY5Nfj9/mxiIcqGMy6mHXwtnTI/8PeIUvSmaCi2v5y8kd0wDGToVz/xl//JOLYeVr8cebD0FB/8hQAkd+Yl73MYjFBxYza8esds8L1bGzLdma/ydCaFpNsxLpDXhU24KPl2yPX+Btxduk4FwZGRpr6d+fvLvuRFezGvYtiztf1odKJZHdgM5qRa4/JGq10dehGlTz8/JYdM9oRnYXuyWLUYcrIMGFb0OvM7XPMeEFuOIzvP5gmCESCvABY4KMunEf8uZ54nUkyqh1jsSsj0GXIunS8atfv67VkNGcmVKdu9dlQNpvZE9GUThQ+05+uH1FbwchvKjBZxa/M4M6kq2PbnDSNb+UCeER9j/GOQ+OlUCdwCbTpHi5MfCJ9jxrFgR9pPtrwxzqkF1p57QCLKpMNZoaFYL++KspfvkNSj/9lFp3LVKXTkh6PS1uP+nWSEadowbqQ8dPCUutc0OB2mxFOuMxzePmOcwEzSE2xWGIXq78IjwEocNIllF3ORH6R/mc6E1CKj7ixvjHaKmAvUuTP0fhQEHBikUyBeSlH8K18yP/H3wFlMZP5DmWcOv8Jxj22r3M31jP7roGZq9PMolbRb/sftzY8yU+XCzqsLf9d1XSNbJLXMfeKEMqr9onaG2MCXDBAATcNP1SwcHbItJvc69e5N58M4bMBKZJ3tZwTVvSZK9W5OY6WPa8mDwfgt4I/c7DlNudHnkO1ZlS1Kq9fnVnGFtidORBVmlYyQhQnGlleNcs3MffCLes0K45uAbr9mfpOetdLMdFhFK2kSPotfxnrF3Sk/Ko9UEdAfWj8pkl9P7UISnQpvKuz3iAzOFiEo+v+Og18SQkiqUszBkiQNuyRVJUmsKCRO9Wh1L8QRPI4VgRvCRpBBQqMaUE1VqxQGokQw2utW6hfuuaWYQ5KDrkcaWPoJ+dO+fzTsVibrZN4PyP93DwSsEPbfX4SU+QUe8tOpfSSTZY9Dh5TnHhryy5kOXP/cqVI2spvl1kv38f3weGG+EVOl760Omh9BTtsYWPCjvR235Jvq7XGfDXxfGZst8Dh1aLLWxGZyFSid0Ch2DLEV+agC/x2KZNX4iSTH4MLSura2LXNNA2Hke3Lx75f4nZ68tZenAlQcmKomQRxMeDX4m67uShicdS/bClmde/8+PBjsXck/oWXdI1ik8kC56oJm4oaBdbY1gf6pRxOSBprlnF7ydQU4NesqPzxuxOFAXZkAE0hJWJIKxUFUV9/OjgnlUKf/qY3bVtLF66hwuP70SOw4zFqBeCl9dPgvz+cPF7kTVr3oOMEi4b0YNOmeJ1nTWgkLMGFCb8fPC2oNODrmsPiPb6MJnQ5eSANSMpj7ouHez5Mhx3Kf7ffsVYn3riTlAVxFi+v4uT6qFm8ElYbe0rSzuKPFsep5Schi+4D4DCiyZzm+kTevs/ZhiJlblGNVDrjgV6niRJekmS1kuSdPTtqpI0AiqUHLyBKHGB6sZ23UATp/QScs0aVw0GnYGRXUq49oox2K+7Hn1WlvaB2mpwfX0DhpkL8V57J0M3tnHhC2tpnjOHb24/hZtHR+ShxRlWzhlYKGrggy6FuzdT8MAh7hh6B/X2cynevw3v0piMNK0YLvsUup/esfe7bW48hU2R259/aM1S5+LFsC88TfDhJNiu+vPuXQo/Pp14tl2IS51I9BL0C1bJ1m/jf5ZVKm6o0WKPvcvgi2vCPuHifSgdm3SeBLPXl4ebcKOeWdxutnu4a577fjsyPhTZCLIRSfLh9gd57vsEZQkVzyxaQsC2CiXgwH3wBoLu0qRrcm++ie3/WYDZHLkJ1lvS+aF0JBeMG6Q9OaQyDGiTC++uXewadwZtBwLxGfWFbyFd8SnWoUMxRFmndpv9NZ0fvUvzuNHYXN7MU/O30egSNxKLUY83IAsOf+z5y56Hbd9w8+geTBocI/uu2wUrXo0rr7gbjNR9NFPjGhhobKTmpZfwNBkT86iB1otPoPl0Jwy5gpJOA8gIJEgeoiA7nXgNYMvviyUrQJdbTsXSu3fKNYeDoKzwWP+LaLpqDLw4EOnJXGjYhbt+V9I1Jo+6k591Wcdnnx4mDqf0cSew7ag+ewjjHo1zdAvqrfzS7TY0TqMGM9hy6O9w0jNfbDPq3fXkW/PJdpgZPeEUutx/L/qY6Rz4XWTsNPKnpZHtWqCqmsqpj5K9cjGFGZEsoDDDwht/HsawrpFgbzFY+Ougv4K/GK/VgdwSCURLd9Ry1UcbaSg5M6GXQUL8OB1WxNR7rdnCftSXnFjPvp9hw6fxxx0FYLBEAv2uReLLlsgPOhVnO/TlS9RMzOwqIkpLVBA8sAq2ztayQX5+UcxZPIKBuLPXl/PgV7+Fm3DlTW4e/Oq3lIH3cNdUNLmRdH6QTSiKCXR+QKGiKbnwpT6wDUvxl0g6rXlRsjWTh5Xw1OSIKMnYqRMlTz/FOZNj7D7TO8GU3cim3Lh6M4CicwjeewxMXbtS+t9PsY+MWORKkhT5PUSXGTZ9ATO6oW8Ru1azQZQyXr5sCP+8ZLB4/CT0vAanLywzX7e/gTNeWMKB7WuFzWr0deBtxd1gpvbV1zUT5WWnk/o338KTPwn+lLhp+8DIB7ly9FOQ3Y0ehQWkdUndAPcbJcpzwJLbi1VZRUw6+CV7mhIMPzhCbKj+jd88dxD87R/QfBC/U+KC7/2kb9qUNPgGMk1sHxbA4C8HlMjs06MYrDsUqCVJ6gxMAN49as8cjUGXCh/mjBJAgowS9Oe/wkXX/V0MD4iCa/B17LYPxq2avTwx6gm+Pl/MNvzp171s3ro/ntbnd+HfYMcUo/xVPB72PP0cu2vj6Vaxj1HjqqHSeZCg1U4wKlA3OH0s21mHZ8ePcHB1++/V2wa124TCMBodEb1s+gJ+mBZ/PNbutGk/ZJYktsnMKBFNzEQucInELiH0OhOumg22qJJK1SbI6qYN1HbVmMZ5+MyP577fjjvGf6K9bPdw1xRnWkHnQ1FM+GrH0lb2JCCJ40mQYY9cC/Yez2LMXBV5rBg0zZpFzfMvcMYAQVXsme9g+QNjOX9IMUqMvzk6PdhzUTw+TUYdEr7IPSfATUu0a+bdC2viv4YNn35KzbsqsyI68LqbwN2ASxGlmFDNuXOWTSQo5rRwCUY8qSyYJSYHw55cyL9+FJmkL6Cwq6aNNsUa/xzeVhRUi9aoRn6osajoHUkZSAfunUbNT/Vi9xd4F+nusQnPC6H7XffDpBZsmaUEDLnc92orzi+PHtui3t3MFYubMGwToVEO6hi+SUdaA0lFNdN1+5ncqwa9KSpmHGURTkcz6peA+4CktmGSJN0oSdJaSZLWHpFrmlpmYFoT3L0Z5bhL8PiD4eEAISws+AvjFuRT0ewOPW+YC7viqZeQLj43/rF9LgKuxLJfU0Mt26u0GcVZLy7loa+1fNQHlj3AVv87yI40gq2t4UBuU28kWcseE1Lq9lCxXgTJTjGBuiPy7liL02hEB+pU9qYlI4RZU8GA+J+lCtTpxdBjjLYeXb1Z67IHES516+EzP5JlqKmy3cNdM+WsPkiBDJRAOqJFI5R6U87qk/Q5RvUSWa0iW9GZGpAMbUnXOFespHXBAlxecfO4/pRuBFtaKBswkMZPYprjNWWw6Anyb7mGgoceDB8Ou+G5EryHbXNo+3ExuydOxHfgQPiwe92vtPy4Ah6qFE6HIajZdasifm8h9saPZTX8d/UBVcASdf37nYBC0ORAUSKB3ayuc+miJpGHcNoU5MFiFJnOEinLhTjVctUuWP5KXNMyKAc5sP5ntpUtgYwSXsjO4sYd78e/5yh0k4xMaGvDkNUNc2YBuS0QaDgCn50kaPO5OWGHgrFRvG+dUcQfvV9K2kuzNFcT8CYIpUdJhAMdCNSSJE0EahRFSdJJElAU5W1FUYYrijI8L+/32/39vKuOvlO/Y8NBrdlQk9NLNi1h1sfjKx/np4M/AZChCxIwmOKlun4nBltiI51aa6ammQgiQa1t1W5zc6256Ayt5JQUYcjORlGtEENddJ8ps2PNxLAicZj2eE5PGHRZatWgp6n9QK0ogkOdiJrXHlIFahA18APqRG9vq5D7F8bUXR1q3fQIKHrJstpU2e7hrpk8tBNPjniPvMBE9JYDZHeZy9TzuiZtJAJ0yzMhYQDFgCLrSbMqPH3hcQnXyB4PktUaNhSrbHKjmMwgy2IYQDRqtsKyf2Lpmod1cIT+FVYmHvpNjFKL9uLwthLw6vDt2i2EUqE1NqvgcJts2hmL3lbQm3AFtXzoORsreG3xLrFTGnSZ9nzApxelRXOInqeWTNwkCNSOPBSdA8lo1Iwg05lF0Faqd8DCqXFjxTxBDxafguwpB7OD0gMm7nqnGX9N8t3Y9hkv8ptrMvQ6E+ugi/HpIdjawWk6HYDT58bmA71B3FRCfw9s8yXtpX26t4ht8wrif3CURDjQsYx6FHCeJEn7gM+AsZIkfZJ6ye+HTTVJavVqPXz7bH+TXy03k2FScPldzNwxk11NYnuWLgXxJpI5Fwwk/4bLkCzan8lmMx/0PyfsnBdCtt0UbrqEkGfNIyA1c9H0e+i15Kfwts6mBmqPsYOBumqzCKr2mGBYMAAufAtykvvepsyoT7gBrv5GbLl8bcnFLgEfvDFKzNGLRY+xcONPyV/D/+6LbLudtWI8WvFQ7TlhdeLhB+opZ/XBatTufNrLdqec1SccTDq6ZvLQTiy6ZzSPXVSA3/4zJ/dOPZjYE/RglMS1Y9ZbuXh4QdLALrtd6CwWXD5x3b6yeBdtsgQ6HbI7pv+gBrvWVZtwb94SPiwZDBQ89BCOfoWi6RxyRpSD4HciB0VioRGX2GwoLjf88A/Y/KX2OcxpXH9qN1Y+OBaD6mljDjUTB10KYyLZPI5CuG8vbb0nh8+DSCbuDAfqqDr4b7OQK7Zq6IIAktEIBgNyaA5iTJPZ5XNh8YFkEzcFK1a6VinIzcmH4TasXcWWHRshvRhL5xNwm0F2Hr1A7fe5MAUi7R3JoICkMKhNTiqqcfklfLHtoPZmnx4m2qXnKYryIPAggCRJpwP3Kory56P2CpIglKk6YwJ1rSRquUZXDZXq9zPfJrI4h+LX0KLCSCsk49YnoGQEO5+Zhq3ehbG4mP0XXM1P5bk8ZtWuybab2FKhvajyrHl4gh7a/G2kRQ39zLQa6ZnvIGjJhroO8KgvfCd1EJNlTaakgacZspME0dxekX8/VJnYzAcEJa9+V2J/aUt6fOCNRnR5Jbt7fP0URI36lL9DUXKBQDKEgt9dn4tJ6flpZh46t1/KbHfy0E6UVbXw5hLRUOqUaWXKWX2SrmnxtXDH4jtYtnYAkiRj7ZxawAJw46AbsXtP5fmtTeglU2rBi9uDzmYNl8QAXL4gOosFJTajVgN15YxXSBs7DuvASE0z++qrBPtmS+S80N9KUFwf2rq2FdntRtnwX6TeZ8LAi8QPOg8HgwWbyRBOfkAEXq8/KK43v1PM3tTpxB9bNl6PuKmEBC/pViOn9c7DnlMEd2/V7rpW/ov84zLJmxo/rb7P6l+Qds6Fr79Wg3tkjqa7bg96BXTpIvnQ2R2AJ2WGbHB68OWIm02Gzkit1YTFefSGB/SxiRKkJa8r0IQkgc4ClfmnUJRAVKMoChafgjPaqz6jRATpoyTCgWNF8JIAdrO40GMDdZUsPsh5O77m6v+JWtzza59n3p552JUAbl2CQN10APYuZUV/ietu9PHPl0+i1+JFVAwfDRCXUefYTdS3aX/5GSZxg/h81nwO3HQTnrIyAEpz7fzw99EUF5eIzCeYYIpHNHS6MB9cg4APniyAn5+P/1kI186H8UlMhPxu2PBfMW1Fp0tsoBSCLSdxLXz3j+IxkqE9X2oQCsUzHotvlnYQ0QH2vWtOSBmkQ7j2ZOECN7p3HssfGJtyjcvvYl31OnR6J4os0qD2rE6zLdn87dRRZNtNFBiG0icrebYuGY3oMjLomZ/GK5eLm57LF0Cy2eI9qVWPDRHctZ4jvn378DWq54cCdcADGSXIamMw2ldDn5GJPjMTxeDQliWGXAFnT2fBlireWRphR1iMejyBoNghPd050sSu3Q4//IN0fw1TzurDcZ1FEM11mPnoLyM4tU+hGBxgjApM3lZ09gz0mTGKWVBd/dTjMRm1p243v3aXkLqIMp2+mygH+lpjvNWjYHD7COjEdzPP76N7bgOduyTRDBwBRuQMxVhSQrojkiLPfGEid40+mPB8n+zD6gWvWubhmjmi13YUgzQcZqBWFOUnRVEmHtVXkAShjLrNq60tjx0xhHl2G9PKPqTeI0oNDZ4Gpq2YhvusHnT+a4LRQlu/hQ8n0eQSTc5nT3sWgEuHl7DigbFk27T7lpN65HDh8Z01zI9uaQNxl19KmmLBuWQp/ooYB7WhVwoxSqopxHuXCke+RBPLDSYxyduVwtQ/vShxkAdRm559M3xzO3xzW2IOdQjW7MSBeuN/YUmScVsgMmpnjTCv//A8+N8Dic9zN/2uRsrATumM7ZsfDhLtoTDDQt/CNEyG9i9nV0BkiopihA4G6oX7FzJ/z3z+PLILN/a/jyv6XZH03K4ff0TnF18EwK5m1W3eIFmXXYb9xBjFp7cVxWBHdruRYqYSHbz1Nmo+nBs+D4C0Qrh7M8bjz8Jx+umauYw5111L7xXL0dlj6HYq02TB1mreX743fNhi0OMPKsgmh/Y5asvg5xfIUNq4bUxP+hYmEJMsfwXK5mneR9PGFho+jq+I1r3xBk1LVIl1DJc6LdjMrnNc5E8UZZbB/YT7nOJMTFFVFAWTVyFoUXcrGZ0pGNpC9qj2b+YdxVafmWl/egJrbpXoI535BJLBjieYOGv3Br1YvQpyKD9MtuP9nThmM2qH2cAtp/dgUMw3qPZnAAAgAElEQVSXtUePXryclYlH0W7tPUEP/8paxoAbElRl1CbGfpdQGI79YizjZ41n0cHvKM60hr2oQzh7YBHTzhugaUqalFwCLceTnScuimCLuOhkWeHiN1bw6XbEeKtkpvKbvoDPrhD+02+dlphjactOTs/ze2DJs4I1kggmm6gPV/wKm78SvOpksCVx6nPVa0d3xSKrVPzdsAcO/pL8vc76ixhoegRonjOHBz58gHufuZqdY8fRPGdOu2v2ffYlD374AHdPv6rdNaGgrMgmFMWIQTISkFPvgmZun8mMFe+yu9YZLwBJgs/XHOD6D0Xj2OkNkHf7baSfE2ODOf5JlDs2g6JoVIagSsJ9MuT2ifioqMi88AJK3nwj8RObYjLqd06Hz67UyMEB/nJKKWsfOQPJEuJea8srHp2dgw2usOBMURRGPbOYt5fuhl/eEr47IXhbadlcT/Pc+M+9ed482jbtF+WSUi2PvGjAJTx29rv06SJ2tj3zu2Ht0xmjLnFpSfH7qSoAZ7bIXmWDmTO6lPBBVQLztiPEFzs/YYNyL/rWQ9BrPIy6A+NHm5i0KHE5RlEUvh9SzJ4hvcUItLQkidTvxDEbqA16Hfef3ZcTSrWB46cDfqqMiUvrwfJKvli4ieqW2C2mk3lpGcxUDXgUFCqdlUz9+TGm/C8xHcgb0FIDG51edNb9uNPEF11uERe0TiexuaKZmqpDsO5DaEqwRQqZToW+DC2HEhPibdnJG5LuBmHQX7Eh8c8hQsnL7JI6s+86KnEt2lWfnPEBYjjCbWsASWzDY6l5ITgKjshBr3nOHCqnPkpOWwMSEKiooHLqoykDb/OcObRNf4J8d2OH1oSd72QjsqcTM4bN57TOpyU8N7wm6MHnN3Cw0cWdi+/mrwv+mvTc8in30fzNN7S4RfB/ZEI/uufZxXittpiJ55KEHAz5OMcEaptNeDzfvlo0eUFYhX58oVAHxsC9YQMHb7sdv8cshEkheFvBaMXjl8ONQYA0i5FchxkpJKiJCdTrawKc+uyPbDzYrL5UidpWLw1Ov9aTOtTgDBA3VBrEMdnnF+WSGMuCtp2H2PnXp3CtFxm3y+Sk5cQN6AsSZ9Q6nULuWfWMOVMEdp2k4/yFMgNe2Z3w/COBZdt2ps6qx63rLmwUmg/R51AtQ/bI+BP0fTLMGfQ7/y26XvksXPJB8v7S78QxG6gBml1+mmLYF/d/9RtmKXEweXgmND79FNsqYyTMfhcvZ6bhk7WP5Ve8LKiMD9Sr9tTT55HvWL0vknU2uvzYurzLKtdPABrRi91kQO+sEsE3UcabwHQqISE+WUkCkhsyRSOU8bZHzTv9AThnRvzx9gK1NUt4U9eK+nzyQK066B3mSK6aF1/SKNtAiJJqXkzOT6958SX0Pu22NNUao85I9/Q+pJsyOa13Hr0L2vdncAfcyLKRTYeaWbWnhiZv8hpqy3ff4d21O0zP+8uobhRlWDl4/Q0cuuUW7cmr3kC/+RNKZ84k/azxmh9JNtEc1KD5IOxeRMX0Fzlwg/ZmEWhspG3RIgInTRUluBC8rWBy4A0Ew8wNgC0Vzfzz++3xAhb1bxfiePQas1EnlIrR3GtJB/fuRDFmxQ1/BpAsZsFGWfKssByIwtqVbxKoqqJC9dJZ667iyuJC9tdujnsc8f4PMdjrZXBhhNqqkySMzuQzLA8XlvpmBu1XqJv0iTA6++Jq7PpmbD7wBX0J19zQWeGsJDYoRwvHdKCe9NrPTPt2i+ZYs9vPSMtkLHpts8yit5CNHa/eRH1bzAfqc1GlT5xhyrr4mnCmagDe6IzcQYsyLdj0WbikZsx9+2oyILvZQF0qT+pk9drY4wMmayeARyNE0UoVqEPy850LjsxvINHQgFis+wB+elrwl3KTeCw4CsTUF0/ygJYIgcrEk1OSHT+SNYPyBvHNBbNY/8C1vHnVQN4pm86yQ8sSnhuCJ+BBDopdXFA2JvWjVvx+8PvR2aw4vQHMBh2bK5qpavYgWS3xzcQts5H2LMB63EAMMdoDndUmBge8f26ESqkGx0B9M8HWlrjzgXiutkrP8/rlMBcaYGd1G6/9uIt6Qx6cdh9kR43lMlhxyyF708ga4Q8SG6glcOQje/1x9DxQM2qvV9gm7NWyhPxlYs6mOU1c01ZzBtPfD+CfvSbucQA8NV42/XI8ZTVRVhA2Mwa/lHge5RFAr4qMzBnqDTy7B9k6PzaPGZ0UHy7LarawZ9J5bLrjZFjy3FF5DYlwTAdqu9mgaSZ6/EE8fpk76lbwaHMkiyqyFzHt5GlYgzq8BiP1sXSdk26l0JK49mok/nioudgQlc0P65pN37xOtPgb6D77a3L+ErEotZn01MihQJ2AopeM+B57fNi1cPLfEp+bbLpLCJu+gN1R/t2p/AY2fCqmT8dm739bB6f+PfHjh7DqTUHvG359/JivEMKil8MrfxiKEtf3kh0/0jUgaot761x8u/tbtjcml6iDyKiDKnc5GDAkbT7K3ogfutMXxKjXcd5ry5m9oVwErAQ86oDPQuPnX+Cv1n5WWVdcTv6994jBDKEZmSETJ68/vqYdUjPuXAKzrhe7maBflKjM6Xx8wwjeuzbCxAnzoo05MPZhyFOZLGc+DvfvxaNaoEYHd4tRJ46bHZHSR0sl/DgdxdWWMKPWWa3itZjTtawPVwMBr0iEQoHaYrCQ3QbBusQ86mBTM8a9VfxUuSp8LGC3og8qYdfC3wuTujvLWvGwOJDTg2LJidUrYzXE34jaGsX3XTYGRbP3D8IxHagdZr2GntfiFr9Yv62QE5oFg2PqiVNZcPECJnSfgOLxEDCYqYvNqAsGcOeI+7HoYy4kxUh3/SVxzxuyOm2IepygrJBrzaXWFS+PH9w5k045mWBKS1y6SGA6lZAQL8vC1S5RdpBsaEAIix4XX8poJPMbkNTp07EOemmFye1RQQT9RpU5UDY3ecbeaRhMeL797DwG+XffpbHJBEFBy7/7rpRr/EZt7TPVmu/2fceEWRdx0Vs/MOFl8YVPNbEF4POJnzMyQzRHAwFj8kCtjs7SWS0M7ZLJZSeUIEng8gbQWa3xPGpfK94mHVWPPYZv/z7Nj+wjRpA2bpy2ORgK1B5ffE07ZORUewA2zxK/ezkobvwlIzAb9BoedcicyeMPiBtqaMcmSWpNWyRI0aWPcX0LRHN/8pvCkxoE9XXJDHq88whFTz4R95l0euVlus38QnD0o0UyDXuR/WKXa0tXhxkYLLjMSaTzQHC72PnoHJFyVZd8wbKQD5UlXHO46G/LR5HAFFC/Gzk90VmDkOHAl8BozNUkztMblfYnNP0OHNOBWmTUkUDdrAZqJa2Ig+o4rM5pIitVZBnF7UZns1IXw4Fm71ImGPOYdvI0iuxFSEgU2YswNFxKL3t8I8mo15FmMWjUiffN2sTP23zUueuofvoZKqdODf9sxsWDeGRif9EMdCbIqAdeHGc6xaRX4rmWq9+GGaWJLUgHXgT37U3u4dHR8gpEmB3RN5XmQ8IatSGJE1moIRoKaqky9uxuQimZKugnQMakSeinPBQWLXnSMil64nEyJk1KuYa/Cm9wBdAXFaVcU+2s5oBzB78eaAEk9JjbDdQ51hzeuOI0bh/TE09bCWeXnp34xEAAQ3ER+sxMLh1ewiMT+2M3iV1hwtKHtxVZETeZ2AzZX1mJc/VqbePOnA6Fg8R1HlNm0DkcGDt1Aos9/NgYLYJ33300L/2wg283RuxoQ94dHn8Qnu8jrEsBVr0BK15jeGkWj03qHx55BzDtvAFcN6qbYBiFdlPqzUOyZGjk4yGEmVOxGXXDHlrSYVUfCWu6uB5DgZq0xBQ3eYewF9Y7Igb9E068kMyeTqhK0WQ/DAzuMQpbbhApTy3rZXfnt+NlrrqplT2t++LOd6sqSqNBTq0q/p04NgYHJIHdbOBAfWS72DnLxqybT6JrvYuFe8VL75KmNs4UhcJ//INLOpWSc3yM4dAP08CaxYQ/f8mE7hPCh/1BmUAwcW3r5tE9NI2mJpePjMBpPDXmanxPfoj/YIIAeNXXiTPefcuENeQVX0DxkORvOOSgl2huod6Q2H40hIzOIngmOp7seaIpenU7BYe622nxM/QgdUM09oajKEJ4Y0k/bM8R7+jxWJ4QO42eM6aTNnZMu2s65zqoBvZkFHPSnPlkOJKLfaJZH2aDTgTqFErDoBzk9Y2vM6p4FCf37IJRfwm3jUj8hTQWF9NLHawsywo6nYRd3RWmjRmDqXPM70KRw+KV0EDbEJq+/pq6V16l711FSKHhsyfdCifdir32SUzdu2mfu6iInot+EDfOrxAB1JYtfkcmB/9dfYAxffI5T6UXhmrP3qCirTlv/RZ0evqefHtiDjUIYVTZXDjnOTGBXIGqlz8mbZIbx+jRmlOb587DtXo1RaWxGfUeSgrdrL78VvTqTafQVkhTQW8cwcRhydsodrOGqIzadup4bMuaIXgERnAJsKDLQC4fVw05qtI3rw+ceAfs/W/CG7pPDdQ6szHiHPkH4JgO1BcO7URtz0hWZjXpGV6aDbouSEB3awGFdlEXkvR6sv50KVmJHsjnSugVbdTrMCahAt82RruNaXT5yLd2YUTRCCrSZ+NpjVhzv/TDDlbsqueLm09K/GB7l4hMO1EAjEaiTDeErd8KE5/Tk4hMxj0qMtzoYJrMbyCRU197hkyHk7EDvDtOjAIbH78dTgWnL4BNp0dvs2EZkMDhLwH27S7HCkw96Qa+8QbJSTERyR1wo0MP6MlPN+MnE2MiNasKb9DL25ve5v1llTxyyq3ceUYvFEVBUZR4868oTH59OQXpFrEr9AVwjB4dF8R44ADKzFnASn6sXckLv95MlbOKQnshj7qGkAPIuQPRx1gcFE59BIB5e+bx8q8vh9fcefydTIj2pD60Bt4/B676Go9f1jQGB3XKYOvjZ4kadLQntbcVMrtQ3eKh2e3XJCu3fLKORpePzwZuEYrGcY8J0U4Qmub+gLH3oLj36C3bRvPs2RSt+VnL7R91B6cMmMwpeRGVp81oo8vIUwjuXAk12+KmDMk0sqWLHmNapKF+38ppVBR34uP6faQgpHYY/yl/nNX5ubwYsmQw2dm01cHDs4O4+uyDfG2ipe/cnQ/HZjNx0IjUlNjfiWO69DGuXwGXjYhkZLtqWvly3SHcGT25YOwMvjnrAww6ca+RvV7cv21m5Ya9vLUkhlcZ8jKIQovHz6PfbObXA4mVgC5fgKrmyB20yeXHbvXz3b7v8NgMGuOYJpefsqoW2PNT/NRogD1LRN3W0s7IIFto+kqCQL1zgWBcJEMCT++E5RUQd/6BFwtuawjhoQFJAnVHG6IQZgIciTGT0+1DJ8usOm4MM9Z0bAblil9302a00mhJ15TKEsET9KCXzJj0OjKtJvrJj3H/iPuTnh+qR7e6dbj9Qd7d+CmDPxocVsVqzt28hQPX34B31y7avAFMBh1TJ/bn+lO6Ibvd+Csr4zypQw3Gpza8QKWzMszxn31I+GbIpz4s6v0gvKjn3Cn+uWceU39+TLOm9fb7WTp7NtjzBZc6FHzN6Xj8wXC5A4ROwWYyCLFXdHlFnUD+3s97Oe81rZDEH1RodgeiBhS0ivJNiAueiJ5ntqD4fChGu7b5bLRy8LVP2DUxInSWFZnd5/bGW7REcMaj4XORW1BNz3snMq7HWeHDWQeaePgFhbZ1R2emyfnzKxi22Ap5fcPH8tuqGbxPwVsTfz2eOGg8nS/+gPxJR897OhGO6UDd7Pazszri/bx0Rx33zNyIx5AGx1+lCRL+Q4fYd8kl7Jr/A88v2KGl6/hcWh9loL7Nx0cr97O/PkaEoOKxb7Yw+V/Lw/9vdPmwWFqYsmQK1bpWZJcLJSCCgt2sx+kLouxYAItjMkhPs1ALdj+9/TecKqNO5ZwXQoynd1K/AUu6mJHXLao+H8qorQn3JB1viIbgKDiiQH18thE9Clm15exdvbFDayyuNhx+N38rX9puUtPJ0YkS63Ec3zWTO8f14vpTUu9yQmURRTayZm8Dz8zfiYKScBscqKnBuXw5sseL0xvAYTIwpk8+x3fJomnmTHaNGRuZDtRSCV/eQMYJXXj0ljyaTdq+issorq1QgxKAqt+Qa3ZTNvR4Vr/0OH5Fu6b3oSAbtq6DKTuF73jIxMnkwBvQ0vNaPH4en7OVtfsatKUPlc4Xq2SEKCMnc5Ts/MRbUW4WdDopwVDp0KBpZdNsUf4LYfGTbNy+mPKocp2ExA0rH+HbNEe8aVhLOUZgSOEICuwRS1FJbarKTYcxWDoFimoCGNrsmiSmxC3q376WeDZKWnMt1+u30ysjydb8KOGYDtSfrznAmS8uxalOcwk1E9MsBi76cgKf/vLP8Lkh/qg9zY4vKNPiicqs/G4wagN1iEGSZk687c12mGhw+cIB//IRXTi9hyiHNORasA4bhuwRXxS72UBQVghYsoVcPXqc1r6fxaCA7qPjniMOjnwY/YCYBB4LT3NyxseRIjq7c9WLx9cnqYYdTsYOR6xOtHlEwOi3ax0nbVjYwTWihnvumm/pk5NCOg9c1f8qvrnkXT678STO6F/AhrbPeHHdi0nPj9S0TRSkW8L+IIkCteIR2bfOasHlDWI3G9he1cove+ojJvqhhmJbNfw2Ez1tlGU0osTYGHhUIouy8t/wpjoI2duKLNlR3G7ccryk2WsEvFHXnhp8vXo7ep2kCbz+gMy/l+9lc3kzjLwJhkd55FhEBh4d2IHIQNxoNaNOhyyLayaRMlEyq+9772rRqAzN1Fz6HDqnm4A58hySJHHBGj2nvm9DaYgJ1Lm92Be4ibXTP6TGFbmudOrk7+DQGDHREcLiDeIxaWOCMbMUgGxvfO9j0ZsPsu+mKbSsTTxq7GjhmA7U9hir02a3nzSLgRZ/EzvaDiCHhrkCirqFdGSKbZnG/e6abwULIQqtaiBPtyYJ1DYTvoAcvkncd3ZfLhjcG4POwI7h+ZT+5xP0DlFOsau0J68pQekisyuMvAU6n9D+GzbZhTdwIovQjmTUh4O3RsOsCBecc56FO9vJYDuascMRlz52GTMpe/srmnOKsLjih7TGwh+Uea/fuVSOEE3HYGPHRTYHG1ysOLSeNVWJBRYQCciKYiQ/3SLMnEhsjRpSEkpmM05fALtZz+s/7eK+LzdFhgGE1IZqg7Bty0HOWBsfAHYWS8w4Pw1juiQ8zEMjsiTxOG6dLW6NxwhmrxH+e7kYoKwGaosjk93Tz+Xm0ZHdQ7iZGJAFoygktLp/L4x7VJWca8ODxagT55vTxFBcvws2foay8m0kmy3M5Y6GLs2BPjsbRW8T5Ri/O0zx1PsVAmZtYmDQGTB5QK7dF/dYbeUHqa7aze6mSGnTmCZuGiGq3++F3RvEbtby3c1qHT27Of56bKutJijBIVPqWY+/F8d0oI446EUCdYbVyIEWMYKoxB354EKZSlqmOvTWGcWl7jw8orxS0eKJZOeJkK1yqRudPvxBOXx+njWPOrd2m1Waa2ds33zkUOkimqJXOBDOeSa17Wg02mqhtSr+uM95dAO10apVUep0ycU0R4Ljr4bzE9Tr28GCbbXcPX8Pnuxc7O72DeGd3gC7MztRMUCIOZatSz4tGsRItfGf3Mi9Mzfy+k+72XLIk9I9r19OP/59+kLGl55Gt1wbIZu0RGtCuzrZbOH6U7oxvDQbu9mAU+VRAxGJvBpEW5Zv4uIVipiKHoVGm4ktRRejz8oBFNFn8bYgq7MJFXlY3BqvUcLhzoft84XMv2SEUB2q/Zno5mcoUHv8srhea7Q8ZG8gPqM+oTSb84YUQ8lImFondonb/4elYRF9f10neN8xyJw8md4rlmMsVAVI3pYwBdTgUwhatBz4oFU1XGqI2Y1t/Ay5ei8uk6QRngwqHkbQoCO47YeIMOhIEfDh8Ch0ytKW//L6DEaXEUBHfElS73TiNoMuJ7n17dHA/xeBOjqjzrQZOdgq6lolrZGAGMpUMtWMuq5Vzah9Lvj147hfoscfRK+TkgbqHNWPtt7pY3N5M4OmLeDH7TXkWfNQdu5j94SJgueK8EH+97UnkJ6tKpNCAdDdCIfWCeFBR/HBBJg/Jf747Wtg8uEHvqSI9RX5aQZs/OzoPX7xUOiThG+cApbtm7mh7DtMFgtZATeynFoabDMZ+LJ3K0MzxaXcWJm63HKo9RBNvkaqmj04zHoCKZSGIIx/TuhayBt/HkHfwnRkfxYnZJ9PrjWeI65z2DH17IHJYefhCf0Z3TsPh6oFCA19DUu8Q/Vjn4wjIxu55mKUoAVFAdmXian8fKan9cAfuld526B4CLJV1E7PH3IGwZrzUBQpvGZfWindeg8DnVE8fpcTYezD1Dh9TJm5kfVRjXO9TsKol4Qn9bIXBEunpRJmXgcH13Dtyd24N2ZKzvlDOvHYpAGiWRwK+t7WSM06FUJJhicSqDf3t1F+nHaElWxTA/Wls7Try+ZBSwtuM5pAPa7rOAquvAi7e0lyZ8kOQmnYQ3qOj359tWPysnv34+JbLfzUM/7aMrjceExgTEtBnT0KOKYDdaj00aaWKaZfcByvXDaUQ62HkIDObfVhOpr1uOMofu45uh/Xi42PjufsgWrQdNbCt7fDgZWax77w+M7seuocOiWZrdenMJ1HJvSjMN1Ck0tk05k2E4+Pepxbjr8N3+7dBGMnunQaJkQp3VXu744F8O5YIQPuKGzZiQUvkpRcsn0kiLU6XfeB4HsfLbibxPtPJABKgbRdW7mo7AdKe3amCE+cBW0sDH4vtmf/QfoO4QkTbEzh540oZShBE3azHrvZQCBoSCl42Vq/lWfXPEudu45su4mHzjyFKcPvo1tGt7hzMydPpsfcucgmM23eALKsYDPp8fhl9F27kv/A/RiLo6Tt9jxkr5+0rDSmj78G/4G/I0lgbjuLJ4afS+fnHsG5Uw0O3la4+hv0J19D5qWXctrowZw3cACSpODefzOZ9f+g8Kl3OPmVZyLNwbYaaKulwelj5rpDVDZr36fFqBcOkeY0UYpprYQtX4GzhpN65HBm//g5gLKsoPhcMPs22P4deFtx1xspv+de/OXl8Z/39h0cvP12vNUucQPxO8XgY0cBBbffQel1N2vOv3CIsCmWnTFN/qb94NfhMgthTDSy7r4He7E38dSiw0HdTrqMqefzQm2ZUtaLm0xLQXxJ0ujx4TFFlJ5/FI7pQN0jz8H0C46jW57YuhVmWOie56DQXshZGf0wgbi4EIT/jEkTMWdmkGEzRrZ5oYGaxvianiRJSbmwnTKt3HBqdwozLGGFYpbNRI/MHhQWCsFDULU63VzezMjpP7B8X4sItCGrw71LBIsidgBsKiRy0PM5YfatYvDA0UJoyouiiD/tOecdLup3w6eXQHnKmchx0LU049MbyfnrDZS8/q92z685pAayQUO4fNIT7O0/MuX5wrfDgN0k/iiBdHKtyYUKu5p28fHWjxnz/PdIEtxwajdK84xJndQAyqpaGfjY9yzcVh3eFfrzCsi59lqMhWoCMehSmLIL2S+js9qYPLQTX98sSgej+zk4a1gpAIrOIXyRVe9vU5cuFD3+D8y9elGs/rqUoFU72SYUeOfdAx9OjPh2xNScNz02nocn9I/Q7UIlN3Mavx1qZleNtvT03s976f7QfFoDEmz4BCo3grcVv1NPy7x5Ya+TaMitLbT9sIiAvTdMrRU7rXOfhTvW86eeF3Nm1zM15/cfOJqMCWeiW/2i9tppOkBbz3R2FksaK4ivd37NiR+PosKQm9hi+DDgrStjcGkJC/zaxGpvnZu7vwqS8+mquDW7x53E7JElcfX8o41jOlDnpZm5YmQXijJE1vvB8r2s3tvABb0u4LmxL8GfvwoPU/UdKse5ejVKMMi/ftzF1+tVIUYoUMdM9/5izcE4Z75oKIrCrpo2qpo9NKoZdZbNyM7GnXxWLryOQ1anBr1EdYtXsFIWPyW2aYoieNXdTjs8j9pEpv7uRtjwH2jYm3jNkaD0VBh5oyjL+JwQ9B7dQB0yZkpUb08BY2szLouDX5UMrl7t1ShTE2HPbvF7rjU6IC0dp19Oeb4n4CEQMGI3G7CbDfjqzuC10R+nPB/A7dVj0uvYUH6QEf8Zwexds+POrXv7HQ7edDMutQFtNxk4a0Ah/7lhJGZFxrt7N8EmbbNTjpKDv71VWM82e1vCXh6yuQCunCn8WV4dhrLtuzAXu9Et6GLmAjFtpfa1f3HwppuFms6apaHaAaQtW8TOsePY1q8/O8eOo2WuOkEmFKhbysP/nzJrI89+V0bznDnhNcPuv5bTD67DG9SBwSrqzUEfsiLKFaGp49EIsz48Xo0gRDHaKDtuEOUvv6A5vyy9jX03n4G5Yra4EYAol7gbGXDj+dw47Suyo4ZbmPVmHpgZpPUnm/Ad+R1wejN5+c0gvfZrf0dmg55O9ZAb48cCMPayfzLsgrdItxzF3W4CHNOBOhCU+e1QM9UtHhRF4an521hcVoOsyEJp2HNcOAC3zJ3DgauvAVnm6/XlLNiiMg58iTPqVXvrWbg1NSvh3JeX8cGKfTS5fOgkSLcY2VS7iWc3vSSmK6u8yhDrw+kNwNr3YJfa2Ggp7xh/OhqhjDqaB94RL+rDRa8zhQ+E3tC+KvFIcIQOekMyIKs4D09VNWk//9BuzdlXJ167OSeTvx1cwuCdyRkcACOLRlKa1ofehWmc2iuXt64aRkYS5g9EmoY2oxVJkrjhw42a45rXsmcPnp07wj0Vu1lPSbaNUT1z0TU1sGfCRFp/UB0OV78DX91Il3fepvhZEaB/UWusrb7WsGVomEftboT6XTQvXkVZ/wH4y8vRG0QGa3DsICgHCVRX496yRQT2c2aIrNqchjcgc/rBddhfe5ZARQUoCoGKCg48NJU5//x3VKBWvUBMYs3AspVUTn00vMZcX4z1ntoAACAASURBVMOdG2bROndupLxyx6/IfcUg3YQ2pyEedWu92BVu/x/MvJbgtoWgKKxv1iZLH2z+gOe2vo8iGSPzOZ21YM0mI6cXfbL7aJSkFoMFt0lCDhgir/8I4Xb0oLAJjDpt38ps0OExSVjamiLmVQDOerqs/A9XZrfEcc6PNo7pQO0Lykx67We+Xl+O2x/EH1Swmv2c8MkJzCz7ArbNCd91ZbcHDAYko5FchylizJSk9NHiDiRtJIIoi2TZjTQ6fZzUI4d7xvdBp5PIs+WJyRynDMNYIlSTmqanLVcEvj0/igfq1gH+dDT6TRJfskSB+miyMhRFfNECPpEZ6c1HN1AbzIKXfZgUPZPHjS0vB0fVAe5b91+8u1KzOPwN4otjy8tl9N7VnFiTWqE2/dTpfHvNFK46sSsl2TYMji3csvh62nyJGSahjNqhCqbsJqvmeDREdmzD6QsFagN1bV7mbqqgUZ0cHm4mlv8K+5ajz8jAkC0yxDa1c+gKtCLpdEgWC3JTDTzfF9b+W6xXaWiSzUa6PaIVaPO3obNZUVwxPGpzGrKi8Jdt3yHFlCYMfi95X/xb9FbO/5fqnpgf5lGftOiLuEEOlqAf75uvRcorgKI+rs5iYd6eeYyfNZ5BHw5i/Kzx/FQjXPZkj1fsCrfNhS1f467ZJ9bYtTvdNJ+exx8qo+FAUSRDzulB4Po1bL3mSRa88ZDmfKvBitsMipQWcfQ7QvhrxI5VsWqboxajHkVKJ9ejQEMUKWH/crY9+TJfPn10ONypcEwHaqtRj04SATAkdgnq6/DJPjItmfDVTeGp2bLbFZaw5jjMkeEBXUeJX2CMb0Crx5+UQx1Ctt1MvdPHyT1yw94feWo9s+rBq8j6k+AR20IT033BSO136J/hmrnt+3vEomQEDL9OWy75IzLqA6vE9On9P4tJLY9UQ6+z2l93OEgrPOxAvfJvT7L/3iex5IibhrchdXOwZsDx3HXa33B0LUGflXVYPOoWj5+V+/ezrnodTn9ihapf9iOhx24SLCCHyYyEPjE9z+NGZ7FEZdQGdtW0cfun69nZHAifA4BPBNG6N96gbdkysUuURKMzE9G0Knn7LbL+dInow6iNstCULZ3VypldzuSEAlGTb/K0iEnnbjfK0n/C51eFA/WYPvnkuRN/Lukt9ZDVVVyvI28SqkZHPh5/EHtz4rFwSk21mA0oB+CrG5Ga96HPzeV/FYuYtmKaRtY+47dX8BdmI9lUkYyaWLmMggKnt2kDtcFhxxAEWZehaQ4GW1uRnG7mH/hOc77VYMVlAlzu3zcGy1mPb55wxMzK1zI4zAYdbeRj9Spa9lj9Lkw+OHj0BswkxTEdqCVJUm0iI4HaJ4mtcElVmair/vIGvDgQpXwrOquV2evL+amshj11TkY9s5jZW5uhYECchLzFEyA9RUYNkG030uD0Ut7kplHlZefZRKCudUfcuswGPZMGF9M91w72HMF0MFqh26mHb9TicwqaUbQlZNAnvK6PZqC2xcjVJenoz3s7/1/JJeZJ8OKinczbVoctT7y+QDuBukVvZXt2V9LS7ez26tmzK/n081ZfKyd/OorhLz/J/N8qOVDv4oOfxXY5mYPe7UNv595eXzFxkDD1cpgNSIop4fmKS9Sb+xdlcMfYnmTZjBEtgCI+WyUkeFGDaN2bb+FctYpWbxtICoMdf+KDS28ChCe1qbtKkWsRTXPZr4AkIZnNfLkKlqwVP69oaRBWqYqCUrdPsJxOf0B4upB8kEJTWo4YnHxwjaZM5fHLuLMS29TqCgrhunlw9gzY9DnZp3Wj98/LeHnDq3GfS63Fy72324XtrCkNqkWjzqMKdvR2bfZqNtrwGNVAHSpBrHwdWQ2iIZ51CIX2Qnp2Og6dywPf3gG1qYdAJEX9TizqhmPi8OGaH9nNBnJH9CeQFdQEaqV2J8aAhNuk5YL/EWj3mylJkkWSpNWSJG2UJGmLJEn/+MNfVRRCgoEQRc4piwytZPHTkfSi+SDy7hX4ZB8PfvVbWE1Y3uTm46++YdOXM8TFGAWrUUdeWmq5cZbNRKPLz18/XMu9M0UmkGXOQifpyH3hM/ZfF1H2vXr5UM45rkhk1LXbhP1n6+Er86jYAG+fru149z8fHjp0+Nl5KkT7ipTNg69vjvuMfjc6D4eQC1kHoPj9XLv0I7rt3UxGobghWtsRvZwfOMi3/ZyYDTpaTHYMbS1Jz3UH3LT6W2h2+wiq1DlCSsMUFL2rT+7OnWeI92E360n3jufk4pPjzjN17465Xz+O65zB38f3wWYyRNS1viCS1arhUStGO4rXi85qo8njIeAqpTgtn2afuHm2LfsZ59r1wnXOYIFe41H8CjqrqJcfdO5AZ2hFDthocrswdSnBNnIkit4ueNfHXw09xvBjWQ3zRkwOy9hD8BtM/O/EyaIG/N4Z8MmF8KWYxfjq5UOx3Xp73BrJYqHonrvD7wEIS8qrnIkbx+HjIVMyaxa+rGy+GSkhlWpNvUKljGDe8XD9AnFw3zLkciHICfGsQyi0FzLm0nvIv/5ylHUfQnWSeYvtoW4nOeYAjlEj6FWiHfxsMuj4+NQDPH+pIzI4A5ArRdCOlZz/EehICuUFxiqKMhgYApwtSdKJf+zLisBhMeD0BhneNYvVD41DMdSRLSvYfVo2QE6fZtIH1eP2a/chw+VNDPptOija41/dOoqnL0wynFXF1SeV8uA5fVWhjbhr6nV6vrHeQ+fV+3GtXMXOseO0E6/P/SecMQ2WPX9kbziRV/QfAWuU3L38V+FjrD/KmUHNNjGZvYPz7AJNTZy+bw05TdXk5qSjs9noZoyf/BwNee432D/7AEmSCKSlY/THU8RCCMvBZZHpOswGFNW7I5no5fOyz3l53Svh///llG48eurfEk4uL/rHNAoffohGp4/a1pAPTKQsVvjYo6Sfo4qAHIXIDiE71lmtGEnDf/AWVlX8woQvLwSg9pVXqH/3XVEPLjkBrpyJbdRpZF97DQCbPR9gSNuMc+ejlNj7k3722XT98AP0mTkQcIvfq7uJXTVtvER3Mh99DEO+aPIaCgpYdt5f2dr/5Egzseo3URIDzuhfQL+rLqXoicdBHQhgKCoi69FpWM5R5zh+LjjP9fPXUvHQw2HL4Vg89qWexs8+h3SVPlg4iJzSPpQ88DC9h4zVnHtx74vJzClGbou6QTfuRzaKG7cSI1NXFAVlSH/sf71RbF6PlPlRvxNTicLF3S9m5tZ47r/fr6cld4CYbqMiWC2CtjcB2+Voo10/akW4EoU+NaP65+hMkuwAHpnQj3SrEYNeR366hZFFJ9B57Qdx51myAnRSasVtJQo2ST2QYN5ZexjRTQTNuz7fEB542zxnDp6nXgw3WQIVFVROfZSXfthB135BrnV/JAz8dQbBo07lh5EIiRz01n0gtqaT2+cVdxh6A5gzxPMEfVr+99HCzoWwcCoMvDASDFKgrUbURCVVwtv1P5/EDX2NRX1FNUGzqHNuOe8apnc7m2SzPsLBWDFhMwnBixK0kWfqHrbLjcXKypX8uHsrh/aM5rlLBnNqrzyavc00eBrITjKH8/mF25m3qZL1j47XMIIyJ0cNLr78U+SaGmABOruN4kwrO586h3M/+ZFDAfF106k1ZwZcAPn9AUgbNy4s1fYpThRZfD4hiwMg8lm/MwYmvoTHL0ydcs4/j8ILI6+hF3AbaJWz5jR8AZllO2vpW5ROVqdOdHrxBdLPPJMd1a2MfHEpr/WsZmLtdqgTZQbP3ko8e6u584Y7mbZimqb8YdFb6HsogHfPbngoYrKV6fVyWcn5cSPFih3FmC6+DINZhg/Pg9OmQNMBDMXnsnWkm0CWtlTS4mthzMejeKj7TVxozEZ3pIG6bhdLc7vgsj3EIddLgNa7I3txJZevriY4tg19utgZGK79hPd1L7HD2jfBAx5ddOibKUmSXpKkDUANsFBRlF8SnHOjJElrJUlaW1t7dKYtAJyu2kSu2F3HSz/s4OzSCdysxPs6O6tNVDTEf6mtePFg0gQhpzfAte+vZtG21KWJBqePH7fX4PIFyVIDdc2LL8V1wv8Pe+8ZJ0WVhn3/qzqnyUweGJCMZBBFRAQBAQEFRTFhwBwQwy66q4Jrdl0XXePqumbFjARFUVFAkBwkh4FhgMndM527q+r9cDpMT/cM4OL7+P6e9/oCdJ+qarqr7nOf+1z3dWl+P+eveI+plX+Pu6yo4ZatqlpDLNNtUpstXxNnkZxMDL0HOp578ptdoohw3I+XouetFpmMLhKor1rm5JUtrW8ONhytYZdPZK1WiynBY7M5ooFaUwWP2mLQofqLOT/7KU7NSaFYGDlGVQ1YjOIaR11+pi28gVk/Jhs4lF06lZqXXsITUc4DYXz8yc2DmdSvCP+uXQT2Nqlx+qJqexZWVqxk4hcTQecGKURQCSJbIoa4Y58WbIMXB6M0NsbkEsKaF5POhLnoHZYfXop37Vr2jBqNv1YWkzAIHnVYyCXI7kZ2nzOc2tdfJ9y0q1bWxfXaTQ6c3iDXvbmW73dUUf/e+1Q9Jdy1zfom+iDRycCSiRpSkSwWxnUYx+zBs2OnzbPmMXvwbAxWO5o/MYOq/OJjdg0YiOdQWcLrBxsO8tOwHAznjxKJzoGVEGzE0rs3w1/5jL9N+FfCeLPeTO/9Gj1ueZGAkv/bM+r+V2Nen8+T/wlj1SeXRI2KTG59CPWzu2JJlNxhEBde+S/uOP/G33bNE8BxBWpN0xRN0/oAxcBpkiQl3dWapr2qadoATdMGtDlGFnQi2FUpZCJX7qnl+e924grUoQ1/IEkbuWpTBvWHOmFpxmdMk4NIzZpdXL4QP+yspqqx5WUywMq9NVzzhuDlRksf4SNHUo61uj2YmukDt2gu2xr0xmSTXL/z5G4kRnHmHdB5lLjW7xKoo1zq46vV2/yCeXHWAMGwsW9Zi/Hbxa0dgsnTSMAmJu5e/ioe3/kp/oOpO9TSTGkMzhvFme06kmM3IcsS704fxMUDSlo8vz/sR1WMscD73i8H2Xk0gC9FTdu/axeKq0FoUUfGS5JE/3aZ5DrMHJl1nwh6qgqvjcRQt5wumzaSNmYM6yoOsN+1HzniZt8QaXrRokav7ioINnLojjs4eE1EklT20augGGPaNoJyBZqiEjp4ECW7D1z5aeQLShPuLnqZcFUV4SNHqHr679T++zU+XX+IGR9E9DGigdfkaNLJqCNcXU2ovJxDM2cSVSQVUqeR8XftQNMMMcbViLZxYaY3Rr/BuA7jkM1mtKM74bEimJ0OT3di36+iSeeIkrhZvKl6E7OXP0C1zytWwUc3Q35PtKyOZJozE7SoAYyyEb9JbNir5oL4vtWJovMo1KAZQzhOwWyKaHlD2fCZsK07upXQkn/Rect3jCg+8dX6ieKE1rqapjmB74ETV9v5jXj5h73c/dEmnL4gDruTcz46h8UOh9BCjtprOQpQzflkte/K45N6xvQ7jHqZwW0tmCyJy+7oMvFY3URRBb3zexUwKFIGaWn3XG9tgaMTsapqzi9duG9hyxee+C/oMzX+75MtcRqFzykyEIM5ojN9khHLqI8vUEuhELLDQVqeYBsMPbCWnt993OJ4TdOw+BoJRTz0huab6LF1Bcrh1I0PHdI78Mp5z/DWVRPITxeBpUsR3LPyGr498G3KY7xhH6qixxbJqO0mHagGvM1q2pqmofl8SBazsBMzxhOGhZuPsGJPDZLVIlQeQx449AuStxbZZEIyGjnoFBOzXScmt1pfgxjv9cLH18LmD8GUJpglVgsBJYBCiLM7tiPN5EDS+WIyo6rP28QQ14HNKBpvwk1WuuHqanZXuVm8JbLRN+E5SG8LWR2EUBOClhauEquhxsVfYfCIzcOEQB1oRPX5Y6YBrkBcXL8+IIKwLAVRy9bEeNd4qgjvF4tyS3pi+ciit3DjYhXfZTcJv01JgpuWU/3lFrb27c13B79LGC9JEkpUyKn/rXDVFyl/x1bhc8LB1UgeDz4j2AzJNWdNEhZcakgWq5udi3G//whVsx7khW/+kTT+ZON4WB9tJEnKiPzdAowETo43+3Egyvpw+cJYbeKHL3YUi9rvlZEfZeTfUDUDktnCBX2LWDFrOFNPKxE36GXPwbWJWVlUi7q1hheIB+oxpxbQKeIdlzvzTtRmZgOS2Yy1bwtfZXoxC/ctTOKXzl45u+Vg3eOCRE3q3ytQL/6TUOu74hOY9MrJP/8Jlj6cg89h8ePvUBVhEQRsjmNqUj9y2aNsPkMYFkdLJoqzdUpfU6zaV8+22m0JYvRNocOAplialDL0aJoRX9SbcvM8QQ99MBM0Ddm1J6H0AaJm/d4vB5HNFsGjjgr6Vwc4+uhjhCoqcEUCa7eM/gSrxiJrVnJuupm2r78GUiTomxyoPh+SxYqExDNDn+Pctudilu1UeurjUqpH98LbF8aOuWtUF766c2gsUOtycghXV2PW6wgqKoqqQefRMHMLjH0q1nIezaij+wR6p9hDCITV+G/73hT0ubkYi8VEb9QZOb1AcA2cAVG2MhmrMZgTtVHUoEZYBrM5MYmK8qI1j1cE6kh3ouJ245XDLD24NOk3UiKTRJKQ0/Hi4Cr4zygMHjc+k0RxZnJpVTKKVZ4a1kHtHqjbS0gn7reVR1pfmZ8MHE9GXQB8L0nSZmANoka94Pf9WHGIQK3g8oUwWsQPH3Meb7K01ny+BM+2LnkO6r0hqsOWJF+/qLvLsRteRKBevqeaYFgsB9PHj8d152VUp4EmSehzc8mfPZuKiTMJyc1qWxGrqrnr5ybxS/2Kn7nr56a+cNUOUZuLwpJ5wm7exwVLFniPP6id+PkzRbNR76nJ70UCHLMzxJ+b5wl2wre7Y4yJsC0NU8CHFgymHC9JEkeMaciRAL26VgSYIwdT08Q+2/0Zfd7sR9/HPoo597z4nahp+hV/ymu8OvK/TOt8H72KRVeo3aQH1SBKH5vniX0IVzlatBFl13z+2nYrlw+Kb0bZY5rUZjSfPx6oa3zUv/02SkMDjcFGNMXEfSPPZsc9T9ApJx9jcRGmTp0SyhKqzyc2GVUdN7ziZeH6MEfqYWdVVdycINqB2PFcyIivlKKB2tyjO+GqqphIUyCsiEaUshWRf0dKH0oQ1e3G3F1sZEp1tdwxohMD2mVC9wkw+A6o2kbx3H8KdgiQac7kpXNf4pfLf4kxY4oGHiavXyJtUgtL+I3C0LYpzHozPhPg8aEVDRClj3cmo7o9+EyJgkxRTO4r2CfK4d3wzmRhtHAiqN0NgEM1kdemlP4lyeyViSNLcPXrgZyVJ7jUtXsI6sV9pzVr2vk9cDysj81A32ON+71gN4lZv9YdQHLU4jA4SI9ulJjTReuzuxLV70/wbOtemE6nXDvhdW9BThb0vCj2nixLtM+xkXGMQJ0ZqUu//0s5d4zoFBOHcpw/jsvkd/m3aTrps1/GVNqO0/pMhNIsUZN2HRKTw4gHodcUjm54JOX5W+Kd8uPTULE27rgybf7xfFUnDmuW6JD7zxgYcqfIqk4mZFk0GzVHNMBFs1JXOXx5Bzm153PjDhm7STzg2UViIg7//DaG5X9JGh+sque/+iCWviKj1iK78f7a1NRGb9iLQggtpIupJtqN4p7xV6yDtZ8kXSNtPNw3Js7csZn0hBp6M/H04eK3jozXAFuBH6PVx4A9z8P4+AaTzajHG4jwqP3xQK1F2spliwWTlovm7Y5O1jjYeJAMUwamsqN416wlM8cmHLY7DEP1fYBssXDAWYne/isGYzv0Sh6SakFOS8M+bBj6giIoQ8gRmNN5ZslOGnwh7i4qwjFqFPr8PHxr1iaYB1i/fxx2LYYLX6Fz58m8N30Q3fJsWBctRHG6cC9bhlJVzV2Tz4p/oZGmnYTvOOQloATizyiIZ8GVuG9Q2Vblm1yZ/s027kSglpA0FdVahE5vhj3fom4uTDINiGLqgOuofyANa4cs+Pph6HN5aju7llCzG6zZtBk1jsLCAgwp5IT3Zmzlz6N3slnfHcJ+qN1LSO6EKtWDKVmZ82TjD92ZCHFN6reuPY1ORX5K0kri0qSSJJZgnmravvEfMi+9NHbcae2z+Oausync9Y6o7zXBOV1y+f6eYZTmtD4TGnQy/duJWTMatEG4fqy7Yh0DRl8FgOdnoXUd6D4Z7c4tSVZVudbclOdviXeK9XfOdKOIMkwOrkytgX0ysO2LZEOCJgEuhpCPtE3L6VZXFvvNx54p2v6Vb/6Rcnxw4XMEXn2RjIjPos1uocqSQSiqoNcsQ/aVC6OHpg+7w2RE0gz49y9LeY17Vz3Mxzu/FOUBoHdxOi9ceClX97w0tv8AoDdptD27DnthAM11KMEKzmbS4Q6EybriCvIf+KugbhYNQNXEPSVZrXS2jiYvcC1bj1Zw/mfn899NX+BdvZrKRx5B1SLBbOB0sqdfh+PcEWyu/hVLydsEOUq29xo6Sjegczgoefkl7MMiG3p7loKmsbHcyeYKF2ljxlD83FzSx44l74EHyDDrKM60EFbVeAett450i4HBHXPIdFgwdeiAuXs3dNnZaEqY6saA6NKt2wfr3gBPNQevv4G6t4QC4aL9ixj64VBm/TSLJWWiYaXq6Bkc+jmxy7FvfpBBF1+ALCWGoFPST2HaQKFRrc7/kwiKgOIL4DaCOWI60BR1SiPKhaMw9z1TvOA6QbnT2j2Q3YkVIyYwZKeB3ZXJ5TZnpKoSuuQtuPBl8NUR1qx4TWBqbvr8O+APH6hHds/jnesGYTfruaTrFK7pcU3iAHsbcFdi7dsXY0mKDbGgN6UW9fHg8w0V7DwqlmwjnlnG5xuEDKRe1mPUGdFnZmLq3g3Pyp95Y8V+uvz1Kxp8ibvOmqaRY05uxTXrzMzoNyP1hS1ZEHCBEhZZyxvjRPfgyYa1yUbO78H6ANj4HvzcjP/dJMAlwBeiwWSLBWr7WUPouOwHTHKyID1AuE5kzjt94ja2GfVMG/1XaiZdnlCWAA1c5fh2fgka2E3xLM5m0qMPdqbAk0wDVIGvTBL3f7k05o6Sm2bmjE5WaoPlaM1KalEc1rJ5bXm8g81m0uMJhrH06oX9rLOgsA9cvxTVKGq/stXK/WO78d3dw5A08dBXuOriCnqZXWHg9aAqZF99NfahQ6nxiE27bGs6DrM+tu8CxKl22+eDJOEPKZj0cqzcY+nTh4wLL2BivxKW/3k4uU07dE12yuu8zN90mLqt26h76y20cJjOK5aTOWUK459fzmOLtic0MXnXrCFUKVaH0br0j4d+5OcjIoEJhdPxB/ITjJFPOW0O5/e5J+m7M+vNtBs0gpz+ErIanzgtbf383E3CvC9Zk/2uH+7i6Y/uIPjje+L83zwYK10dE5vnwcGf0Q6uYuuK8RjbPoZelxwWf9nr4sUXwlS//LIQG7tnD+l33s/fzj+dbEPpsa/zP+KYpY//0yjOtFKUYeEvn2/lvB69GNG5GfXvkndRFR0Nn36GtX8/jO3itcEnv9rBdGc92SWJmfMbK/bz/c5q3rr2tBav+/mGCu77dEus07HC6eO+T4VOwQV9i3h+w/Pk2/IZesYZ1L31NjY10uIeDJNujS+dPt/zOb/W/cqY0jGsOrKK+kA92eZs7h14L+M6jEt98WgA9TtFlndgOfS+NPXY/wWF/aDjSNjzTWLQPpmw5yZbJKUVxrWPmyAUNOCy2WJNIi+vOcJHaw/xfWby0hkgLGUCGhtcomU27rGpwI/JWbtPU7BoWsJGn82kR7dvOlOtW4HETCoQzTLVOD3PH1L4+8q3+Pzgq6weNgvrgjtBCeGrMXBoRRaFQz08aZtClybXmDWmK2FFI3joEMF9+7CddRaSJKGFQiDLyBYL1359LcX2Ym7oPgtN1QlNaotoW1eze8KSG9DSigiVXoQ+K4s6vwiIbWwZBC1fsJ2fgU/Ye94YHKNG0XQN5w+pZNuNbB41jF8KPLw8NEC/xiwmDbuFMX0vSfxSjXZW7avl3o83s7T0KMF//p3rtDfZS7VYAdrPxR8eGSt5aJroI4g6kDcEGjDpTORb83FGPqNkMaOperHKjGDvlMlohiV0ezcxmAaVIJ9IG+jTo5o2wfhkkNvJw8OSF11VsnaORW/hgpfXU52xmqJBkWMipSug5aaz6GSuqWhhicnPa3COj4zun0HOFYlfi86MOQihir3w7kUw7H5yu5zGjMvbxUqivyf+8Bl1nSfIvLXlvLdmFz8eWJ+syZBWQNgT4sj99+Ndm+gmElZU5LAftVlda1elm22HXbSGp7/emdSO7gspPP216Mb6ofwHfiz/EdvgwRAKkb1vG0BCw4Un5OHptU9zWv5pPDH0Cb688EskJC7pcknLQRoSuxMjN/vvwvrIai+63uD3y6gjpamE7rd2yToZGCyoYRMTh3ZHF7HfCnp8nL78c9wF05J48xgseLPPICzJWDJEbTrdauChhjWc8u4LKbP2Pv4AlzQ0cl6PeMnplmGn8M51g8R+QrNr+CJ8Wk0zxCYPly/EB78IuqG/21joIMoMSkgm7NPhP+0O5qtDEuh5BekWSrKsNCxYQPkNN8K6d+GlM8mZdgldf92KpNPxa9UBfj0iyg6aaqEh2BCn2238BNQwysKH2TtyFM4XHsQQ0aLunJNL/w56fLpdgrLncaPsXRdfRT57KoO9S2mQVqEercKpecl1atz1ShULPnycsa/P5chPb8HeCO1t0T0UHBSSCOVlvxCWYY9WyUU/hTn/40N40z6gPLhcdJ0CmhKRXa0Xz4Uz4CTdmE6GOSOWXcsmc5L7S01dOdu8yWUMRVN4atXjrDPkoobjQVkNStgUDUu0Db0JzHozPkMYNdjMNOJYfQxNSnBKWEJCQtNrpK18PGmoSWfCZ4TQ0X1Cb/614dTd3oMeK/9F5/z/v0bN/ho3f/5kCzrLQT48fA9ba5rt6B5cjfad6JySnrREPwAAIABJREFULYkbE13y07ASwKUkalg0+kPH5FAfdqbWfjjs9LFw30IONBzgh0M/cMnBh6i8/0p0pwq7LXeTQG0z2Hh15Ks8OuRRZEkm3ZRO16yurKlsXdye9mfBlZ+JzPP3kDiNQlXEjrc5/fcN1Jqa6Hg+6d8w/IGEpbA29lkMRSXY28XLVzaLkat2fI2r0ix489ElvTkDxj+HlzY0GG3YIr9lusXAKLsXx+a1SUwfgFFeH3erDm4bHheKKsmy8sqOh3igcYu4BpHgYMnEP1Loj4lORhF4bSZ9zP3bH/aL3wpQbeJzN3YcHRsXxaZyJy/9sBeibicL7xfiQS8NRtryEQC+sBuPLzIhKGY8ocZYe7W2TGiNRAOXvP0j9M5NmHQm2malc2qBmHgag43Isoq6d2Vch91Vzl3+F2gIvos5BPV2ifpIF7ajMUSV9i65P8RrwXhrGbR1DhPk5ZSVrRVjJYn8eui9X0OTQlSq78Ciu8VnigRqefd82DwPV8BFujmdDFOTQG0xx1UDI9D5Q4RTPIMmnYniGhj4uoq7Kp617/o8nwV789g1OLkLUJgHaKjBFOGspTJbs/fUkDhWMWjIKVZ7BaZeIFsxVMT1zis2BFn6ySes+OHvLV/jJOEPH6jtEc6ybBD1yLZpzWhqRzejrn0HSHaY6JrvoG/gFVaXTE94vcHfumkAQGELprc5+b8ye+VsAorIEA4GK7lX/oxNoTXo0zZw58qL6fVmL0bMG8HCfQs5NefUhE3DgfkD2VS1KXZ8Sjjy4ZThwt359wzU4QAsfxbOvPO4tDh+E5paclVuE9QmSRLt65d9CGf/GW5ajtR3KuvnvMRHTbJtq82MW28mUFsnlq/dJ4g3Trseek3Bf/s93Dji3lgQBdBlZAiD2xEPJum7BAwWQuf8NeG1XZWNbKuq4FBjBZw6WbjeAHQ8F6XLGBy6XFCscR61QTS8QCRQD74N+l+NFmkG8eki9fUmgXpNWR1PfrUDpUokGWqEG16/to6qOX9G3fQhmuTDZrAjyxJWz/l0to7E0rs3p1wqY84UQTcWqKUAU3au4KkzX0DTNEIh0aDREGxADtWhNrMjM2kBdI2i2cRpB48ZgjrIcGsE9V50SmIQNah+/qSfh8XpiwX1OjtkuAFNwyN54mUlDczZQfQmPyx9mAkdJzCt+zQyzZmEI12CxtJSLH36xGrkAPqAgmpOFgGTJTkmZap2v1xM4qoEqsRqh4FDBcksIrPOjNckoYSTyyKpJuxU70UNGRSjlvKYLFMb8nVupEATmaOghM8E9vX/bfkaJwl/+EAdfQhlYw1G2RQT7o/Bnhe/gZsF6o65dvySmW01iRt8x2MacO/oLknt6BaDDlPu10mcaIvTh/OdJynI/JS6QCUaGlW+Kh5Y8UBSU8tp+aehaip7nK04l4QD8OvnUL1L0A/zev4+NeQdCwAJls45/s2XE0WnUfDnMlFmmXclvH+paKEGoR287ImYQfHXvx7l843xrkK7SU+DyUYoqkkdFb+PtNd7wuA2WmNlCYDXN9ejejxoXS+A4X+Jfw5HITO6nU7/NW/zl8/i5qVryuo4UB3CHfQJzYvBtwlXnvoyShwlzB3yEbeffiEmfYRKJ0uYIlzemMiTNRvVJ2gBbbLTefqiXvQqjk+s0SBv2L8IEBxiAE+licZyHZ7v/gaShsMgSjhrZt7N38dfhGyxYKQi6msbLzPoNYqcFVz3ag2aBhvKxKTv8jeILsBw8mN9iivisxjJkJ12yHRDfjh1R22hVEsbr456u7im0y5hVMDmTzxGb1ZpP7KGtGI/uA4xou0IJnacyIOnP8iXF4oSSsZFF9HurTcTjKSNfgXV0oJaoy26idoNZm5FnSGeFZ8x2YEcYEz7MbTNKhbNKE0R6WNoESMejGleRwP12WoIKcUx5/fNoL40gJTXpHEnJAJ1RiBZbe9k4w8fqGOaCcY68iyFya7h9rzYjS830841hxv5b+Hn9JL2JrzePsdGt4Lk7qOmuKBvUawdXUK4kj8+qScNoWTBqaxGmPKtj+5liVlySA0lNbWcUXgGK6auoEd2Cn5xFEoQPpomeK2dzoWbl/9PDS+fb6jgzCe+o/2shcJMYUNFfCOFZpsvvzFYp7wGCLu0l88SbjK1e6DbhLhAVpQe6K3Dt3EjF731CO2btJuXZFmRMjKRXJEAfco54s+IBGzHRe+z8rQwfdrGLcrcESW9sNMJJU3UeCe/hs+SjqoYMOnjD3RU6tQX9oG7WtDOMtpCfRkAA0uzmHFup4T7zkIJPY3TyTc44OlOsGsJBksIx8gRZLbJ4uIBJRRnxuuW0Xq1LiQ+d7RcoCoSsl5Dbawg5OxHoVXojR92H2ZrzVYUt4ea/YX46yPBJHqf6zQWOfKxp+8X9nCWHBRfMYEw2DuYsOUmr9bGAkv76TmSKc5Rb4dsj8wVdakDddheiP+lOfxnnCk2HiDfZ2RGoAV/wPRi9jr34gq4kp/TZlg0LodD/VrIdiO1eSUidRqVPPWZSMmjHlQwiF4znyLv1quEFR6Iktv451pXr+w1BdoNAUlGb9HIPFXi7PPuS3lMWHeE6aMcVPSLB2o5JOEzgmpKbbBwMvGHD9TRbCQ3s5GOWaXJA+y5WNoEaf/kDZg6d058z1vL0Np5nNsmcePwH1P6cP/YRGuuVIi2o+9/YhwrZg3ngr5FKbnP+/LBbYZe+5PVX6NNLVE3572n9qFi9PhEDevmMNpBNiQKM/1GRNkrFU4fGnH2infxgyl5wycsItXKNdbMf6UJRS6CVS/EJ4Mm2tuhw4dpV7ErplIH0K9tJp06FaP3RLraBt0IV82HIXcB4Hr/faTNGxICry8jm9qcIuHj11TTu34/fsWPouiFXkcENqMetEin4cZ34Lm+YGsDnmo2H17N1Yuns+5womLCC1OG87dzryPb3wieKuh3FfZHV1I8dy51mp51B+pjbdgQTzYM7TIpGVaLwSbeU0MiUNvthRSGr2FAxFZrxuJnuGbRTWjBANWrNbyRKGm0K+T1c2HM0vPPrHz0mYKq1iG9M96y2yixdSHn3tnk9EkMvl7NiNzlJto/8gS16SKALhyVif7G66nQLkdp3u1nsGAcPZuxPSZxRrdRAFSlS5QXGpjW6ToG9PlTbOPVV2dg31dt8LnsaMMf4OIvL+b1ra+zuXoz9yy7h0pPJQ3ffMOe0aMJVcYn4XNmPMmYiTNJhTfPf0f4RbrFKkWJ/OltIVA7/U7KS63Ypt0vymkAE54/PolhswNyOmN6toYnpj7HGatSB93aRvFs+yMZvaaCHJbwmiQOdf6DqOf9n4RBJ/PJzWfw4Bl/5dpTr00eYM9FZ9Aw5+iStG2jgSioMxNW1ORjfwNm9JuR1MZqMljY2d5IrzItSSQ/35aP68svE9ycw4cPc+D+WVR//knqi0iSCGK+OvjpH/Dm+NhbLWauLaAl9orZ10JXZGubLyd4jZL1T7c+GTRht4TrI+WNjMyE4UXP/J32H30UOdYPHc6Ggl5oikLY5eKXehVvMF7a2t+5H69e+5jg1Ec3MC96A3pciDfkQ1ONWJvR8xRfCZ3T+ogs2poNRf0gpwtV9ftYV7Waez5en/CZ+rSz45PKqK/aFvmQ/SGnI8g6lu2qZvJLK6lqCCRcA6D8jHuwl8joDOIeURUJ2SAhj3iQ7+4exqRIhuny6PCrnpi7itpxAqSXYLCpZA3MwnDJXJyyDoMsVg+OyKZcoz8kgtP452IbtWpaMbNC0zmUPYKxbUdzebfLAbjw4r9ywYUzuO/PD6Gb+HzCxu6u0x5lobMHlU89zSl14tz2Pn0Z9d1mVgfOYsKywtg1lIBMwGlAO2Mmvu7jCamh2Ebi12VfU+WtQgsECR04iOqJ1NqDQfo40+lhbk8q5NnyyL33HuznDANAn5NN/RXncSg7dQv5F3u/4IZ3J1O7bCmaKXJPHa9Xp7sa7Lmofj9rXU+hZn6WctiWQx4uWabQ5p108V1JEsHLYEe7Tvg6TD6+a/0P+MMHaoCyGi/frLfTJ7dP8ptGG/5J31NXli3ac5sisvN94wfb2VIhsupgWGX4Mz8wb80Jdi9FENXcLbAVICFRYCtg9uDZtD1nHDkNkN+kwS/a1JJKw9oQUql69tmWL2TJEhl1zW6oE80TLWWurQXrFtkragssj9Y2X07wGrlaC7rk0cmgSUat1DtRkdCnxUtSB2o99Hl6OQu2Voq69mMFwlVkxyKUhgYkVWXp4USxH7tJF6dItj0dJr4Inc8Dow1vyAcRLeoobCYdofozmdR2phAAyiwVrde3/YLPLDJZa7MsbsnOnUxdOJXlh4U2BiY7lXdOZffQs2LXtjbJ2vu2zeCXv4yg3cCLaGhzIyFdMSAhG43oOg3ih8xc+r/dnx11OyLXc4AUJmiQQJLQMjrBzK2E79iHf9ynaN0nEdK8mCKB2mKUsLZ/jvn7Puboo4+x+7YXBGd5tpOGmzYwXx1Ct/dfYO+4cdzUS3T9uQ+V0fDVV0JHpdeU2HhmbuVfNf34eP4q6v7zH8KHxf5BVAnPbNAJGdTIMdrF7wEgnzo2ppyXYcogw5QRO042i/KJFhDPQKiigv0XTqJscWplxC/3fsmy06zYThN9Dob8fAb/9Vm+mrExmUyAyLIH7tKouekOFDUSyI9TCIxJr8K4f1D3xhv8+6lyjFpqkoHNYCGsk9D5w2i3b0Sa46TDnzZz+6WvMag0L+UxJxN/+ED9+YYK/vT5Mj7ZuZjBTy5KGZQ86zZT+bdH0MLNtGiDYsnkUY3sPCp22hv9IfZVexKysBPFuA7jWHLREjZP28ySi5YwrsM4Tp9wA2FZplONIyGAj+swrkUNa6kqtcszEMmo6xOU847F7U6FltgrrxmvSMlNPlEz2tauUSW1oEsenQwMVvjTfhg8A6W+HkN6Go9fHJeVMel1tD20k4yXn0F1VYn15vYv4ZPpMbfxRpMtYdN3bKmNexc+Q8PixcJjsu/lokV+9atM7jiFc9qeQ4/C+GTQOc/BD/cMY0jHHJFRZ5bG3otuGtubGSPP+0WsRnyeSkEZlPWou1agBf0xemZT1odJryPXYUaqraHiH/PwHQ7BeY9Tumw7hS+/x+bDRwiqQWobRKbtMAoGTmOoUeiDRDSpGxYsYP+EiSgNjWiSjz5FogzXpzgLs6UGRa5FkuVYbReIaUubGuqRs7Ko8YmNL3ntVirunMn0Zxbx3upEsX1/SCEnKJ6XUzoOpNhezNnFZ3PgmmvotfSjhLJO1ANSMltidLx0Y3osUDsDTqQoLTEyVomo3K1tSC2etGDfApasfo/ggYhyXmMjocpKdJqU1HIOTYScADUQFk1cjtRyxEnIbAc5nVDcboJ6QJ/aVstmNOOL7H2qHg+hqiqcr79I23AZ2fbf34rrDx2oP99Qwf1L3sRcOhdL8Tu4sh/l/iVvJgVrdfdPAMjNvcuiOgF6KztigVo8SMdifZwoDO3aceslT5HW75WEAK5pGlILnmoNGa14FJ7/rKizNQnUrXG7W8K9o7vEGAtRWAw6+oy7IWGJTHrJsTdfWrmGMcU1yvvd2/pkEC3xyDL6NjlY+vdHluObUDaTjkJ3DTnfL0I5UiZezO4IIQ+qsxZV1hGwpSVsXE0d2oX0PdvEQ175q/AN3LkYvnuEW/pO56ULr6Zf23h5xWzQsaL6c0Z9OoyQqzweqN+fij/Stm9r9n9wRIwo/PY20OcywfpQJGSjDm8wjE6WEr5zX1DhH9/s4tdaUQ5RPQ3QJOAcaRTZqkXviJxf/NkQaBAuL95IySASsANGUFHoVyyaPzJtRtLNaQRUD5LVgubzxahwkgQD2mViaazHl27iwvmiwakmUievLqugvD7Rf9QfVsmK6KeM6DuZxZMXc+/AewkfrSSj6hCBsBo7v+qPutSYcQVFRp1uEg0vIOrH0f4GLTI24BYBvbkDeRQWvYWxH+zj8Kz7AHB9MZ89Zw/j6aUPoajJm59mXZNA7XbDFR+LCfpYCPlh5fNQtR3V48FrlNBLqZ/VTFMmLrcQC1Ma3YTKy3E//zL3z7sel691X8+TgT90oH502bvIuR8j6yM3g6EBOfdjHl32bsI4rWofyCAZmgXfLmPgwTqUvJ6xjDpqGuA4RsPLiUKSJPQ2W0LDC0DtK6+i+f1ousQlVcig4+2zVLyhxIckhjZdIPuUhEDdUuba0usgNkSfnNwrib1yQd+ipCXvbwnS0WuMOzW+yRq9xsAJNx57Mlj1Mqx5Dft11/PssOtZvjtOdbIaBT0PIFwZKZdkC11gS8ci3przLvvaJm4KSwYDktUquNTLnhTu6pnt0QIuDlfvpsbjRlXj+whhReWn3VU4A078E/8V79R0lWN3HUYO5ZPWTB3NEfm3P/9UGPd3MKejKjKyHjwBBatRlzB5aGg8t3Q3G6tE4qAqElizKb/1NlwLF+KKqOnlO0RwOzWrNw7XdWQYc+gw/wvy7hO2X6rPBzodJouDuWe+x9CCMYAo58malSON9cgWK2harNSWl2bm45sHY3TW4Y/cJx0zOpJeWApAbsidkCGDyKgz/Q2g0+G26VA1FUVV0LXJwRKZVKJSqPrsHKxnnI5ss9E+rT1zBs+hfXp7HAYHuZZcJElCl52NfdgwZEdE3bBBBGq9NXWgNuvNeE1xtkf0zw8PzW8xo/ZGcp6mq4ljovEILPkrVKyPyKhCl9zMlENtJhNuVTQ1qR537DM1yDqOulp2sD9Z+ENrfXhtXyLLibOVJIfw2r4E/hR7TZXMyLoW/HZlHV3y0/lmeyWapsUz6mM0vPwW3N5BpvTtJ/D1fBBLz1Np/OEHqufOpeHM4bweKuCWtR9iVMNUWTJ4r/9Aak534ww4kzR5AaEPfHAV5PcUHGRE5tpUfwRE5nrv6C6tfq4L+hZxWvssjrj8MTXAk42iCB1tWJc2/PeaJhoqvaa0PgFs/xI0lYauV/Dp+gr6ts1kSCex866TJQJWkV0qVRF+dSRQ46vDE1KwNmuaeOKrHZyBmTSnM2IxlgVZ7fFJEqMXT8ZfOYZ5l95H30hWLUsSS7fVYy4Af6dzcVgj5ZrMUi6s3oVyxqfkpyVuYKWZTWiNMv6oY4kkoalGJD1cMrBElFGawGLQIUnQqIkSjRaW0YyZuJcuFfdJbiOaaiQrQku7ZegAbhk6QBzcRKZG9XmRLRZ0so7r/1POTWcbuHd0PoqqcaQOjNTGNtRVny+uT+3zobrduNPEd/XiiBdpEzCym7doE3THyiNRBMIq9pAPfXY25346imJ7Mfsb9vN++mlkHDrMUxf1Qo5MRI7h5+AYLmiTeaQxqdOk2HmWTomL/Je8/FL8/G6ReRvsqZuszDozHqOGUh8J1B43il5Gb7KkpP11yezC1YNugff/JZgii2fBoTVwfbLJQAKidWx7HqrbTUZWATMHp94Y7N8uk0OT0gkXn4fObicQCdRegz5pxfp74A8dqGVDamPT5q+rqhFZr4pGkaY1pj3fwvYFTOhxNx1z7SiqEOQ5q1MOuWnJu8f/K84OVFC5fQtlF1+MvrAQ6+mnY+7Zk1vaj2e/W6F34Xa61+3nmlGiEaNol4XCSYWpT7b3e/j2IbivQnQoIgIuwKxPNuMPq+Q6TNw/tlvs9ZbwxcYKZnywEaNeZtcjY475//h8QwVPf72Tw04fhRkW7h3d5ZjX2FT/HbZT3mOd5GTUxwXM6DejdT2TKKyZULOb+uuuYWowD7upd8LbQ/p3hO9BCZtFB2VE37rhm6Xcv62SrAcTa+o2ox6X0SqaZLx1opSR1QFf9AHXjAmbibIsYZTFPeMv+wm6TBAO7ZmlsPsbLupbmOTObjPp0VVM5LyKx4AMGHAttg4WsNhpX5CWxNGXJEl8LlUEajUsoUY2AmWrlTSpE4qzIaYPHVACrDu6jtL0UiyLV4CqkXnJFFSvCNR768uRM35E1otJxWyQUf3tSZMdmLt1JfOKK5B04lybyp3c995qnrz6Ro50agC3EPfXWY2g15MTaKCiWUb90uX94PJ+pBn8BD4eSml6KXtde/FlWLDV1XJx/+KUAbO8sRxXwEWP7B6t8qjDXUt5YZzM+PzUMr8WvQW3QWlCz3MTNhtSNruAYImMHDIN36s9MffoAasXxcwAWoUnGqjbkDZuLPqGoWRmdE85NM1s4J/u/3DFRVfQs6gI9aflAPiMhtjv9nviD136SDem1nFu/nretLGUnlsjxH+a4vBGWPcGZ3bK5fqhHdDrZPqUZPD2dYNofwwt6hOF68svqXzyqdi/w4cP07hoEZmXXUaZWzwI9SY7GQF3jMJ32OnDHWxhqRbV3vAlcqkv6FvExocEt3Xa4NJjBlCAXw8LHnIwrAo3j1bwW5glC/ctZHPgNWSjEySObTXWFJZMNG89yo7tWMIBrMbE3GHG5IFgMKAaMmDkHGFucO0SfAcbaFi0CLM5saZoM+nZkdkWqbBYfHfWLMgsxRepfWvNWB8Q73bzfXFz/MXMUl61Gbl6wXVCf7kJLh3Ylk/HnUvnUChmSZX9zyVkP/MF6w7Us6k8OcGwmXR4Qirtnr2PjHFno+pEOUuyWOiXM5Q+tnhNde3BI9z47Y18+OvXNCxahOvzzwHImDyZvPvvY0vVDsx5C9F0IjOVJAlz4wS6GC/H2r8/+X/9C7p0cX6nL8S2+jDBqdM4UGLCZrDxzvZ3GPPZWNq99RaV506gJCtxRVeYYaEww0K9Iu7NjhliFeNql41x0Oms31OFLxipcb/4IvvGC/roBzs+4Nqvr40F6efWP8djqx8jXF/P7rOG4vxE0FELO/Xlynv+Q/8OQ5K+J4Db+97ORX2uRHW70TQN1e0hYNGn5FCDaOXf4t2Df2B39NnZYMsVJcPQMUoSUQqfLRfruPO4uDrAnR+tSDnU5Q0hYaDW6UILBlE94rvxGAz/r2TUf+hAfd/pd2FoVtw3SCbuO/2uhNd0ee0wZDviLcZRhLxi00ZnpMLpo7yuhXrwSUDVs/+EZhQ8ze+n+rnnYjVkp9mBpGmYFPHgZxf+wlkfnoUnlMLrLUpd+2fPJOF9s0GHzaij1h1MPi4Fmo5zelvf+PgtzJK56+eikvhZWrUaawpLFlpjHVIwQIPJlsCWAKHd0WnjRjLHjxS/rzkd2g5CafTitdj5cE0iY8Fm1PFS70no77xH8KitWWCw4L9WiNijGmNGtVFY5VwG++1Y7fkimwbI7cHezGI2VO7ms2aTVH66Gbd/AzuMBsgQsrqaOQuMNh5ftJ0nv0q2FLWZ9LiDYaxjrsJw7buoiPtatli57PR83pk+MDZWjwicVR4nssUqatOAtW9f0saMocYr7vMca7xN3W4SmtSapqEGAjEGlD+kYA96MdVVM7bdefxlkFjNVbgrkHt146kbRzBzZGKj2Fs/l7HhjnupXyQc9zpmikB94PS27LjtQSa/vpYDdZFst6aGcI1gL7kCrgRnl32ufaw5ugbJYCBcXY3iEgmD/mgtPY8YyTanpohaDVayzhtL4eOPgaqSPmECW8/vSpoxdTdxta+aKxddwaZP/o1/1664vkzzxK053NWABLYcqst2ELD+Hae0PuXQGk8Acx1cfuuHOD/9jKwrr2Tew/fS6BqByfB/eaAe12EcfxsyJ4Gz/Lchc5KW1M7tflw9/pVsvxP0CvqUJDHxXyt4buluXvphL0Oe/C5hQ+lkoCUKXvjIEe4d3QW9LPFpx7O5YPzjBPQmLAYdU/sMJKyGWV+Z4uaINoNAokQocMf7G/AEFWo9x2eqWddkXJ2n9eD+W5glLVmKtWg11hTWLJSACI5BmyMpUF/+2mouf201fPcozO0tViMb30M5Uka1bGHl3kSKYzRb9gTCokutj8hUfRFnaU0zJmXt6bpS/lyrUpzepAGj3Rk4CwYQUs1Jn+lQvZdZO+fxcka6oHcBe4adxeFrx+MOhJPOD7Dg9iE8d2lfGhYvxrNqNagqhpISdBkZXP3V1dzx/R2xsVlWC5pqwOl3CX/ECOvDv20bgT17qPWJgJdjjbfOk/4jy/x34P1lDTt794lJ/vpDCsPL16GbOpFuxraMP2U8WWZxb1Wv+hFnJFtvirlfb8e8ZAH+PUJjo8RRgklnos5fF/NZjNa1mzuQpxvjgTrDlEG9vz7GxooyRA698wZl066iIZjooxjFxqqNzHV/iWHsSCSdDvtZQ7juz+8wb3xqeYNopl3w+Ds0LFjYxEv1GFzqITPhzs2gM+CaOp3Lf1Ax6VIzsUx6GZ9eEBBUjxvJaOTmMZfx0ZW3YNb/X176ACiwFTCtxzTWXbEuRnlrDueH83B++mnywSEPRDiwXfMd7DjaSFWjH5c3lEADOxnQF6TmbeoLCrigbxEPnN+NTLsZSZJirIhJPc5EL+tZczSF7GlTEaYmynneYJj5m8TG2rGCbhR1nmDsAWu+jG+O38IsaclSrEWrsaY44zbCVwht40evPoveJRkJb5v0Mmf9+DE1X28R34kkwYKZKEcP4DJak4Jil3wHT5j3o14+Ga1kiGDPALlHtnK9rj1XDzgtiUr49rWDaK+rTuBQA6JBpllNG4TinuoL4tMZ4wL6Xi9y9Wa8gXBCi3oUVqMenSxR/ej9OB+/EVPHjnT8Zgn2IWeyv66G/ZXxydhhFs7nDcFGQc/ziUB9ZM4cKh9/AqNBTLz9iuP33Pm98ghRT8AU0RGJHBMIqWT7G0CvZ2uwjPLG8ligblywkP0PP8Zt7yUmCpZGUVLJLOrArX1upchWxNU9rmaA2pa8aydz9qENMaaI6vfFTANcQVeMPw2iFu4KuECvB4MBzS8+d01dOY36cIvO77udu/ls/dvU/7ISxe0hsGdPQvt5c5h1ZpAkwlaTYGNknQI9L449+1H5hu3durN7+Ii4fIPBDBltBdXQ48VrImXnI4hVrE9vQJVEzdz15Zc4336B3CzvSY8lqfCHD9SowjfCAAAgAElEQVTfHvyWf677Jzq55VlL9fmQ63Yme/NJciwz7ZLvYFdlI07vsZXzfgtyZ95J2JBYppHMZnJn3gnAtMHtWXVDb1ZoP/HNqEw65toZ889VODiFNzcsTW4Jz2wveNSQEKg/3jkf2ylPYO86iy3Sn46rDqzZ1+Po+CSObvfx4PqprR7Tkmpga8ySW3vfjtSso6tVq7GmkHVIRhP2s8/GUJRcb7ea9LQ7tBPPzpr4KsOSiSSrVJoykoJi5zwHo7tko1YcQlkzDzwi485zHeaOPct44Jxkn+Z6z04G5Fr5ypDIftCq1tNBq06QUQWxYelWHbhs8UCpBhVknQKBxoQW9SjmrS3n+aW7kXQqqpJ4voDqIRyOB4g0ix5NjWpSW9Ai/GnN60W2WghLHqx6K4UZcXpbpxyRRfr0kUw3koW3cZjoagyiy2nDzGV38fqW12OB2ptuwuxt5GBlXAtH0zSsHkHBy2/XjZt630SGOYPb+t7GkO5jkOtqyfG5YoFa8/ljYmjOgJM0U7w8kWHKIKyFcYfcyCZTrDNR9Xjwt6CEB+Le6Vyh0XDd7QT37aX85lv48f7pvPnrmynHmyIEgrDFIGrHbTrD5Ncgt1tK+YYjDzwogvWql2DrJ6I7MxzGZ5Qwt9DwYtLL+CuuQDFbUN0eGpcs4dCHb3HnN3NSjj/Z+MMH6jJXGe3S2qXkT0ah+XzIwWo4tDbxjfFz4dZVgMioA2GVrRWuY2pR/xakjx/Pnqtuo9KSAZKEvrCQgr89TPr48Rxx+XhjxX5q3X5cX3xBYNcuuuY7OKWNnSqnDsVwEFvXWTizH4o39OiN8cAUCdQL9y1k7sbHkI1OJAkUXd0xN+0W7lvIEf3b+KkFNCp9R1s9JqoamJcmbtiCdHOcd90CTs8bSbBB7JZrGmQac2NdmcdEfRnmX5/h4BVTuGttMqfXbtTjMtpQ3IG42p4li7ZXlvJMn4uTsl1F1fCaI9zrj2ZAzS4AGtMKOKjXU3NoW9JHWFXmJyhL+AoSGSelqp7OwVBS6cNm0lOnZuOMZI+aoqCFFSS9hiFYnzQeYPnuGj5efwhZVlAVHZ6ff+bA1dcQrKhAk/zY9PGgazHoKAxdxfD8K8m9+246/7IaEA0vstXKRR2m88jANxP0a6pdIqtz60RtOirUf07XXM5I1zDktqHeX0+WOYt8Wz5jSsdgyhUTjbEhrnsQVFQyfZGeA4eOaq+o84aUEE5dAM1sJsvfECt9WHr3wnam0BD/y6C/cHWPq2PnKrQX0jWrK/6wn7SxYzF1FZx3zevHb0wtsATidV90ZeAWnOUDSg2bqjelHG+QDehlPSGzAaWxyea8qqSUb9D8frGntOol2Lk4QZ2vV3FqUSazQYcazEMx21DdbhS3G7cBdh35/TnU8P+BQH2g4QCl6aWtjlH9fiSzpVUhlq75YqbfXeU+prvLb0WXy6dQ8fIHtN+8hU7fLSU9shu+ck8tc77chitCswvX1qDXyVSqK9HbdyEJSQdkozOxoefXT0HSxWpuc9fPJagm1qWPtWk3d/3cJP3sYx2jT9uApcMTpHW7D0enJzGkb2z1/13jDqCFRQlA9bXjrq5vHV+QBrEzv/kDXIe2s2jLUfTNlpFWk456g5WwT4mXg6xZqJ46bEZdUlAsr/NyywJh8aQE5NgxS0M1jCsp5KnPvkj6CGsPiu/H36yx5S/pfXnU56FDm8TGDLtRxqIpBCJ61NFAIOs0/jmhLVNPS9ajsJn0eAJhZCmEpuoIHT6Cd9Uq/CEfSCp2Y5xTLEkS3946jTvOOgvJaIxR7VSfD8liYcnWeq7/z95Y0wnAxgOipNUoiz+jXYwA4eoqtOwMFE0hy5xFrjWXp85+itIOQjvH3CRQ+0MqJiVEyObg3xUfc/VXVwPw8KqHuXThpejb5DIqT0efSIkq5+abyb1buL0MKhhErza9Yuca2W4kH43/iDbWNhQ8PIeMCy8Qb/h8+A1g1ae2sIo2vIDoAlTdbjxGtcXADvDM2c+QnpUfC7r8owd8NavVvSM81TEONcCEXpcysXv/lOP1ssSTVxhwXTgY+7BhqG4PXhPopN8nljTHMQO1JEklkiR9L0nSNkmSfpUk6TjWsycHISVEhbuCdmntWh2n+v2C3N988+DbOcLBBOiUZ+e5qX25bFBbhnb+ffRjuxemcfmgdkm8yo3lTuwmPR0LM5HT01FqxXLcZ1uAJCd2MsYbeoCKdXDqJOH4wm/btDvRYxbuW8icn+dQGzFAOB6qXZ0niKQXN7vDN5amFNoW64NRWLOo3mqn5Nk3MOmkJAfoM0/JoV37QpSAjHbqRQCEVTsV8yr45bw0pp/VIWG8zSQycAAlGC99+SO15FLqaY6uoTIxppnSnyW3IxZ/FVnGZll+qJp3G3/kOiKa4rJM9pSxWLJD9MxSU1I/7SYd3kAQSQoKHnUk4w0bTQSqz6WdNVGf/NfaX1lStgTvunUcmT0bxe0WJT6rjXV1izBmbEjwZcwx5xFu6IUtPYfs66/HfKo43wvf7+H5orNRLxgJECt7AOjaiOfA5o6zpRwmPc+8dA8dVq7kkMUXG59lzqLWV4sxtw25ITf56Ylli6AS5LuD3x3XBvLeiwby7jk6TLrUZQazLq6rodTVooVCNBqUFuvHAMPbDqd0zmPkz35IvGAQiVuLe0f5eYIVZmuDnJZGzqxZlA6YjE2XuiFMkiR+qpzPi932kzZ6FGpjI16jhk5qRQbiJOJ4MuowcLemad2B04FbJUlKzQo/yTjsOYyiKZSmlbY6ruPSb2kzrlucwB7F7iVQ/gsgli4Tehfy2IU9EzzzTiY8gTBbK1xJbeQby530LEpHJ0vos7NjdKZWG3o2zxNO3Vs+irmv/JZNu2xzai56S8f8lgy81i0CddfMnqy+6xYm9hFlklbrg1GYMwj7dEihEPYUK51zu+cxZHB3DPkFaEVnAqD0uRXPQQXFlWxQbDPpqDc7CJ+Si86oxsolvsjkkSkly90OcH0vxjQzTr7k6Lf8Oz2NcG1ZwuuZgSN0C4aY3Efw2WWLhdzZT6H9/QBfuLtxqD6ZBmoz6VFCQXKvu4Div90V2+zT2zI5I2sqg0sSM7l7Fv+bWT8+RLCsDOcHH6K6XBT94xnSL5jIds/XmNK3JDSVFNnb4qu4jNKs7uTefRfWfv0AMYkuyT0VZ+9SALIiE9ek+ZN4rOodtjz5OsYz43xmWZZo4zBhN+mp9dcmBOqQGkI3dDDVnXvFqK77Jk3iyEOzqfJWMeP7Gfx8+OfYuaq91UxdMJWlB5dy4IorKb/5FgBGj7udB256v8V9p355/VhyldDvCR0Vq+RGQ7jFmjbA+sr17M0OYeoQmbjteeCuJnfmnUnSEpLZTO4Nl8fG6TMzOXrecM6Z/y0fr0823I3iqEvB42wkXF2N6vXiNWno/yiBWtO0I5qmrY/8vRHYDhy7y+IEkSrzapfWjtWXrebcdue2eqzObkdX2CXZoDXoibsxA3uq3HyxsXX95v8Fm8qdnP/8crZWxAOIP6Sw/UhDzIXEWFKCpBfL9ZYaerJ1DiG4r0Q4zxH3lRk5g5KyCqNsanXTbkzRtWjq8W/0/ZasXZLAaPSilyVWVKwgGOGJt1ofjEJvRAkZ0cy6pHoziJqzbsJE2r/3PLJeUCrDYZGJvbihlu1HEileFoOORrOD0PjO2NpaYrzoqHv9922SNc1zgkcY7YQO6V0TXt/tr2G11A5Fasbtdh1kr0HPT2HxnWihEEqjm8OuIDM+2Mj6g8kTsN2kB72ZwKSnMA6+SGz2SRJ6q8zTl5Yyqkei0qA/YCKkekRJD7E56DjnHMydOxNQPBikxLKBPbLv0ugPobhcKA3iewm7PZzqPEgHfQHPD3+erpni/2iSTdQoLqZMHMzzVw2Knaeq0c+C2/7CzjmPiZq2JR6oAdyTR3ORpxuLtoiSglJbh6aEY4JMTVkfJr2JrbVbqWisQENDjajmWdbtpFN9y4pzsiSjS0ujaO5c0saOpeDJJyjvkkmmuWX5g0dWP8Ln85/G+WlET9reBjxVpI8fj6lHj4Tu0syrriR9SO/YOMXlYtOaz3EUv0pYSk0ZBNhb6efiT49y4KppdPzhe74ZcR0Z2qAWx59MnFCNWpKkUqAvsDrFezdIkrRWkqS11dXHIJo3Q2uZl9VgbbU2pQYCVD75FN700TD928Q3Q74YRQfg6a92MOODjZQep+j+iSKBwxvB3mo3qqbRu1jcwCWvvEzRP54BWm7oubehAddu2D0/l+0fFLB7fi6u3TBuw2ecmXETUadsVTEzue3MVuvBp1iGEqgcgzWyWaVTslrd6PstWfvEPkWsv3YxEzqez03f3sRDi0R3V6v1wSZQFAuaxUC77OSa5fxNFUx+7F10L50Ou74S4/dvBuD78oakBp5ou/ayNlOFk3sEvrAPND12U3IGlB44zDk1+fTNiRvrappGiCDLlQEYczsmHuA8wGKbjbvXP42mafi3b2fXoNOxvn4r4+RV2E06Fu5byKiPR9HrzV6M+ngU+YXb2PnQOeg3rKLuzbfQZ2Zh7tWTNUfXMOKjETEt6iisejtIGkFjxHTV6aTxu+8JHT2aoEUdhd0kYe88m9e2vsq+88dT9fTT4jyHypi95FmMv+5hWMmwmKpdliWLOn8d9R/OE5KwEVS6Aihrf8GzYyf1gfpYgI42p3jCLnSqgj9yj6t+P7LZgssfV86LwmFwoJN0OANOZLMFNcL6OHDPTDa/Eu/ibQ5XwMWc1X9jZ+9MzF06kzFxIu/c/D3Te05v8RiLzkLbdRUcnT078oXkgbsKLRwmuH8/6RMm0GX9OiSjEQIBKBkIf62G9mfj/vFH+t/7Im1cYDO0nLXrJCNeo4bqdiPJMi9PuZFXp1zQ4viTieMO1JIk2YFPgDs1TUuadjRNe1XTtAH/D3nvHSVFmb5/f6o65548QxhyzhkBkSgoyZxW15wD5oiu6Kq7ZnTRNaCI4mIATGACFJUoOWcGJscO0znV+0d1mJ7uHnC/uD/Oea9zONDFU13VXV133c/9XPd1SZI0OC8vgw5xBmTKvEqef4Z3drzT4r6RxkYa3n8f//40nXPBaMMLcmv0qv2J0sjJtEb/UcQDdSBR0+zVysLOJycxplvqdxJr6InddPm6Ap4eNZtRv9dR+buFkEcJCIQ8Sip/t+DYXoervi+CpKR7Vm88h++nnTZ9G24MDe4AQftIfrjgFybrP0Jb9USLgX3mwJkpUo8nQ7VTiArammR1se0VsilDS9zypgjr25PdaxgfXp+anejVSjq6Kjj+czaeo3I7ffi4zNxQakJpGRb3nt2VCQveoPKtRDPH+Hbj+YtxHE/UPwihJlzySASzr4KJI4diNSRKCTGXeLWoRmje5m87RliSb2hf2BfXWTbWrOcMcTc77D/x5NonqXRXxuv8s9fNZtna53A9fzk1L75A9l+vosMnn7ClTObEVzYrnRtUck3dG3WDCRw/Ttltt+Fat5aI4GV0p+QFy3Hdi9BrRASFF0Gf0LBWOuTvrFTt5teyX+Pjc7Q51PvqOfLehyx78d24PrsvFCbb54ScHJ4840nGtR0HQEdrR+4eeDe56/bx1VcPo6iS1QwlrzdJ4rRpRi0IAhaNBZvfhqDVIEW/p4jHw+bG3SnXLYawFGbxwcVUrlmJa80aPJs2xe24MkGr1OLWILd3BwLQcSwMvhbvtm1EHA5ZvU+vRz98GP6jshEHSjUoVIQbow7yGjCoMyeFSkGNWxMhVFtL+azHqNiwGK225fM6VTipQC0Iggo5SC+UJClNZ8n/DZkyL1Wtg9/Kf2tx35iri+Crg3lny/oeMehzwCAvmLzw/X6C4eRuxBO1Rv9RxPi27mY1aoNGGV9gbFyxgmPXXiv/mJCD9fQ2dwAwa9ArTOk4hZpdWUjh5EsjhUVqdmVR57EjCUHO7TgZKWyk4QRt5Fa9ir7tBL49tpi1wTv4+8UtC6pP6TiFmf0ewaKKPlhCWSek2s36aiNTP55JpVu+jg6/HBzy77lbzmCaoCm3PAbD6NEYRpyR9r2NGiUW0Y27SkugXg4+gt6MyhhCpY4kOanEcO3IDhiDNoIliSy1X14/Hu48GGvNBrA3aTtvrEQIB7jQ9iuzfpsV3xxzGL9G+h6WNPPE6385WxWyQqAv5IvXm0M6I1lCI18eezdtnf+5I98iKCSkYCje4l3vkQOcWZOsJGeOskA8ygiCRkPYHnUoUolISPQsTHYVsehUWDUWXEFnUtt5t2hzzNeO33jst4Qre7ZWzqj9liyMLkecbufzBcjyu1Dk5nN+l/PplSsvShYaCrm+z/XkFXZARELRUC/TEgMBBK02bhrQlEcNUR1nv0POqH0+pFAIZTBCRJu5thsr77WZ+xVld9zJsSuvYvanNyXVv1P2UWpxq6Mccrcbuk2GiU+hGzSIDl8sxXimnNC0mTOH4rffhl1L4NuHIKolAuBRg1GdOaPOCZ2LUS0/uJyfL2H+98/xxsb01l2nGifD+hCAecBeSZJe/jNOIlPm1WART0jNi/FFRZ0GSpvdhDO3wej7gf+uNfqPIl3p495PtiXVxUMNDXjWrY8zPwDaW+SS/2GbnKWEMjykQ25o8MmzgtLGY8y+PMg1I9u3eE4XD27LoP6/88yGZ3AG7ZiNJ9brHVHcB7NWy+whc3l37NITUu22VhzlWHAVwWhNvTEkp4eWadOwXJiQjVRYrXFueVMUnGniUNVS5v50KOW9DRolao38vmGPPFOxTptM56k1mJTetBl1jdOHGKggXHksvu2ovYRfY5e6ocmCkamI8mu3YA8ZqfckfzdZ9MMQscQdyePoMJpjmj6AHKhjs8Gg1kQWLup96TvuHIKXWLm78m9/o/zBB7H75clpoTG5/jqi9XB6RJ6g3bDxdN++Df0geXHQYMnh5aHfMjgr+Zo4PEGCQU1UkzrRzTjUHAGFgiqVJ4nxMbhwMH/p/hfCWVlRXrT83QbqG1BIEYJZBnbW7ozX9kHWB3GYoo7qtnoIh7FcdCHanj2Z2G4i7579blJGHTtOsakYw8iRmKecG2/EkXSZA2Js0TCoVcXv77WO7TT4Mps9axVaXKpot6QrKnzmcyKE/Gi7d0c0RNUKo9KvHF0NuxaDIMhcbYVIUCnQJd+a6RDoFRb8ysR36FXDrrI/Tz+oKU4mox4JXAWMEwRhW/TPuafyJPLvuTtu5BmDoNXy0VnSCRkfsYxatEYzjAxc6v+mNfqPwqBW8vIl/eJljgZ3gCVby6mwJ37sylw5w48xPwD6F/TAc/xaDMhaE8qi9NKnyqJW2IOysP6v5b/y+ZF5J2WAUOepi3NWv9y1C8cJhJl+ObKP0sZSPj70GtVSejWxprD55c/SJasLIOCLOOLNGKqYlKVKhWnixJQgLUkSUu1BujrWUFKX+oQyqBUYlD4QJcKx9vcok6NY60u7AHnXoq0IigBhb6IE9dzGf3L79veiJ3w0MVgUqVfkUOcSsfsSx8/SZjF3/FymtRkoB+qYaXE4CCW/YY3eOd6QN15mMOfmMSA3QoE+fT3fHFIiRW2pfDt2EjxeSmOgESmiIseQXJ+/7oxefHrtxehUicVEkAPNvZ/s5rNNyb/zRn+QKptAtcuW5AoTqq1FmZNDfSCxMAgwqvUo7h9yP+TkY/W78HrlzDvo9nDEXESp2cMVy6+grDFhdnzx1xezsGY5AGflCghqNa3+/ndMY8eSq8tlWNEwlGLy9Zg1fBZ3D7ob6/nnkT9zZiJQ6zMHalEQ0Sq0BHSJ9/JqMncyAtzU9yYu6H+l/F25XFC5jcCs9lTcfXPc0iuGmpdfoXTeBlllLzpeNBiYO2Eurazpud0A90zRY50IhgnjAdkVXZOhk/FU42RYH79JkiRIktRXkqT+0T/LT+VJWKZNo+jppxCioufKVq0IPXAja3opTsyhjj5xBWu+3DIe41K7auHD8+HwKuC/a43+o1CIAhcMbEPnfHnaGpO77N9Ev0KZIy/KhOoTTibtsnIIu7vhjpJHMz24cu++m7aGDkzIu43BBYOpctemqMc1x00LNrG14ji9c2XBqs+274wrn2XCoq3yYt0h+yGW7PmFOlfL4k+NAflz5uvz+WuHp+luHIcnmqEFy8pQZGdjHDkSz++pmibB48fZ99C3SMfCGNWpmgn5Ji1th81AMBkJO+Xzrpwzn8pNFp6Z1DptRm1RS6g1AcKexMzGE/QSlLQEFfrkjHrfMlrvfhsi6qTsEaBPGwutOvSQNWPc0etlPw7zpzAh0Eie836KjEVoe3Qn98470BS2RqdScPegmSkcYY1Cy7n1esKxrkmbDVGvI18xkEDNuSmKfp6gh0/3f8r+ih1UPPQQzu++B6A8VE/AsgRBmSxGZdKqCDX2plg7COvFF5F9xRUAPKfpwxfjr6bB15CUUceOIWVnISLhr5Oz1bMnDGLsbz/gGSavNzQN7jnaHKrFRgSNBqvHKT9kow+w9ZXr+aXsl5RrEYMkSUQCARRZWbx9czFVfTPosEdh1VoJ6RLlEa8mcycjQLfsbvScdBkdly9D3akTGPJxVWhxrNwIzbWxBQHXfgdhpXwvWqZPw/rQoxSpBhAIpdI3Yzjq2s1Lrs9QT5c13b1qAU0L3O5TidOmM9EybRo518vUqU7ffYvtrD5YNdYTlj4MQ4fSfddO9EOGgj43waX22eUgHdV6iLVGp7WkOoXYetzGgWp5cWJbqR1RgL5tEivhihw5ow7XJ6ZxZp2Sc4Y4EXTy1N8ybRoFs2bFH1yKrCyKnn6KrOnTWHb7dF4591Y6WjriC7t5b82BFs/nQHUj3oiNIkMRVnUOgsp+QjEnZ6gaEQ1tDB3ZcLwkrmedDv5QGJ8k10+ztdk8MHoGX90yPd79aTp7Inl33oF+yGACJSWEmjGCwjYbRCSUqgg5itQylEWv4qoZ52IYOBRFlvzA8+07SDB/HAy6Ju055Sk86HMDmId3jwcS2YFcTX3ecGhaR939BdbdC5AkFb5w4vjba7cz6j9j+NYd3RYrf9jl7Ozq8RP48sYr0Cl1aHv0IO/229k29Gk+GbKIKR2n8PDQhzGrzXHVx3sHPEqFYxwlZ15B519Wo7BaEPR6RrYZyrntLkwR2v/5QAVPr3+a74+sxfHlV4gGA8Xz53PAEECdvRalqrn7upKgbSRdtdMxn3MOlhkzANhnLOJIp34pgXpfwz6GfTyMw6MK+Pej72NoJc9IRVFAr1Zi8zcgCmKSGl62NpsGvw3vhVdQ2rYbgcOH2derN87vvmfB7gX8a+u/Uq7FR3s+YtLnk6ibO5f9ffshKJU8dNMH3HX2k2mvXQw/XvQj3drInZOSUkFQ0XKgPmA7wA+1v6Lp2BFRrQZDHq5yDepCC+ri5IVX45izQAJXufxw1PXvzyf5Jia/NY9qZ+aW8INVPlQhCe/+vUA0y8/QtHOqcVo5vGh79sQ0aRKS18uZbc7k18t+jd9oLSHGS6b9qIT7cNSBvCk977wBrU95YG6OmYu2MbDYyquXDWBbqZ0u+aak6bkyJxt1x44I6kTJQhAE7Jqv2Ggzcz1yE4WuTx8kjwfjmDEUPvE4qlZyBrK/YT8KQUGuTg74MVfpTKh3+xBwkqfPY3zbKSw81ojN03Kg9kr1mMRc8vX5HFEeobYxc0btDYRpk62kUdRjVBnZUbuDem89Y4tleybjmWcC4D9yFEGjTVlcDNnkerZCEyFbTJ/p1x3ajPnhW7G0k+vCYZud48YCXlu6lxcv7pcyPlfhxlzsw3zRpfFsyhvyIkX07B3/GrqDG6gZN55QZSVKk0jO6GxC2X3p0S7RKu4OuHEE6lleruOcMY/gWLOTmrcfJlRRgVKfj77zXjYqbAwvGk5eUIvk97N8ZwOLNh7n0iHFXNT1Ika2GsnCvQu5oMsFFOqLeUFr4IzO3Rien4/kDyDq9AzoFGJ419Q1Gl2UTlkbdIMoImjUGIYPo3bHZwDk6JIX7RSigEEtYvd6CNlsRBwO1O3b0+3wFrI13XjnsncwqRILlrGgbcgKM+evw+PbN736Nt5vl1M3qx9WjTWpKSVbm81Rx1H+njcKjVtkntcHkQiCWo3D50ipT4PM4KhwVxBUytchcPw4ul27MIwalWQzlg45N1yPftgwjkg1tBe+xqhK77EI8EPJD3z4+1sMVVVhGDECVes2uGs1ZI/OThmr69sXhRZch71YkOVjD+z+CG3RUTSqWzIeY3+lj3bV4Fswj6zXX+Lwxt2M1HbOOP5U4rTJqAFMY8fSZs6rcXcKoEVLHyDeYhuy2eDi92GMbARKzDQ2nR/hnwiDRhmn5xk1SkY2888TdTo6LV+WUqvN1xdQ3phgvwQr5AXI3FtujgfpLcdtXLl0Fg+sfiweqJ3Bhoza2oFQhEZfkNFZtzKheAL3DLyboH0YDe7MNepgOILfXUhH/XBamfIRlLI0bCZY9Wp+uuEZfr9yPYIg8O72D7lnxWxW7KlGikTw7dlDxO1G07ED2Vf+Jenaghx0Aar1BRQa0/8cj3x4O47P72yyjw3RV0rOocVpx3tN7ZkUnoPUcRxSWL4WvpAPJDWWNauSOfvOMDXf1zNmn0QvU2KBLsb6QN8aR2MvKv/xurwPEPIosT//b75/5zH21O+hYd48Dp89iTzbFv6leBmclVS7q9lVv4sP9nzA3oa96NVKtt7eiUuLgtS+/i8UJhOarl146JeHmL0uVYHNqtMghTXYArITuW/HDhzLltEQNZfN0acGRU3eTyyxXUXtv//NkQsuRAqFuHXlO/TYtZaeOT1pa24bH5ulkev8dnslVc8+i3udzKiw7d6HqrKUhqA9pVSSo8uhwdeAXoygstfH1fBEnRan35nEoY5/jmjwjtEMvVu2UPHAg+zcsSJlbFO8tuU1PvCswnr+eQy84Ca+Pv/r6BpIemiVWlRBiZp/Po93yzcvoXcAACAASURBVBbca9dARMDYIZVdIigUGCfNwH3QgRQKUfnE35i4fD9SRNmirZZGqYm7nev8EmvuupOZ41LVGP8MnFaBOgZJknjol4d4f9f7JxzrP3AA+6JPIJRMiSPw/yhQqxVx1sfcvwzkiWkn122/p1TkuLMiPoMIRoNCxOPBvXYtAJV2H+5wA7nafAYVDOK64rcJetpktKuXM2cFw/Mn0yu3FyatEoUiREMLNecGd4BA3XjOaXMt7S3FCBEdNc4TM2NiD9Q8fR4hwUG53UOotpajF1wYbxkP1tTQuGpV0n5hm1wCavv4RsaNHpP2vbMFN427wpT85Uoifj8Rj4dC4RgTI+mpm5P6FXNn1zz2DR6Jd4ustTxzwP3cPOAqjO/PSeXsByM8WLqKS4Ylgp83WgYxqnXUvPRSyj5iIMAVP0u4gh5Z1U6nQ/DZGSttgMZKPjvwGff+LDsRVbor5UXI1wcSWvUmdXPnknvXneTeeCMH62rZW556/UxaFVJEi9PfiKDX4V67jor77keh8CIgcFaXtin73DhSVqcLaZRIHvn7F5HwWHV8fuDzJP1nlUKFWW3miLMO24IP2fGdXF9WOhqwac1c3/s6Hhj8QNL7T+04lQeHPsjkXz5l5oePx/njMXqeRWPhi63ljPzHqrhs775y+UHpFeW/Q1G201ZXqgtOU2yu3syB7aupfOJvuDdubHEsxBT35H+HXS4knw9NcR76yVelHW+eNg3LRRcS8fmIuFx41QJILdtqaRWauFhUxf33s9e+AaWi5YX5U4XTKlBHvF4ODD+D+nnz+Kn0J2q9J+5wjP9YdHrY8Ba8NlBeoVeoILcb6DLTbf4MxFTSWirZVD31FBWPPpa0LVuTjyT4cQVliliwogJBpcK+ZCkVs2R+b4Pbj6h00MpYiF6lp2NWMaDI6PQiSTCmhxZBcwx/2M8Xh5ei7zqL8wand38GMGkVfHzDMMZ1z+eGPjeQ53iCOlfmH+PynZUM+/cdvLllPgCtTXkIYoiqRgfBcnlWENOZdixZStltt8fLHQDaHj3IuvJKREPmB6pVaCTgV+DdupWIx4N+6FC8Zj1WGtOOHygeYYJqPUQi8WOd1+1s7jlzIuH69PoqocpKJn4+Mf7aHZADtUVjIFSVnkmU4wSHzy2rN+p01Iejc3lvAzWeGvJ0eWRpsih3lctGu8B2p1wGiwX+kOSJW281hVmnRArrcAUaURUkmDMRVQST2kS+KbVe28osZ8ABVbTMUCo3HqlbKZi9brZ8Hk2Qrc3GITXKIlZ1cglNbW/ArjPTL78fI1qPSBrfP78/UztOxW/OQhfwErZHr6NWgzPgpMompvhtzv9Vvofdovwb8tfLr1WGzL9BkDPkov212D/9lMOP3M/V316d3rIuNl6hJaAEFCIRlxvL9Ol0/OEXhH5pXMUrd2Ase4OCa6ajMBoJu1x41AJIStSKzCGxra4/jrJH4q/vWHUHvx093OLnOFU4rQK1qNMhBYM4y47iDXlPSM2DhJOFqNVAJAQNh2Vjy45nwR0b4w4f/ysYo6WPZ5bt5cI316YN2MGaGnw7dyZtK9DLizlljdHpdWUlylZFqIuLCVVWIQUCVDbaERR+ii1yKaRW/IG3btLTKS997a7QomXGCCf/2HE7Ne6aeLnEI2Wua5e5j3LnukkcbJQZGm9eOZDHpvTIOL7c5sWl3MJxl/yDzdPLx6hy1RIsk6ldsUCtHzIYIJ7lAhhGjKDuyuvZ88wISn96L/UAkoRZasStNUBEXpFvt+ADGtrlYZbSB2rfgZ9QbJEXtsI2O5Ik8c2B1fywfy/K/PT6Kg6LnlAkRDAiB5RsTQFBZ1+sWhNKS/oFo3ozOP0eJJ+cUdfEArVHDtT5+nyKjEVUuirj/n0HfXJQLr/7Hmyff05E8MTb+5vCrFUxWHsf13R9gA6ffyY/zPR6zmt3Ew90/yTeSdgU+yqi3YXR2X7wuMwIKugi17OblzKu6nkVY9pMoF5rRmiQfxMaRwNOvYWfjv9EqbM0abw76GZrzVY8UcMCQa0h669XocrJZemMpWze2SPFb9PnM6H09kXbtQs5N95IGPl+UBpPEKgVWlxRI4dQJMSWmi0p1L+k8UrZ5QWDnlBdLVIkAv5GqEmTuTcchn3fIPm9eLZslXnURpEueVktlloNag1OKXlt4Fjdybks/V9xWgVqAGVhIY3l8sr6yQRqyedDUKnkBUXDSXql/Ym45axOPHNebzYft6EQhLQXXpmTG58CxtAvdyjuw/dgFOUgXDh7NsXvvouquC1IEoHycipdsghQK6OcYX2870PWVv3c4o+r3icfJ1efS1HUkeSLnbsyjt9cdphAJIBBYaassYyXdtxHmTfz+DqXD0HpptAoB+jYw6DWW5fIqKM1dm2fPghqNZ6NCZpe2OmktjFE9+BeVPY02UnAjZoQjVr5xo7VtMParIyBuqyilEDUoitssxGIBHhk3R3c8dU8LDPvBiH54SloNXx+hqyj7A/Js5Oz2o7iw2mvM6NfR3RdUhf7ImoNH48RaPR7476Bj10kq/vhaaDaU02+Pp/WxtY0BhrBIwfCWkVihhfwumQtalVq0NKqFCy4ejLT+8rGsxGvB1Gn47eDtdz9yfYUhUaAHcflc/dF68H+Evk+qtPLAa95oL6k2yVMbHc2DVozCruc8de17sTxvGLu+ukulh9NZuHurd/LX7/9K137yg8kZW4OhY8+iio/n46WjlQ1pNaDpZAFe8kV9DtjBvn33Us4urCuNabWs5M+v1KLUxXVE0FCQEAtZu5mHNlqJIumLkJpMuNYvIRDY8YSWfMmvDEsQSyIwSU/NG3frePYFVcg+XyM7jaBF8bPSvPOCVw8zMKzrRK6KHPnhmjz+4nLMqcCp12gVhUUEKySA9KJONQASBKiNXrR46aW1bIt17xJiVr1/wh92lgYUJzF7gon/dqm/zEqc3II22zxhS6AtpYcIoEC7G75plKYTKjbtkXdVq5FBsvK6JTdht6KexlcIGem2doc1h8rYe2h9Bnyh+tK+NfqzRhURnRKXTxQf7dvb8bz/+3YQQBydYUoRSXrK9ezcMumjOOrXA0IQiQeoPvm9WW86R/0z+9NoLwcRV5u3KpJVKvR9euHZ1Pi/UpvvgXz7AexY0QbTJUtRaFm04g3sQ6QFRTtn3/O4cnncGbb1mgjXginBix9yIlDYUTS6gjb7Ql+tKQi55zJIAgITZyjjWPGsqO3PPOKtX6rlSJD2mdTZNGRNWkUhkIfyjwrICHqtXjHTeYH3X2MLJiC9eKLybn+evLyCsHcBkQFtd5aWaB/9PMsnLIwzsOuEhMdiIJWj7f8EjoZEw7kTbGmfA0f7P6A2rlzcSxegqjTsbJqAarsX9KaX+Rpi1A4x2MdMpzC2bMRp87gwVG3srK+BpWoSmFNeIIeanylNGjNEJRnEpOXfMAdb9wOJHOom74W8uUZRrCsjIjPR6WrkgW7F1CYnb4E18qqQwqHZTbKlLE8dI0CnSYzgwMgT5dHl+jaur7Sztw3Qji/+SbjeKvWSpu1RyAk31Nhu53G3VEKbPPEzVUNgohx/GT582g0SO8sIjTj5lS99CZwL/uG7u/8lDhHJxTPe6vFfU4VTrtArSwsRF3fSN/cvuTr009TmyL//vvp+mtUbMbYpDvRdgxK10MGV+E/C0fr3Lyy4gCBUIT+bdPLMipyskGSZA5xFD2KzJw78igl3i1IgQA1L7+Cd9duVNFAHSgt5Y4xvfnPldeSp5c7H/N0eZQ6qtlYkr61tqbRj19ykBcNoka1ERV6PBE5aKSTlq3xVCJFlLQ155OjkxsClu85kGKRFT9GNFOM071UBl69YAr3n92HrEsvo/CJJ5LG64cMwbd3b1xkJ2yzEdCbsEtGNOkCtVLN4LOvYOC4seiHDSNcX0+gpARx9J3weF1cxrQptCEHdsmE77xL0A8eFGdwqEUdweOlKM062t4xkR5P9MXQToVn8yaMyIEvNvbptc8zYuEYahv9GEaPo3hMA10eHkn3SyvRtG+D+fff2HPvJYzu1B7TuLFYpkxh3trjrJm+GmnIDcweMZvzO5+fmK63GsDCnDs5JBTQ7uOP5d+BzsjlPc9nXKe+KZ8B4KFvP+HVTW/g27sX0WCg9auvcti9AZXhWFp2Qr6+EF/NJDr1OZOsSy8hXNSGnbmd8AqNZGuzU2Ze83fP5+JvzqP0hpm45s6Pb7f5o8wSbbJscOz1TtFHxaXX4167lv39B3C4dh8vbHqBy0eY4ibKMehUCjTtX2Lup/dz8IwR5Ja5eH/mas5qe1bazxzDjVXdGPOLPHsSgFyHlKpl3gRli/9D2azHCEVNcKVAgMp3l+Mo0cXLTnG4a8CQh3fXLhAEJL8fkBBqqlo8hn/ufLTN8gIx4E+W7f2TcNoFauOZoyiYcSEfnfvRCal5KTAVQtdzZDGmoFsO0mlu5D8T3+6q5M2f5Sl8poxa06ED+jOGIwUTi3Rts/Xs9y1lQ/VKglVV1L/9Nv4DB1Dm5VE8fz7mc85hd91uVpeuju+Tb8hDoWrM2MBS7w6gUrvigR2gr/ECvM5O2L5KLy3bcfMuFJEcRFFEJarQKywISmdGLnX7XBUGMS/pobrk4BI2Vm5E16c35okTk8ZbL7uUzit+RGGMurDYbHgNJuwYUQXSLPQ5K7Fv+4rjKh3tPpiPqk0bAC797CCfb61I//0G7NgkI/WXXItpwoQmgVqDtltXOq/dhP7Gl8FWQvbodoRr6xh1wInBNSPONa5w2nF4fZTPm0+QHJj+L1DrEQQoePB+wvX1/P7iA6wpX4P/8GGC1dW88uMBVu2rQRAExhePp1duLw7bD3P/6vs5JEocbHc5RksWQtRuLKQVOP+MAEM7ZiAUR/SE8CBotSiyZMlPf8SNKs3iI8iMI1/YRX1DNd5du3F99SUDq/dzbqubmDdpXsr42MP14WntGNstH/e6dWw740y+XvJj0v/HYFKbUApKttpqud7fA0VhEQgC9oi8AD6tT2duG9MpPj7HoOa5C/pg1qpokOQx7hUrUa5a32LzCkQVNf3Jv7kULfMmcL72BqI/edFb8gep2WFiWcn3SZKzy8J2KOglv1ezNaSWjqGorU+7PZOo3KnEaReozeecQ8FDD550kK575x1q5kTdR3RWuGIRdBorlzz+x9Q8kPU+ACb2LKB1Bh0Rw4gRtHv/fVTNxKiyNfkcd1bEqXmqVq1kfeXhw1BmZXH9kte5/+cEWyRHmwMKF3UZeM71Lj9Z/vO5vf/t8W1nFlxCwNmTmldeSSstO/2nSqyhhHRqliYXUdlITYZA/dzUKay/ahWDChIOJf/c8Co3ff4WzhUrCVYnTztV+fnxmrUUChF2OlFnZ1Nl7ImYk2yrBcDxtVi/uIoH3pPrpWGbDdFiob78AL02z4LaVPXDmvM+4bbgTNxuLyGbLR6oTYIaKRRCEEUEJGg4imFQHzRdujDi9w0URCbF9Zo9QS89SkHz71dxrdsCA6+SKXYqA7pho9GdOxXLktUs/fkjSm+9jZoXX8QdCHFOxVzqvr6TNeVrcAfdBCNBvi/5nsNla3jyDBULrhtK/fvzATiosnH1d1dzOF1tHtAr5PJAWKMiWFaG67c1BCQ3ajF9YDdplRi7/p3PfphDyUUXEXzmSc478ivZOmvaMmIsENdt/53Su2biXr8Bja2O7dF6dfOMWhRErForAclJnseGZ99+BJ0OR0DuXLVqrHTKS9Tb7zu7G+cNaI1FY6E+GqgdS5eyf85zSVTBdAhWpn8IZwqKQk36IBr0KHjy6JIkydkn3ftYNvKGk9ZLj79XbnoLv0yicqcSp12gDoQDnL1wDEt2f3JS491r1+JZn+JjEDUNOEHr0ynGF1vLeWWF3NK9o8zOl9vS/9gyYV+ZyMH6MoLl0UDdWg5oni1bsH32Oc5QHXoxkeXc0OcGuvlepyGDyFKDO0ChpntSEDXrJARVHZGq9I4tWU43nTSJxo9uWT2JhMwtdic2h0Fhxeiqo/yOO3D99FPK/zeuWEHNnDmyC4kk0bNHO6Y8uABxehq7ryitrcKv48iM87B9/DFYrJjw0qNiKdSnBrmC3CyeumwUvRa8Ssmll9HW1Jb7+/2TpyWRg2PGEtz8DTyVDWE/QnYHcm65mXaTzuK1y4rwRBulvCEvUzf5wWyR27Fr9sr2aFntQBDQ334nEUFgyNLdRLwewmoNkgS5gVJ+r9zALStuocpdFV8XqNy+ED67Wn7vbduwXHQhm6MSrYer0peVDNGacjA6zvbpJ4TxMaNP+m64vwxvh1Vrxq9O/B4aNGbW1S1hfeX6lPGxQD17yRpcP/yAd/NmAJTmYbx79rsUGApS9nl65NMMzZnOI79/hG/1z4haLQ6/XLIyqU2UNrEhi1mSZWmz4hk1QHm4Pi6LmgmBHHPa7ZmColCQXgPfZlHgk5LrFTFruZPVS4/BccV1+JpN0NPJ9v4ZOO0C9bGtvzLn6WqyNp8cP1Hy+hCbSiYuvBg+vgysbaHN4D/pLFPxxdZyHlmyM+44Uu30ZzQmiHg8HDp7Eg0LFyZt14s5eCL1BCrKQRBQFcg3ivO776h+9lkQ7Vib2HfpVXryjAY8gfQ3+ojOFtoXH0qy0bIrf8bY+UXEwtSbEICCfB5vQsd7bOgT+KvOpzZNk4wvGKbPS09w3ufJ9lYWdTYFHjnLipUqmsK7fQf177yLFAqRd8896Ae20N3llW9om2QkFPVIFIaNwB7rP/Y2U9yPRNCvepwZliOYCvII22yY1Cau7n8uxZt/R2GxoCzumhif3QHLlCk03DCNqcvPZ1O1vNCpr7Yx5LAP/UUXy9KYP/5NFv26SKYQmotb89a4HMrzVITr6nEvXsz87/+O/0iYmpAclPL0eZjVZowqIxVBB7URExe9uRZBq0Xy+mjwyp8nz5Ce6x8rwwRzog7vWjX5uny65qUPJBqlAovajF1MXKviLm1ZXvY+a8pTVRBji4MOU7TNfs8evGotWl0+w4qGoU6zvjOq9SjaGjpRr5UDqRhtdjGpTShFJblGDeO657Np1gTuP1teoLVqrNQ28RrxqQV0ipZLH9V/nfCHgqLprlvTjv8oQym8yl2ZUfwsY+CdcC5z+l9CJL8ACagzi5hmPZHSZfxn4LQL1KUa+Uee78rcytkUEZ8v7isHyDeTs1xuJb9kwZ9ximnxwvf7UzikmYwJBJ2OUGVlyhTLrMolQgBvVQXKvLy4Loa6bTGS10tW0J5kVlvtrqZN5+95/gp5StZ8cXBq/QaW1zzP71UJOlw7ixw4IzddnqK7gVbDa8Nq2edKOIHkGjX89tBYLhmcGnDrXH4CylKq/cmGoDm6XPJd8nWMzQqaQj9kMIRCBI4cIffmm/jnYYm35zwFc/pDsFkZx9tAUKEniBLBYsU4Zgz+m2dil0zx/0+Czw7r36Bk93qcaj2RxkYq7WXMW/4+3s2bsUybilDehMXy9d2w41O2lrjoczSC50gJAJM2hAiLIjlXydKZhIPyotQbZ8ArvdHsXUxYUDLut8p4nbPAayfyYwmKvUF0Si0mlQlBEGQuddiLU7Sw6ZiN4LFjOJctI1AtP0ALjekD9dQuYzkv63263fYACqsVjdHMrZ0+oLViXNrxx+s9OD1KKoIJ2uLIYZ0JRPwp9WaAQn0hjw57lIBO9lGUPB7sOgsexd6MSniH7Yc56tlIQ5QumfXXq7h74N0smS77iVw0qA3vXTOEXKMGMVqLH140nHFdzyFv5l3yJVITl2/NhMD44bx1roBQmI8EOLM0abXMY8iePoO3zhXw5ZplL8pWrSh6+ikOD06fkBQqjXHVTkVRIRHAnW1s8Rg6tZJf2g7F/t7nzH5uLDffUIA0flKLn+NU4bQL1EelWgJKsNhPrjUzxi+Nw5D3/4RH/UeMCQRBQJGbm6RJDdBVPwFrzT8p/vuzdFye4LCq2spBssDpo7DJdDQQCbBo/3/Y17Avre9k8Nk5jNwdTlpMzFLL+6/pWkT2DTcgaDTxH3b9nZezppeCcCCxCPpT6Spu/flSXMHUqWqDO4CocGFRJ7Nb8vU5FDTKnztWj24K3cCBIIo0rlpFsLyc8no3Pp9X1oluniF7Ggio5UAWMVsI22woRIHObYuQBGW8NBJHdP83N9rYZJOpjlsP/ULJly8CYO4swLJ7E+OjxsGWPd/x0OcR9J/IC2nDczujmDQFQ2G+XPIo+QWQ5D+OUoSv7+Kva2vRBJs1NAUjdFuvIF+XF19n6ZrVFXXIT0iXXOO0SV6kiJJcY/oS3SWDO/L09MGIgkjE40HQ6Xjph/0Z7eMc3iB1DpHqcKLMYDPIbJZ0gVqv0nN598vRaorxRuVXd3YaSBU/MHfb3LTHWHxwMYvL/sl542WmStZll6FX6eOemrEGr5V7q3nqa9kybXKHyTw47GFyb70Vf65ZDtQnWEzUKrWs6aVAXPoOj/2zO588N67FzFWr0PLQY8votOpHeuzdQ5dVK7FMm8ZMr4S22SXSRiLMbC3TPS3TptFp5QpU676k/cpvWzzG4HZZ3H3xYRziRtmqTVKiUZ5cQvl/xWkXqEsaj2E3KxDqbCceDCjMFpnuFoOxQM58PrkSlt33J51lKv6oMYEyOzul6aXIZKXOKV8SRZObNybTOMx5Ied1nh7fHuMuv79+B1Uvpy4OCn5ZjyJPlwjURUZ52ryl4gj5d91J9+3bMIw+E8uM6WztK99sdmeC4yohUeIs4cPfd6Rk7O5lyxCULrI0yUHghj7X0ds1jEhOLqImtatPYTSi7dED24IPOTR+AkJDHcFoME7JkM96kMapb/PyJf3Q5GTh3b6d/K/+w9LbRyGYW8ndqE3hkb9Tn8qKM7pGEbLbGLU7QlVxR9Q7X5fXL5oi6GVA9SL2t4bclZvY26MnoU2/02rMSDnYrnwq9ThBLzmNqRxuAEOjQF6T7+QfZzzFS1VVRHTJi3OtjGPxll+RVlMbwBVw8dKml9n21ftIgQD1taU0Wt4CVXppBZNWSdA+lH65Uyl69lnKH3iaC7fKY9MFaoAjjiMIqlqqc9uQffXVzPz4ZXIsgYzjs7XZeENestrJD/zAkSMs3LuQ70q+IxKRGPD0j7y1+jB7Kpy8t+ZonNYZDAfxVZSz84EpLBwrxu22MsGqsdLZ2hkBAW/Ie8LxgiDQwdIBszq5tj3F2Im7m1xutajkyboGphSPj29TiArqG3KwOVuWLBUEgS8Pf8n6yvUEwgGIqFLoiH8WTrtA3TOnJ4rCAoLV6fUVmqPDZ59S+OijiQ3GApDCcGxtRreXPwN/1JhAkZuTZMcFMKl3DmOHbWT7XTfg+jUhOKRq3RoEgeuK8xla3CHx/kodGlHPvtryjIuDOc5EQAdoZcxFiiip9VbFTRcidgfeTZs55ixDiigptiQcSmL7Vi35MiVjN899gTMP1JJvSM4UO+YUMP3Fp+jw+msZvy/90KHxf9eJWoIxiczmGXJOJwp7nckFA9tg6iObHwiqaGC7Zyec/XTy+Oj+AbWVsrxi8u69F7dWYP5Ekd2TLwFHGemg3uOgW3nU312SCFVWcnzWozKnNsM+Sn36tQGhMI/7hz/SZIMAly7E0f4cxpRuRtLLD5ALnn+W2ZhRZtCX+Gp7OfN3v8++qJlv9ciuCIa9aNXpdWRMWiWhxr501J+F9YLzaeg7DL9Wpm42b16J4cHVD6LIXUbd06+S/6AswpTOZCCGGBNkCfLDvGr2Uyzcu5Cfjv9ErcuP3RNEr1bQJltOUMrtXn4t+5WBHw3kyEUXMn5ziB9u3Jgkn5oOQwqHsHTGUrpkdcEX8rXo7hLDp/s/TfVYNRbQ3i3Xx1sbW2NV6Jji9iS6mJFdz2/7eg6v/5q64NoUDe4ALq9AhcNJMOJH+v9zRn1598vpc+09WC+44L97g6J+MPg6OWtS/e9YH3/UmMA4YkRSsAIYWJzL3mOL0fy4lkBpwrlF1GiQPpnLqrOyEvKbUVg1OQjKRsK56ZuD6s1CUpYhiiJa50VkBftzYNhw6v79Fpoe3fHt20dlYwVS0Eq+OXFTxMomU377LY2CnJ+rfgvQM6dr0vZqdzVv1y6lokPmNmFNjx5xH7t7P3qcoiPRz9u89LHzc3xH17P1vUXUzf8AgMo33+bR21+gPp0KoF+uzwbUViqMeeTedCMOo4Jd7UV8vQaDJbXWDuDYYUXdLEFWByMypzbDPvaRKsLqZtmwRkur+x6gV06v+KYdDXu58ugi/Nu3cM/2xQgeudlHUVvNwM/eyNhgYdUakSQB1YESAAoemsvcuSF67Uzv4G3UKkH0EvlpEfuHDKX3VWfz7uKlLFE/Qtesrmn3ydZmM3RPOcMfuZZ9vXqzpf9gum6sTqHmNR0PsGHZCiSFAu/27Tzyz2P02lxPaYPM8miTradNlkyNLbN544a3EYWI49PPEPamemO2hAH5A1qUOI3hnZ3v8H3J98kbDXkciir3nd3ubGqCjThbD5B7LqKoclcRylqKl2Rtk+YIhiM0egVsXg8jrbcRqD4fleIP9nr8lzitjANCkRBhKYxl2tSTGi+FQpTeehvWCy/APFluB6V4mPxnz1dJpgH/C/wRY4Lsq69O2RYIQTuPGahLqe0+u38t2z2LmN79/KTtebo8ygUvdZddR8Hcf8aFiwB8ChWh669O4aTnM5rsilqkQABV61YorBbsiz6hr68vG+rzyTVqkt4fINuVXrkspzHEzf2vT9rm9Ngpee9NXunsYO7Mx1L2cXz9NVVPPBEP/NmuBgZ9/w2OKUOx6Jp1cy6/n4bGIbB0P5Goea7C5eTinz8k8mYp9FTDlBcT4/teDL3Ox/XOBvps+4WDo+9ndE0NfYxQdck6mPwEfH1XcvlDpSOcyVC4shLGP5l2nwXDBxDR7eLuTa0IVlRSo7PQ+o6rWFn1NMO2O2jdT16IFD0N7OcFFQAAIABJREFUbK/dTvbCIyhDyc1Jgj9AzSuvpq2NWnQaRu0S6bpSzqgF5Lbl7IXzcfTslLKPRqlgkm0x/b/aRiQkjy/w2gn/8wU8RlPaYwza7mb4Z8cJRWvtOp+bG5ZDWftKSEOaytZmM3J3mJt/X4EQlUDIdUTIen8D1cpvgBzaZukxRCmFZTYPHQrlaxpzXv9x+Vym930r/RceRYWrgod+eYhb+93KK2NfaXFsDFqFNsVODWMBM1xuekz9Fx3ajOS8LudhMLWDJhl9ICxfkxNl7RqlCJKSQNjPk+eM4YlJ0h9vyvsvcVpl1LvrdzPkoyGsLVlNoKSEiL9l7m7E58P9668EK5oR1CNhOTP7f9Dw8kfQ1HMO4HiDB1W5fEmaB+rcPfu4/CcxZRHmtTFv4S27mmP9RoFKJdt3CQL+nHzm9L+I3lfcTnOYDF6U5bJQvKZbN7Td5VX/1mVaIs7BZOkTbBC1Qk1H/TDqMsiQpuOcZjVGuP7HCLlHDqbdp+aVV1Oyc0UwQM3GCHQ4M7ExEgavHdfKI2jDyYvL2nAQ++JfYN+y1AMolDyqKeWCnz4kVFODAGS7oOfHc3Ec08G018DSFhDkv6e9hjLNomf88/W9JO0+h0Lt+aWnROeVK1j37jKumTSLxnH9+Jvay66a7fH3KKqTzXQVNenXXTI1WJi0Si5fHUQZTvbxU7TQtnzbrqMpbc4tddsN/mI/6mYLotoQdP0s1d8SoJO1E7ety0YbTi77KAIhsj5+F4A2WTryTVr0agVObyhuKCBF5H22NrasRQ3y2si22m1Ue06+fKlT6lIDdYczsV76MUPbjSdPn0dHS8eUsktsH+0JjGo1SgVSRE1YivD14a/ZXJNZA+dU47QK1CWOEiQkCnZUcHjyOfgPtjxFijsz65sEL78LnsqR69T5meU5/1+jccUK9vfrT+BIgtqWb9KQ45AnOapWyZl5QVkF568PxF3XY8g2aMg2qAkj0PnHHyh+699YLryA8N9fRHFBHsdcqdPk0YOOYLItQ1Cr0XTogKZrV/Sjz6RPTzU/3DcchZicJVzXZTbvd58BmuSMI6BUMWegj931ycfQ1sr84DJD+lrqSXeE+RyARNiWXlgrZPenLj5ung8rnkT/4TsIzR/0sYDV9xK4Zxc8aZf/7nsJ+ffcjV+V/LkDSkWCU5tmH1laUyIQCcTNIpyinJ0VNAlk2X4P2kgET/bJP+xAljrNbUxvtprpO1TVpdFLaWG8LoPRcaQqPXNKr9KjqkuvLaO11/GXYcVoVQoUosCuJydx65hOmNQmFIICKfbA0Z3YZzC2eFjjqWHCZxP48tCXJ95HqY0bPsQgmVvzXrCS/W65iWzpJ+fz46LkWakr4It+thNn1N7jNzEx+3GeW/8Sz6z+6ITndKpw2gTqZUeW8Y+N/wDgmaPytChUnX6BLIZYVpZEWlcbQKWDM+6AAVf+OSd7CiAaDEiBQBJFz6JToQ6qqTeJKUL65RY5EMQ0nmPYULmOM0d+w2XDCuT27DZtcHy+mA7lB9gX+Ijvj31LcxSbW9OuGuhQjKBSIer1hF94mCtrn2Wfc13K+HN6F/HOgllkX/kXUMl0L0GnY9G4Uazu40QpJFfQQuVyUCgzpWdFZOwIMwrwzT2JDdGFQWVuBhXCbCOEfMkliUMrYd/yP9werJl8Lu9OsmC3yrrGdSYt306b3iJdSx/lAvtCPtyBEBqlSENAzprzAomHhOCpozAcZu20TvgUyap3AZUiY4NFjlGN1/rH2pbdlgzf1R/s6FNkaogCAhmuh6qoiGfO7xN/HeNRi4LIjX1vJDwl2n2ib5maBwn6ns1vo9pTHdcJbwnpSh81rkpe2fwKWw7L98Eiz1E+8yd3DIck+VqN7dpy2VIUBXIMahSigDfko6zhf+PuAicRqAVBeE8QhBpBEDKLEv8fsezIMp5c+2Tc3eSASlZk27ZrZYv7xdxdxKSGF0GWO/0fMj7+Gyhy5MWacEMiUIuiwA+97uGLBz9OqX1VWOWsMubaEUOdr45VpauomP8O9sWLURYWoszPp2HTJpwBZxLjI4Z6u55fegs4pifKDBWuCtRBiaOVqdnO69te4eKvL0AQRZAkum3dQvetW1jRWb6Zc5rRzoLl5USASoM/rXFCuo6wsFpD/ggdNDa5btGFxfyrp6cEuKBKTf6lY+QXTZkiXhvos3Fb0i+GZQpYaoXIqi4m/n7PAHrs3UO3leu4/tG/pR0bQyyYeENeHp7cne1/Ozs+Vc/3JbjMeOoYFhLxTxjCawMuwpuVB4JArRm+njY848PApFXR5bEHU74rNJm7574ZMTalQy+oFjOOb3XfA4RUydfcpwTt7denHQ/wyRgFwWYMJ0GrxXjHnUnXe8mWMm7/WDaJuL3/7XSbfKn8H7oTB+pYvdjmsyW9bgnPj36eNya8kbQtpqPSOVp+6hQMclhITiDObDOKby/4lhHFJ7bNe/hSOwHzl0QIohT+d8qcJ5NRzwcm/5knMWfLnLgOMIBTDyERtu5u2QATQN2xIwprs86ucAh2fga7vzjVp3rKoIwG6uZNL/kmfVpdjeFdnwcgWJqcUccCcf28Rbh++RVBEND160fVOrnG2JRDHYPLbeLXPiJ7hySEenyffcGCl8Ic2J8q8CRJAkccJVSs2YC2V0/ZiUeSwFMLCCnu08GyMiI5uVzW+SnCaYx3Yx1hylatQBCo1lmpvOEeLAMKk0sZhX3gtvVYrroD950PQkFhvDmn3bN/xzJ5PGS1l7PqGDz1oM/h4PS/pgR3SaPJGLBEUUBEjT/sIxQJodH4yTK0TL0anDMefcU/yFLLzS1alYIaTw3ZggpVXvfEQHcds6QsHhjyAL93GsY3j/6bzru2c/20OwmMTF1UbopV3WDtVYNQtmqFBNQYNS22LZf2P5sPx4+KdvQJ1JpFNl0zNON41eTx/HrRFKr1FhAEfLkm3jpXoOj8SzOe07Hh7fjxss7yOQngyTFgmvUwozapeXVFYl2i3OZl2Y5KfMEwnqAHV4GZ+bd1xtk5c7YegyiIDMwfGNfQPlGDDMia1M151IcbSwDoGAiCJNHJ46JGCshmDlGEwkq2H1VQ15iebtkU22u2y5xxAqjEE5dwThVOGKglSfoFSF+UOkVoqkUBIAkCDSbQ1Lsy7CFD260rnZYvwzB8WPJ/xNgeUvr63ukAhdUKokioPiH6L0kST659k/4VL7G1ZmvS+AcuHoNoNBJqSA7subpcsholzHZ7XDND178fOY56TB4pqSsxhvaShqI6gWP2RHZeZY4gStDdkVoPLjDkoQiFUB7Yg37AQACO33Mvs79eh040p1gkFTz+ON3+s5BHz+2ZkSNsmTaNLqtWElm5jmsmzSI8bhLospKzY5VWXmfQmhl1y5X0WP1TUtcZ3SbDzO2Qk5DWxNMAuiycI8cxp/9FKIqK5ABnUiI+8FiLpQwRDYGwn331+xm1aBTvb12ecSzALWd1Z8MjU9CoFHywtoR/rz7M3QPv5v3pn8PYJjzq8X+DabLglEEjmx+LgpIHz5rM1J69Mry7jNk//MBrudvosmolNz/enpuv7kn++TMyjs/SZrO+8DK6/7yafz2+gDtu1eEak1lLxea38Wb7r/jsyWvovGsX3710PjsGWFEpUo0JYsjWZvN1hzDlb/6HzYsf5Zqb/DhGjSYckSiyJDLfplzqeS9fQ+V5F3PNG4e45bmdJyW2/8E5HzCtk3y9TqQNArC6dDXv7nw3adth+2GyJIEcjx28NjpF1y2aKhauLtnMPd+/xPqSE8uV7ih1Y/PJQV7VguPMqcYpq1ELgnCTIAibBEHYVFt7YlPapoi1nzbFwjEi24anr8+1iB2fQmP0C1/+gPz6NISgUJB91VXoeveOb4s4nei2bKGmYhf7GxIaIYdsR3h506uYVywh/+7kjDBPl0f3sii1aqAcRHX9+lFpNqc0u8RQtO5n5rwTZJDmjPi2fTlyva1NQ2p7cr4+nw5VoAiF0A2Sj6Hs0JH2DR7OSONOojAa2Cge5+FfHsMbbLmO5/bLWYxBowB9dnJGXfq7bFgcDrL5WAObj8nT4L++t5EHP9+e7u1kU2NjAQaNkp/bDsL65XLumt2VW67ugWlqy7RPk3cixeJ5NHjlBbbS+vQ19vjpOUt54fcXOO48zve7q/hxTzUWjYWO1mZyrfndWSsEmPDZBPp1CNI+10CDr46C1rvoVJjZBBlAIxoI4ycYCeKPuFFIOtQtOGUbNQoaIyWUu8oJhCRaO1/mtv63ZRyfpZGpcwM7qNhb6WT5noMYlS0bQmfrsqn3NvDTvhocfgcCAg1RbZ62TRZMY1zq2qVfMmbhHjQB+bOGKipbFOhP+jwqIxPbTTwpE5G1FWt5f9f7SduOOo7SUdDIZgGREJ2K5XJfmSsxM91Zvw1N/vcoxZavBUCVI0woEqZX+DnaqsafcPypwikL1JIkvS1J0mBJkgbn5aVfoMiEmQNnprSIbu2jZ+qFD7W4n3vtWkquvDLuzceOT2W+a7TpAU+d/Po0DdYFjzyMacKE+OuYDnW9RRH3RwRYeWQz8/e8x4+HUmVTLRoLvcu1+JQKFF3kpgbtwEHcOPFR+vd+nc7WVElMfelRanRWRH0ioIzpcxU2rZbc6mMp4/N0eURE2NWlC/oBcnZmHTYEQYJnss9LGisFg9S8+CK7f17FsqNf8cPeoy1+B1a9igsGtJZb7duNgh6JFnkOfAffPQyCgmeX7+PlH+WHV5nNgzsgU/dYMEPmzMdwzy4Y/3i8LdvlD+EP+5AiagzqE5QyCofRJ2cIDp88qzBpWs7i1h07yoI9C9hcfgh3IIxBo+S9Xe+xecUj8EpiUY1tH6NtrKLaU83Vo83cOqYTO2r38Nhvj3HEfjzzAQBd1Pi2MdAomwZk0KKOId+shdZzWbRvEb5gBJ1K0aIprF6lR6fUcdxRQ4XdS523HpPqBIFamw0KF95ACLvfjlljpsImZ6ptsxKBOvZv7Qdvo2ym8NgSZTCGu1bdxeKDi3l5zMt0zkov7doUWmXqYuK8SfN4ydBbXrMy5tP6sk9Yd/k6pnZMPLS9USGwE11vAKWgJkKQRddN5YOrx5xw/KnCacH6mNJxCk+OeJIiQxECAkWGIp7ucR9janLSLkbFEKyqxrtpc8KkYeVTaXUcWPnUn3fy/wdIkQhhV6K8EwvUVXoDx5yJzLasUQ7aXfYfp+zOu2SH5ShEQWSAegR7sjphj2YsTl+QcFhJB0v7tFKViqOHOJ6dw+a6n+PbCtTdOGIuxliWGljbmNrgaDWSN8++BGVMPL1Hb1AqcW9K5pIGq6upf3cexfUyTa3U2fKibtcCEy9f2l92Uu97MUx9OfGfXhto5RKRXq2IZ99ufwijWglKLRz5GeoOpLzvmV1yWXrbCFpZdfxr3L+Ye85jmNL4DDbFfefmML6/C3t0IdCiaTkoBkNyAKx1N+L2h9CrJV7Z/AobPWXgOC6bV4T88MWttKrYAUC5S76u+6ISCUdrWi7PGaKBut5bT4QA153RMuX09rGdydVbaAw0Yg8do1b7QYqbeHNoRQufbNnLgWoX3tJreHjgcy2O/0uPv2CpfxxfKILD78CqsVJq8yAKUGRNJFz5Jg0dcg2o69PPsE/kjFL1/7X33mFSlef//+uZXrZXttC70gUjIIIgoCKREIwYNSamfD6JJkQNRk1U7PiJiaLGJGosSSygIAorClIE6R1E+tK2N7ZNL+f3x3NmZpedsvBddtf85n1de12zZ55nzn3mnLmf+7nL+7aVUdQQvnw/7HXoTLj9bnz+0KKg0+hIH/8gzJbtzzRCQ4Kheb9Gh9eFoggs+tg+Z6PGCorg1X2vRmz4cDHQKRQ1SGW9ctZK9t2xj5WzVnL51y5O//gn+GojE4z7HWoedYCPOgInQ8TjHYzSBx/kxI0hizRQuFNhTqGkIWRRl9nKUHxG0mw2GlatwnuOa8kz94/8Z+Y9OD3yR6/TanhY9wVDH/phswa6AH6XC9+pk6SNSmbxmWfx+r14fB4q/Tu58t4fknf7D1vImWnO5BrN7ei8XYPHPj16lsOZcGxd84ITT5FURCk9pLVe2hjdDdZiIfb7Q9WVjhrpDgESjLpgrrLN5cNi1Eoftt4SKjuvOgrv3QKle0lPMDK8WyomvZahXfoyqe/AFvnh5+Kdg+8wZ+0c6l3yuUoyRVfUyer79S47dpcXrV6l6DVnheRXm9pmJnVDJ3S8v2svt/9zK9UOyT+RaYnejTtRn4TwW6hz1TEiawR903pEHQ+QZEii3l3P6AE+arWbJdNb1HOkILSNkktdMZBtjb4jzjBnYNVk4fL68fq9pJnSGN07nfum9EffJCah0QjW/m4C+tzzI+gPwKQzsa5oHWPfG0u5LXYWV8CPHbjeA9UHeHLLk1RYU2Rgeus/4P96sfLoUh7e+HBwntPrBEUXtg/lueiiXEcv18O8tPsl3ti2Keb4tkJr0vPeAzYD/YUQRUKIyHk7bQhdtvRbeyOQM9UtW0blAkn6c+L7s6S/KwInQ8TjHQxtahrempBPVhgM+Hv24aw2B5SQ9VflqMDvTSa5Vw8APOek6B1zf8yQy1bQLV1uNROMOmyWU1gqanEda77qu44dA58PXb8++BQflfZKSmwlzFk7h32DzWTcMruFnO4TJ5j51M95r09o0SxrqOeTMX5Kb7is2VhPsVwUs/pIMqpKe/gO6QG8ufEk/f64gjqHB46ugifSoXSPfNNeAyqZkFVV1IqiYHN7Q4xz5rRQALL2NBz+FNx2au1uFm0/w5kaO0+u/wcvb4ye6gmw97SNBpedDH0PXBWTybZEj5GkmVW3hEvu4jR6VfmqDIXYa4KNVbXWLLKt2dR7KzldY6fWKQtTuiSGb4AcwI+HX8/cgYsY2WUkV1ofpbF6UNTxu0+fpbxWUGGrpWe2osoZnmApgJt6/hpXxTRq7S6MWcs5Wrcv6vgKewVO6yrqPGU8f/XzvH3t24zpncFdV4d3T2Td81swNbdWAwT9S3cXM3b+Gno+UMDY+WuaUbgG3KH17nqM2tD8SHMCKXwBPpzd5btZeHgh2sYK2PEmlB8AZz2nHVUsPbY0mPmRahUkGi30yYreGR3kjsGq8qaW1sbOEmkrtCbr4xZFUXIURdEripKvKErLLpkXAXo14d4ThhUuwL3sr5c/DG+Z2j3YcKMsdmn2QWaY9EiLz+gM0GWkozgc+G0yeJV68w9IemchrvLvMyv/seC4Bk89iieZlN49AHCfDinq6n/+k37z3mVbUahQpdbuZm+mDOI59jUPuhm6dSP/ry/zhV4uXiW2kuB2/PPdThwnTwVdMAHY1RZNL9tC1nNpYyXb+2nQThzTbKynuBg0GtK7DwC/IejvjQSby4vb68di0IIxUWbqBCzkJha11aCl0eXF41OYPiSXS3LUNCxLaigAGZhnSaOq0cX9i/ex43Q1C0+8zFu7V0aVA6QrQxFeZgwazva7n2Vsr65Rx6eY5MJo9zjZ9OAkpo+QFnZ2kjrPXi3jJADWTK7tcS3p+l7YXF7qXA2Si9oaXTlcO6gLt18h0yjf336atYejc63XO73U2XTUOes5XlOGQJBsiG6190+5FL+rC4qmEUP6V5y2hS/9D+Cs8yw1xqX8aLxa/CQER8obgjuepnhz4wl+VpxO7hNPoOmSjR9wZ6aQ88TjrM0fwYNL9lNc60BBZoc07YrUNCUvoIQDnZTCzfl+3++z87adQeKo43XHSTGmkFZXBst/Cye/AmsmvVNkllBhnawKfvCKuayYuRxrBLrZppg9zs0Z4wJVpk6UntdR0HVRLeqylhZ1OK4IxemkYvGWsJwMDPlBe4h83tCmS4utKS91ZqK8+U1zqR+57CXu7Ps4xrxc0GjwFIUUtW3jJiyNXqrctSzaIQOBBftL2UIVTqsex97milqbmEjipEl83SAf5pLGEkoapWJe/7WHUzNmUPOvfzeb49i5C5tVx2fOCo5Xyu19merSyC6y4dgXssC8lZXoumSTbE1j7oDF/GzYLVG/g0a3F4NOI7fM5jQKrBambHtUdoxON1EwTLqG7hjTgzd/MgqDTsOLtwznusGq1ZozjAKDkF2mdz3GlPxcCip3BX90tQ4przEGnzGASd06VzsrcfirYzKj5Samk1G5gCuzZbpcpUN+J1kZl8ClM2WzZVtAUWfw28t+y5DE79Lo8jLQcgP2k78i0RRdOZQ1nOV/P5/Dn3f8hcrkJ1H00f26iSYd7qqruaHrz1m85xB6kRiTUrTafRp98nZG9paKNycxuusjUODU4KnlgQ0P8MmxT5ny/Hpe39AyvmF3+9h+8izayVMp/8/jzH5QR/m/HyN5+vSYXZEGZai0toigRR1tjl6rx6A1BIvFjtcep1dyL0SAKa/mOCRkBQPsAR/zmWoPK79uCHJnR0OlozLY7zEWR3ZbolOx5zWFLiNDKqUwZeRRy4OH/KDTKuZzoVMbHnirqjF068aJm28macpU/nzbQJacepwpZx+mb2pfruqXxVX9pN/TdOmlqKzJKD4fjr17cY0bCGIPhypKgO5UNTgQejv1fXJIPkdR13/2Ofqu+WSasyhC+r8dXgcCLSnWbIx9++I81Jw0x757F6W90qj3nOV0tZ3emQnUOKtBAynP/ZvKLl3p9k+Zv5rzxBOyG4kQ/Gh0j5jfgc0VcmMUVO1iXkYaTo90C5Tay5m36y9gSmJar2lh5xcMvo55m+YFC6ZK9Trm7foLv9daAB31TrlbaY2ituhN4IAnN77MhrLlbJ29C0sUKyvFamDt7yZS5/Bw97u7mD1qMl/efB0pxlS4SU0TS+sN//uVajyA2SBwerxMGdCH7ITMmH7RT/aUsbFsDZXOASj6chKN0XN3k0w6fI4e5BgH4/MvJlkTu7jkjHMPptzFaAySLi8SxWnwutUCpxUHD7OzvoAkbQ7Qh65pLbMm8lPlsWPVldy1+i7mjpzLlB5TgNhdkX4+5OfUuepYdGRRUPlGm1NYW8jCwwu5/ZLbyUvI41jtMa7rcR2fnvRzvTpuU7mWsmMKRq0xqKj/sWshH+8rZPLAeTHvx8YjIS4VcyuCj22FTmtRC52O/JdfJmXGjBbvnW/34M4KY58+ZNx9N7qsTPwuF869+1DcLgbkJLGvajenG05T5ajinjX3s61EKtyeHywi8ze/BsB15Ah+mw3tUFk0UWaT2+LSxhqE8OMYPxzruKuCATtFUSh95BFqFy4iw5qIpeoebup3E8WNxeiUFDKsZkwDBuA6eDA4x1tVhefUaRr6d0Xo6qmolwpx6oB+DE2ZiOWyy3Ds3h2ksATQWKRL4IUdL/PYV00oSMPA5vIFKTEXHHgDp6b5IxnoGH262s6SXUXsPHWWSx/5LOgCOLeqNTDn1f2ylVSdGhhsTWVbv8RR2E//mMp6D4pf3yoKy2e3PcvHR5ezfF8ppXWyN2FwnqKAKUkGsnQGVpxYwdsls5k4SMdp12Zyc2PzMqeaE1AUDSU26Q5IM8cIPpr0CH0Nu6s24iqbwbXpT8U8R7dkaQSsKZQ7o0hNAwLQaXToSWB/hXSReL3yfuentiSdylM7HNU0aNEKbbPu463pinRJ+iXc2PvGsO+dO6fSUcm7h96lzFZGg6eBBH0CtsYM5hYU4VPkPSlwDeUPH31Drqk/frUg7mDDBvTJu1sVTKxqlHPMNT+jd3Jsjuy2QqdV1ACJE6/G0L17i+NZ9/wWdM0tnfZq296W0Ofmknn3XRjy84N+YV1ODqfK5BY0kJ70xZkV/Hn1rhbz7bvksdTLx6D3dqfWLlPi7A4zKeXPMf4Xj5J9/9yg4vCWluKvr8c4oD9pFgMNdbmkmFL49fBfk1z/EzISjBgHDsBXVxcM4gqTiZynn8Y/bjhC46W4QfqDfzl6Iv+5cQGp3xmL327HeegwittN8X2/w7ZZ+ss/PbKDD76J7hse2yeDmy7rGrzecCizlbH1RDX3LtrLiSobNrcPg5pdUGYLv7sqs5Vh0mtocEuL2twKroihOb0Ylz8Ol9fb6jZL7x/8mHf3rgNgR+0SPjr6kXzj+cGw4vdw6FPYuxCAVFMqfvz8z6Q03tz/Nm/tfy/m5yeb9Sg+M41qw9rYilpHVpcjfFj0OG7FiakVHUgCPS8L66TrIpaiBjCIJDxaeb+cTmlZhreopfIuqXXhU3y8tv81TtVLF12srkhvfv0mL+x6gT9cEeI0nzu1fwuXVGBOwI/t9DlJMiSxctZK1u/sh82jUE0y73qv5h3fNTg8PqqP/ZTfXy7rNDw+N4pfH7WQKHgu9Rwvzx7NnWPjihoA5+HD1K9a1eJ48vTpGHr3Bq22Wcfh9mjb3tbwVlbira4OKmp9bi6f7m0ARUe5vTxE8qOmfNWvWkXhzJn4bTZ0WVkkXX89Ay4ZxwD/H3HZJftXjc1NujUBs84sGfrUdD7nIen7Mw0YSG6KmbT0Iv7zzXvkJ+aj9/UgK8mIaYDM03UePAjI/oYpM7/H4BHXQO0kqhok0dLB0rM0OD1YRsrtsmPnDjylpdQXFOAplT/gFEMairYxqu9v1mX5/GaSfODDVagGjgfcIxUN0noO+KC76MIH47pYu7Ds7iv53YSreGfqMp67IbY7bGRvAz+a1IhDqUEohlZZ1D6fnkqb9IPvqP6MjSUb5RtanQwm7nobNr8EQJ5V3p+SxhJO1VZztDR65SNICxm/VA56jZ47x4Tv1BKAxaDj91NkUZKl+9856foy5jmMQir/U6d7Yy15rgV3SziMT3wUUSN3u412A3qtIDux5WKYlWjkil5pJJtDWUyBopQZw/N4aNoAshJDLoRHp18SbL7h8rkotZU2Y86bMTyP/tmJaDWiRSelgM+4adFLaa18Pdv9R5733hQ83tSF4lFcCHQx0zcBrGrXqFf2voLdEz1Q3pbotD5qgNoPF1O3ZAlWCGXmAAAgAElEQVRJkyc3O+53OPCcOEHabbeS/eCDEWZ/O1B4w3SSpk3DOFCS+Ohz88gqr0MpT6bMVka6UQYccxNUJeb14vrmIO6iIpImTw5+N8O7pVDVIC3q8UPr2VP9FY3uoVTc/CP0WVl0/cffcR2Wvmdjv37cmWClyljDn3f8FSH8/P3O0fRM6onicJC3YAHmoUMBuTCYBg5kaP5QLjXfTJIxGZvbx/c+vIucjEbW3vIJ+vx87Dt2YuwrFa4+X/7Q0kzpiMZGKhsddE0Nr1Dtbi9GneQvnjNiTjN/M4BJo2fOiDlY1eKSinoZZA1UGc7JmciDpz9GaaJUTVoTc0bMoW92IgDZSa1ryXbs7DHmrJ2DgSQErWs6ocWA0+sAFOrc1aFSZ3OaVNSuelDzkrtYuyAQPFKwAX9iI5na2HIlmnT4XZloDWeZ0HVCRO6UZnMM8rq1plIyU8P7dJsiO0Fa0EJrw6wztmqBSjam4vYq5FqymNy/FxO65QZpTZtCoxG8/wtJVfCQmnXZ1A3l9ipUNLh4+YfD2Xy8mokDQ6XigXE3fXITS2eECNbeuvNySmodLN9XSlWjK6jYm7IZvrLnFYobi8lNmURxrQMtfrabfsUv3XNY4f8O2RlVzF4+m4dHP4zH70ZL7NQ8gFxzH5xlN7CT5WwsLGdy/56xJ7UBOrVFre+Sjd9ma1a9B2Dftg3F7cY67qoOkqztoE1Px1tdjS41FeuY0eizs8hMNOK19SDVmMHp+hIUv57sBLk91XeVHcldR47gawgxgB3mOfJ6rQNAMZ5gffkS9Fo9pksG4ti7F0VRcB4+gr5bt2CH81xrLl7Fy/xt89lXuQ8hBBqLhaSpU9ClpeF3OCi+515qF32Aoij8/UcDuWtSHjWNboS2EYtOfk7+K38l55mncaul/IY8+cPJsmYghMKps5GLXr778kbuVqkwp/WaxlxfIjmKfCyFovDHgXcyrde0oB/7XIt6eMYgFCFI0llAAQsa5o2Zx7Re01i2t4Q3t23lzqXP8MWR2P7g01XSclMah5LonBJzPIAWI37hJj1RweV3hIpdLOmhghc1H1uv1ZNsSMcjahAaZ7A8PBq6plp4YMSfeG7k5+iq7uBUdYSeYU3w9lehTKn+mbHjNjnWTGyFv0Ho6nFbYzNWAlR59+I3HeSLWV8wfeDlzBwRvVahoLAgmLnxk89/QkGhTPXccLSSXplWbhiSy1PfG0xWE6s8oHi9SvOdR0aCkSH5KdhcXlYeKMerNiQw6UxohAav38vW0q0UNRQxd2p/Zuo2sdggKWsf17/FLMMmfn7lQA5UH+BIzRGSzHBln/C7uXORnWRCq1UrZB3t04YLOrmiDha9nJNL3fjleoTZjGVUmKZu3zLo0tPxVleReM01dHvjDYReT2aiEWfpTfywz13Y3R78rizS1T6Ghq7yB1Hz1tscufw7uI7KgE6Vo4oTdSdQFIX9ZWdI0Cdi1BoxDxmKr7YWz5kz5D7zNN1eexWAYxWNvLcppOjf29jI/iIZ0XYdO0btko9w7NsPXi+Wy0Zg99oZt3AcHxz5gCqbC6FrJE3NDjD164c2IUFWJWq16LJlpkG3xFz8rgzKG8N3HQGZ9dE0f3Wpxk5/r591A3/FplNF3NhXbq8DYzISjNw8sitJ6lb6rFbLYKeLdwfPYYbdhRAaJnWTZDn/2nyS9/ZsYXvdu2wqjF5GDaFc3VuHXc2Xv7wv5ngAgyaBJKORRXdJLuOgRW1RC3FsVUGLGuC6bjfhtfdEaLwk6BJjfn6yRc8dY3rgV2DRjiIanLHdJSVNeK2MIinyQBV6nQ6dNx+d9Tj6hNY1nu3T7SyG9PV4/V7WHa6gtC6y5X73x6/zwPqHgxWDFfYK5m2ax9Kjy9haWMO4PnIh8/sVjlWEjLLA/RCEFOLnB8p4bX0hfr/C6N7pNLq8fF2iFhqZM9lz+x5m9JnBsdpj9E7pzQztRp7Rv0aSkPJlijqe0b3Oj82FGDQGjtceZ/nMT3hx0p9add3XDEpAnymbECQY2i89r1Mr6lDRS/Nc6qTrriX79/ejMbZfeszFgjYjHV9VdbNS6qwmudS/G3k/cwf/jaH50m+oTU5Gk5yM88ABhNmMoafcegl/ImuOHeN4ZSOrDh9Fj/Q7modJF4Zj7140ZnOz4OzBM6FAzrZjsuIPoGHVKkofegjbhvXqZwzDqreiFybe3rqP6kY3Gl0DmRapqP1uN5Uv/5XGtWsx9umDUAO9MwdO5cEhb3FFt/4Rr7+xSXpetaOar/02BjmdpF/+SxIeKoVE2cuwR7qV5b++kt9N7c+zs4YE51yadwXvmgfSPSGPafW12BQv64rWAdJfW++SFmhSDN4OgBS10vBE/RGqnNELSwKYnvUoYxLnUuuqxaAxhBR1n2tg4HTw2MAaSne7pf8deOtG0Hj0IQYlTW3VOZ7f+gZzd07GlLOIpBh8JQBp+jxE3QQAiqpiBxMBjCn70FpOcXn3bq0an6HmUt/26e38+M3tfLS7JetiADsb3gXRnEXR6XPy/M4FODw+xvWVC9kr644x+fkvqbPLsV0TZZC5Kcf0wu1neG/baTQawRW9pAybj8s6BCEEQgiqndXUu+tlYcvqxzEqzUvo9X4n2jVP0jO5J8frjrPmYCXL951/oxGTvv08x51aUQeLXs4pI7eMGkXq7Jalzt9G6NIz8FZXUzjtBsqfka3IRvZI5dnbBX/c+UP8mnp+MrYnPTKkoqlbtgzFrXay9nqpXyFX90R9Ol7qOFLeiEbXQLJBPsTGPn0QFgu1S5ZQ8dxzeNTvMs1qQGMKcaBYur3Kgbp1co7a7Pbsu+9h7NsXrdreyaJNpdxWyYnqOoTWSU6C/IEJvZ6z772HaeAAen0c8iWmWQ3cdkX3YIrWuVAURbWopTLZVLIJBRhXfxZ8XtaVbeWutb/Gr/gx6bUMykvGotcGFzW3z43dmgE/+hgyBzDK6SJLZw1uqxOMuiBvR7Ipdnpeqln6pb+seJ+7P4/e3SWAB68fyIT+mfztMz9bbtnGiGxJA8vgWTD1aZhbCCNDrAsmPQhdPWN79uAHIyIvYE3x+maVm1x4STLHVg7JpgRsdb3wubKCCjUWevSU6Z+xcqgDqKmX+dzf1Mh+mV3DpOYF0OgLTyNQ46pApxFc0Vuec1SPNBQFtp6Qind41nDyEvLoliQXD6/Pz7YTNcHxGQlG+mYlsLkwVDA2b9M8/rpHpmb2Tukdlf+nd0pvjtceZ/72+SzY/FGrrnvXqZDFb2xFVlBboVMran12Nj0Wvk/i5BAVqH337hbVdt9mJF1/HVm/+x3u06cR6g7BYtCRlWimuLGYaR/dwFt7luLzK8HSecUht3GK2x3k9c2yZCB0DRwpawDhI8Mkt5NCqyXnsXkY8rtS/fo/UTzSat5YuhJTl+VBOTSGWv52YD4FhQW4VWIlv92Ou7g4yBucbEhH6BrolmbkirRZjM2XXNRCCHQ5OdQtL+DgwEs4OnESdcuW4fa5mf3JHby+e2HYa3d5/fiVkFtjQ9EG0rUWBrg9sOlFbPveZ33RevZX7UdRFN7Zeoob/7qRy5+WvB1rz6xl3PvjOHr2KPjcaPNHcV3WKL4q+opaZy1WozbYDy9gLUdDTmI69lO/QPHrqLO1zv+46PAi/nXkz6w7XIlOq0Ej1J+UooDHDqZkWaGoYk3xMhL6zich72OSEhsifGpzGAPUpoo+xHESBYkmHULjwlnyA/ITopfBB9A9VQYU95yM7VoBsDuab/sDhS3hkG4MzyWdbenCOz/7TvCahnVLwajTNFO8N/a5kSvzrgRgf3EdjS4vo3uFFpNZl+UzJC+UsvjZyc/YX7mfoZlD6ZPSB4clvI/en5THqC6jGJQxiHJlNT59dLrZAFweeX9dVRNiVpW2JTq1ohZ6PeahQ9EmhbY+VS+9TMlDf4gy69sFy4gRJIy/Crxe9Lm5weObDsuAhcNr56nPduL1+yOXzj//AoMyLsXb2J/DFWexn/w1c4Y0twjrCqSVeepHt1O3bBkv7XkRoWm+HXX5nHz1xtNU/vnPoc+324OLQYY5E42ugQxrIq9Nf5QxebKzTt2yZbgOHQKfDxQFb0kJpQ8/gr3gcw5U7+eTgy1zwAOYM6kvo3qk4fV72ViykSuzL0Mz6RE4voYrT+1FK7SsO7MOIQTzPjnAgZL6YO7tl2e+xKw303PRT2H7a/CzL/juyF9z+yW341MkPzRC7j6SjbGzOJJNZqb0GoPiN7WqRx/AsoPbOdSwGXP6Fp7d/mzojUPL4elcWHhrsz6Q3VWCsI3lBRyvbskvHg4mrVxkjHptq7I+sO7ClPcOlh4v89CO2cEdRiQUFBawuWSLFNuxLOZ4gHJXiFrW2ns+hxsjpwH+YvBdKP7mLhuT1sQ9l83hO02UrlGn5bLuqUFXxsHqg7x94O1gFktAgV/RZM7/jO/N76b2b/a5QzKH8J/r/0OGOYP3En6Mg+YuUrti4OTQ+5jVbxb/d9X/gVBa3a3FotejKBq+PyKfAV1i+//bCp1aUQM0rF0bVDJ+mw379u0kXPXtz/YIwO9w0LBSFoXo80KK+uOdTbZYIhWjThu1dP57/W7AWXw7hRXSggwEH4NWuF26AALdNXpvC+9TvG5lTcTFYGq3G3BVT2DN4SJ2F5UEXRAVz78AXm+LOZUvvIBWSaLBczbsuUx6LfdM7seoHtKae3Lsk9wy/C4Ydx/4vSRb0hmRPYJ1Z9YBIcvbYtDi9XvZULyBq/KuQudqCG5x+6X2496R95JuTmfOpL6s+ekTLPvuF4ztG7tbkFYjuHFsJRpdY6tKzgEUvwEh3AjLUbaWbg29YVZZ8Y58Jv3UKnKtoXtcVB27owgARnltfus2pnw4JaoiLSgsYGPd3xFC9nmudpUzb9O8iHMCjaXdfvnceLFFHR+Ys6rsX8H/NYZa/rzrqYhzZg+cwSDDT0k1ZAX55m/tfR8nTvbD7m7+3Izulc6hsgZqbG42lWzC5rFx1+q7mPLhFHZVrWZgTlKQDycAj88frJg16UxB9jyvz8/zFcNYmn9/kP9HSc6H6S/Sa9KdQIgS1dDK/odGnRYh/Kwvjd6mra3R6RV17QcfUv3qawDYtm5D8XhIuGpcjFnfHriOHKH8aUnU3tSiNieHou+azMUUFBZELZ1PMumYckk2U4cZGDu6gGqP5DGIZIXf9mX4rX1GfXg5vaWlTO01nsHJ1/Dqro/40eqpQda9aAuIQSRj94XnFHd5fVTUO/H4/Og0Oq7udjWXpvaXdKVnT4E5lQn5EzhWe4yihiKsBqmoE4w69lbupdZVy/iu42XO8teL4ZUxYKvC6/eyqXgTbmrJT02iR2o2xlZU6AE8tlk2mWhNyTmo/CAaD4q2rnm7KEsTX28TutSmRT0Z1tiFJQWFBTTqQgtAqa00qiKNVFK/YNeCNhkfmOPxNw/QRZuj0Qjev/Uu1t+yOsg3X1p8Ca+uL2xxX24clsdbPxnF+pLP+dvevwWPl9pK2et8nV9Na5lB9IN/bObeRdIdatKaWF64nH/s/Qd7ztTS4PSS/J1bZeefebWIew5gGSmJwhRFYeKiiQBhG2yEg0mvwdswgLP1Zmps7lbNaQt0ekWt75IdTM9rXP8lGosF82WXxZj17YFW7UaOEOhVRVxQWECtOVRerGjrmbdpHsW3jkeYmlt6gdL5osYiDhvvo9G0kn21G3D7VasighJNrfe1YP8yaU14s8IrD11ODhaTn/mzM8hOkxZigEUt2gJi0abgUsIr6n1FdVz+9Gq2FFaz8NBCCmsLoe4MvDAYGkrAksbVXa9mdM5obB5bMOhoNer48syX6DQ6xuaODVKhUnEA9BbK7eX8zxf/w6u7FjHtjQXMXjg/mEkQC3anQPHrGJQytlXjLXozQiho9DXNFXVTDmhjKA1v7Zm1wdfP7PllTDfDgl0LUERzqzOaUoxWht8Wxy90DhC0nhVFYcPRSsb2yWhRDdgt3cKE/lm8svelFg0PnD4nL+15scXnDs1PYcepGlzeUAWsVW9l/ZFKNALG9m6+m9pfVMctr26h6KwjqKBnjTinz2UE7KlZg9Z6DI2pmB98Oq1VbqK2QKdX1LrsLvjq6vA7HNh37MAyejQaQ/t1/73YsG1VrSVF4fgN06lbtowFuxbgF81Xa6fPydPJX5HzxOPocnNblM4nGZKocdawo3Q/ABmqFRdJiepzchmb8r/o/FKhJOoymTdmHt3nPhRxMdhbuZdZy2bRqNmPFlPQ6sy657cR52QZe+NzhafNbFT5i12c5cmtT8q0OksTBWdJp2tSV16d8ir90/oHXR/TBudwY58beXzM47KtUsDNoDODwUJeQh7Ds4azpmgFx22b2Vf7BW5f6zrSazCSIUby+4nXxB6Myt/hScavsTVX1MfXhF6/MBj2LQq6GQKoclbEdDOcr1KMVobfFscvdM68Tw4w7lm5SB2vtFFS5wym5Z2Lg6X1lJ7HdY/unY7T4+fvOz7krEu62V7b/xoHG9YxpncGyZbm/nGzQcvmwmrWH62kW2I3tELLczufbJVb6ZWv5yM0XoSAcntZzPvXVujUJeQQyqX2lpfTc/FifLWRiye+bahbtozyJ54M/h8IwvWe4qb00pZraJmtjORZ08NymiQZkhDoKaw/ghAy+R+kEi19+JFm7o+AEs3R9aXxWA5CCG4Z04NpvQaCalhUPP8C3tJSdDk5ZN3zW5KnTydTpYX06YtJ1IaUUkCecHMeKb6KsrrmW+sAAkTzh+u2AzAubxwYk0Bo4crfwsRQu6QaZw1//sElJJksZKj+9wABPN3HwL6FzZT8tJ7TeHLrk2jNiSje5KA1HgsaoaGW/dQ4a1pFTvS9Pt/ncGFPKszPkpcgKzLZtwgK7gkNqjsDy37Dgp59IroZItG4drF2oTQM8VQkpThnxBwe3vhoM9dEoKQ+0vgWZftRxl/onMxEI9U2N3a3l6+OykrVcRHiBusOV+J3J6MxtNyJhbvu7/RMQ5+0mzePLMWnZvnUOGvYo32dR69umWbZO9NKXoqZDw99wknxDT5FWuIBtxIQ9n5EcxNFun9thW+BRR0qetEYjeizY7eN/7bgfP3H0SwWIQRGkhHCj1D0JOhlpkDy9OkRrfA0iwGPT8Ht9ZNuDe1SkqdPp++a1Qw8+A1916wOKuJMi5o3LRQSdc1bSEWaMygvmWsuCc+JbFeb1e6r3kIXaxdJ6C6EtJDtNfI1cKjmEBMWTuBI41Y0QvDlma9YfXp1qEjosh9Dv2ubKeopPaagEVo0+gYUv6EFS1skeGjEJ2x8+E3s1l0AQ/JTSNQnMTPrr8zsO1MejNBkucwd3gUUyXoEqRR1onmgK5pSnNZrGnf0nYvfnYKiQI41J1hSH2n8vDHzSDdmgxroizY+MGfuZX9E40tFUSDFkBVzTiB9r/isg2qbm37ZCXRNC5+JM7p3Oq7KqejPuW4thrDXnWIxYO2yKqikA3D6nLy4u6WrRAjBVf0yOOpZ1KI8vS3dSm2JTq+ozcOG0efLL6lfsYKad9/taHHaFOfrP45msQBYtNK/nKjp2oxYJ5ISTW2inANWajSs/roexa/D70mmunRks/52kbD25BYmLryWHSUHWrwnXR9edldtY1zeuJDMjhrY+SaUfQ1A35S+JBuTWXjgM0Y8sYonNrzEK3teaU4elH0p9Bwf/DfVlEq+RW4PtJZCpi6e2qotqqj+PgA+b+wKQICXNq5mff3T/Gn1xlD/vghFFl284VkEhTdyUHFar2lMzb4bv1uOaY0indztOmzHH6Dx0HxWzloZ09qb1msai6Ytx1z0F+7q82arrMOr86+l7sjvaTw0n7+PXxJzToDutOisg/um9OezOZEztwblJmFyjWKQ8afkWHMAgd+dwuye90U8j08bPrMokhId3y8TdOEXzrZyK7UlOr2ibli1ipM330ztwoVU/uUvweKL/wZE8x/PGfYQBiUdRYFkXWyLBaBf4lhcFdcyMSk2WTxAmjWkjNITovv9l+4u5qGPvkbxJuGz96S6fFCz/naRUHTWSaWzmF3FJ1u8N6pHGj+daMGv+KTbI4Chaid0t0xR1Gq0XJV/FXurtiC0jVR4DjE+P6SUOVQAm/8Kw28PHiooLKDMIYsYhIidLRG4RrdTBv5eW18U89qW7i7mlS/3o0s4irXnixTXn+XBJfuxm8P/cG+r8bXIJ1b8ehzl0QmghG0EtuMP0HBwPrZjD+CpGxZ1fEaMexkOh0obqGhw4fG1LmWwKVd3uIYB56KralGfOSvTRMMx7QWg02q4vGcaRWcGsnLWSu7M/RBH4QP8ctRNEefknKcSHdMnAwPhXVvR3EoXYkC1BTq1og7kAAeyPvyNtmDxxX8DogXhxuVMofrQXBoPzWfe8HdbZeUkOifhrp7Av7ecatHRORzyUiwkGHUYtJqInTMCCPSqc1Vcj8/eCzSuZv3tIuGr07LY5cUDDzDkn1fx2JpQP8bB+ck8PGUyG2ZvCFafsW8RHJZl8Sy6Q/4PjM8fjwcbhsyVKPiZ0HVC6CRntoHXCa9cAc8Pgn2LWLBrQTA3OIBo29pA01SfWVr+dTZiLkR/+vwwbo/a4FXrBr8Bh8fH/3luDttkudB9C87SmUG3hN+dgrN0JlmaMWE+PSTX4p0hGc5tABsOWUkmbv1Ot2burFj49xZJ5t+aZgkAKw+ErM7rF2yI+axlJhr55YTerPqmnO//bVOQ8S4SRvdKp7TOSa3dTa9MK7dd0b0Zp/W5mDNiTotcaL0wRlSiSSY9T1x1f4t8+VhupUdHP4rfk0Jr3URthU4dTIxWifdtbBJwLqIF4XRNOjqntcJCWrq7mBUnPiWh/wcgfNR6Unho5XXAHUG+3nPRv0siXz/WOmKgANG6z96dhH5PgfDhOTs6Yg87gMfW/JuNNf9BaKRVq+jO8sGp52ENDE2dyPwVBymvd5GbYmbu1P7M0G6EZb8J+Xcby+T/QINJ+pgNqdsQCE7Vn2JI5hCpyLcG8m2VYOCuLD98RkGkbW1gIbKmbJOfpBiCC1Gk76+k1oFoRpIkldzbjZcz74eXSl91XREk58OkRxjmG8vCJfuxHR8enGHWa5k7MzLnx58+P9wiYyWWXAA/HtODaYNb35ou4O7XaWIr6qW7i/nj0pArK7B4ABFl+nhPCZ/sKaG41oFBq2H5vtKo8t96RTfuGNMDg07DjcPyuHFY5LEglehzKw9Ta/wYr+Ysfncy946+N6avvaLeyXPbX0BjqCPH2oU5I+ZEnXND7xu4+zW5G9g//+Ir6AA6taKO2sT2vwTJ08NncTSl/kyzxFbUT335DtrsDxAa6QcVhlqUrA956ksdM4bf//8sZ26KmXL/JozZkh/EkLEKxWciO4o1uPjEawhd8/xlofHw4YlXWbj9DCKrAGtuPbXeBB5aOZ0p/AtLmCBcwYbHeaoJT7GCwqMbH0MjNExb/Th4XS3mdPEplIbpIh5pW1tS60CXtDtYVm/O/xeuimspqR0ednzgOym1t7TyclPMMGRaiybLge6ff/r8MCW1jtACFUVhxWoAGwm/emcX1w7qwpg+sSsyzxfROoGHu5bAbiUwx+3zx1TsFrW4qbrRhVYjSGnFb2Byt+t4a+NAhuQnU+/0cNug8VHHHy1v4ImFJp6c8Q4zR+S1qmdiR6FV+xwhxLVCiMNCiGNCiAcutlAB/Lc0sb0QNN1K3vLalphbS7t1WVBJByA0HuzWyG6ipbuL6fFAAT0eKIjpKplyeTGmnCVodLLYRaOzY8pZwpTLI8/xRwjwKNpaNNnvo9HXIwRo9I1osj5ktSZ8WeQCow/PORF9j+LimS1/iRi4+011TVh/8Ni028OOz+hyAFPOkqCi1ujrMOUsIaNLyyBoAHOn9seUWCg/W5GcF5bUvcGef+EwY3geGx+YyIn509j4wMSoShpa1wD2XCzdXczRikZeWnOsVS6wpbuL2XRcMtz9cWnsuMP5Lh7RFHs0PLhkH5c9+QXDHl/FmGdWxw5eKwpun58dp85S0eCKOb5XZgJGnYYnln/DwIc/a/V3ZVR7K7ZmfFshpqIWQmiBvwLXAZcAtwghLrnYgkF0H+5/MwIWSACldc6YfkmNPnwEO9Lxc88Ry/e5sebfLUichMbDxpp/hx0PoPGlRnxPiOZBK6Hx8EJq+PFlEcq/69wV0q0QBiNtlrD+4JXbwitGY9bnYa/PmPV5xGvQJ+/BlL1CvR7JeWHKWYI+eU/EOeeLWA1gz8X53tfAeLtbKtKqRnfMZ+18F48L2RUs3V3MhztDi3BJjN/A0t3F/Ev1swPU2j0xr2PZ3hJcXj8Ojw+F1n9XLq90RbUmXtBWaI1FfTlwTFGUQkVR3MD7wI0x5rQJouUA/zfjQiyQZEP4/PJIx8/3HBeSQ/r9nj8Pa9VGivdX6DRhg3AGb/isAr8nBSY9EnbOM+6b8NYPD6ap2Y4/gLd+eETlUO8J3y4s0nFQOS/CWPrReDLOFzOG5/HMzMHkpZhbNHMNh/O9rxfyrJ3v4nEhu4I/fX64RQZKrOtwesL78qOdw39Okktbf1dthdYo6jygaR+jIvVYMwghfiGE2CGE2FFZGfnhPl9EygH+b8aFWCAPXnFviwIBvTDy4BX3tsk5LiSH9NGJt3NT93sQXlkYIbyp3NT9nuiLyvQXg0xnJHeF6S8iGmeFVfgW23TpBw4zZ0fS5LDniKQcLuT62qsA4nzcJed7Xy/kWTvfxeN8FXtbyhvtOtrjHG2FNgsmKoryKvAqwMiRI1vJ3xhHOOSmmCkOc/OjWSCBSPWCXQsos5XRJUYE+3zPcSFlwyCV9aM09wuPLEzj4a8ebWaNBheVXi2DcH/wFfPQSi8ibQVCX4viSUGpuY4/TLlVDhjygxZz5vqaB7AgunK4kOs73/Lu9sD53tcLedZAKutY/vWmY+H8gqjtcc+0X9UAAAajSURBVB3t9V21BVpjURcDTdtE5KvH4rhIuBALBKSyXjlrZZBKMlqa0fmeI1BqnGPNCXIKX2gO6bRe03jiyseafdYTVz4W8bNmDM/j6Sl3kFL9GLZD80mpfoynp0ROOwzMOR+r70KuryMLICLhfO/rhT5r54vzDaK2x3V01u8qHETTpqphBwihA44Ak5AKejvwQ0VRIobDR44cqezYsaMt5fz/HZbuLj4vC6SznuO/HQWFBa3exbQXzve+dtbnoD2uozN9V0KInYqijAz7XixFrX7A9cALgBZ4Q1GUqDXKcUUdRxxxxHF+iKaoW+WjVhTlU6B9e8/EEUccccQBdHKujzjiiCOOOOKKOo444oij0yOuqOOII444OjniijqOOOKIo5OjVVkf5/2hQlQCp2IODI8MoKoNxWkLxGVqPTqjXHGZWofOKBN0TrkuhkzdFUUJy897URT1/wuEEDsipah0FOIytR6dUa64TK1DZ5QJOqdc7S1T3PURRxxxxNHJEVfUccQRRxydHJ1RUb/a0QKEQVym1qMzyhWXqXXojDJB55SrXWXqdD7qOOKII444mqMzWtRxxBFHHHE0QVxRxxFHHHF0cnQaRd1RDXRjQQiRIoT4UAhxSAhxUAgxugNkeEMIUSGE+LrJsT+pMu0TQnwkhEjpBDINE0JsEULsUbv9XN7OMnUVQqwVQnwjhDgghJhzzvv3CSEUIUTbt+aOLpdJCLFNCLFXlesx9XhPIcRW9ZlfKISI3Wr74sskhBBPCSGOqM/7b9pLpiayaYUQu4UQy9X/31F1w9fqc9ey9Xv7yzRJCLFLfda/EkL0uagCKIrS4X9I+tTjQC/AAOwFLulouVTZ3gZ+pr42ACkdIMNVwAjg6ybHpgA69fWzwLOdQKaVwHXq6+uBde0sUw4wQn2diORRv0T9vyvwObIQK6Od5RJAgvpaD2wFrgAWAbPV438HftkJZPoJ8C9Ao76X1Z7flXrOe4F3geVNniWh/r3Xnt9TFJmOAAPV178C3rqY5+8sFnWHNdCNBiFEMlIh/RNAURS3oijh23pfRCiKsh6oOefYSkVRvOq/W5CddzpUJkABktTXyUBJO8tUqijKLvV1A3CQUH/P54H7VRnbFYpEo/qvXv1TgInAh+rxt4EZnUCmXwKPK4riV8dVtJdMAEKIfGAa8HoTWT9V5VWAbbTzsx5OJtr5We8sirpVDXQ7AD2BSuBNddvzuhDC2tFChcGdwIqOFgL4LfAnIcQZ4DngwY4SRAjRAxgObBVC3AgUK4qytwPl0Qoh9gAVwCrkDrK2yWLb7s/8uTIpirIV6A3crLquVggh+ranTMgGJfcD/nPfUF0etwOfdQKZfgZ8KoQoUmWafzEF6CyKurNCh9ze/01RlOGADeg0/nMAIcQfAC/wTkfLgrTG7lEUpStwD+pOpL0hhEgAFiMXDi/wEPBIR8gSgKIoPkVRhiGtwcuBAR0pD7SUSQgxCDACTkWWR78GvNFe8gghbgAqFEXZGWHIK8B6RVE2dAKZ7gGuVxQlH3gT+MvFlKOzKOrO2kC3CChSLQ2Q29QRHShPMwghfgzcANyqbgs7GncAS9TXHyAVUrtCtboWA+8oirIEaSH2BPYKIU4in61dQogOaRWuus7WAqOBFLUnKXTgM99EpmuRz3zgHn4EDGlHUcYC31Xv0/vARCHEfwCEEI8CmUhfcXsinEwFwNAmemEhMOZiCtFZFPV2oK8aBTcAs4FPOlgmFEUpA84IIQJthicB33SgSEEIIa5Fbse+qyiKvaPlUVECjFdfTwSOtufJhRACacUfVBTlLwCKouxXFCVLUZQeiqL0QCqiEeq9bS+5MgNZOUIIMzAZ6T9fC8xSh90BfNzBMh0ClgJXq8PGI4Nm7QJFUR5UFCVfvU+zgTWKotwmhPgZMBW4JeA770iZkPGzZCFEP3VY4H5eNLSqZ+LFhqIoXiHE3ciofKCBbsQu5+2MXwPvqAtIITIq3q4QQrwHTAAyVJ/Yo0j/rxFYJfUTWxRF+d8OlunnwALVSnQCv2gveVSMRfoL96u+V4CHFNnzsyORA7wthNAijaNFiqIsF0J8A7wvhHgS2E37uooiyfQV8nm/B2hE+mI7Gn9HZutsVp/1JYqiPN5Rwqj66ufAYiGEHziLjBNdNMRLyOOII444Ojk6i+sjjjjiiCOOCIgr6jjiiCOOTo64oo4jjjji6OSIK+o44ogjjk6OuKKOI4444ujkiCvqOOKII45OjriijiOOOOLo5Pj/ADBU7ybeHA0xAAAAAElFTkSuQmCC\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "best energy:  -1.4931295501440078\n",
-      "optimal angles:  {a: 0.0, b: 2.70723295211792, c: 0.2528174817562103, d: 1.4755951166152954}\n"
-     ]
-    }
-   ],
-   "source": [
-    "init={'a':0.25,'b':0.25,'c':0.25,'d':0.25}\n",
-    "print('With phoenics we will optimize:')\n",
-    "print(O1)\n",
-    "### to see what you can pass down to phoenics, see the tequila documentation for that module.\n",
-    "p_result=tq.minimize(objective=O1,\n",
-    "            method='Phoenics',\n",
-    "            maxiter=5,\n",
-    "            initial_values=init,\n",
-    "            silent=False)\n",
-    "\n",
-    "print('Phoenics optimization results on 2 qubit circuit:')\n",
-    "p_result.history.plot('energies')\n",
-    "p_result.history.plot('angles')\n",
-    "print('best energy: ',p_result.energy)\n",
-    "print('optimal angles: ',p_result.angles)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We also have returned to you the phoenics object. One interesting object we can extract from this is the acquisition function. You can obtain this indirectly, using resut.object.bayesian_network.kernel_contribution. This function takes a numpy array  ( a point in your parameter space) and returns 2 numbers, x and y; the acquisition function then has the value x*y. Note: this is often zero.\n",
-    "\n",
-    "\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 48,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "random point  [3.506517   3.41045123 1.98397105 5.59827826]  has acquisition function value  0.0\n"
-     ]
-    }
-   ],
-   "source": [
-    "kc=p_result.phoenics_instance.bayesian_network.kernel_contribution\n",
-    "random_point=np.random.uniform(0,2*np.pi,4)\n",
-    "f,s=kc(random_point)\n",
-    "random_ac=f*s\n",
-    "print('random point ', random_point, ' has acquisition function value ',random_ac)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## This concludes our tutorial. Hope you had fun! Happy optimizing!"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.6.9"
-  },
-  "pycharm": {
-   "stem_cell": {
-    "cell_type": "raw",
-    "metadata": {
-     "collapsed": false
-    },
-    "source": []
-   }
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}
diff --git a/tutorials/Pytorch_Interface.ipynb b/tutorials/Pytorch_Interface.ipynb
deleted file mode 100644
index a59c6b75..00000000
--- a/tutorials/Pytorch_Interface.ipynb
+++ /dev/null
@@ -1,326 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Hello, and welcome to the Tequila PyTorch tutorial!\n",
-    "\n",
-    "### In this tutorial, we will demonstrate how to use the Tequila  PyTorch interface. If you do not already have the PyTorch module -- as well as a quantum chemistry backend -- this tutorial will not function.\n",
-    "\n",
-    "In this tutorial we will learn how to transform a Tequila `Objective` into a PyTorch `nn.Module` object, and will optimize such an objective using PyTorch. In particular, we are going to train a Quantum Autoencoder on the $\\text{H}_{2}$, sto-3g, UCC-SD ansatz. We will consider, as input data, the angles of the UCC-SD state prep circuit, calculated at different bond lengths, and as internal weights to the model, the angles of rotation gates within the autoencoder circuit.\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import tequila as tq\n",
-    "import torch\n",
-    "import numpy as np\n",
-    "from matplotlib import pyplot as plt\n",
-    "\n",
-    "#cuda0 = torch.device('cuda:0')"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## 1: generate the data."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### We start by creating a number of molecule objects, each representing $\\text{H}_{2}$ at different bond lengths. \n",
-    "### Subsequently, we extract the parameter value (there is only one) of the UCCSD ansatz, for preparing that state."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "bond_lengths=np.linspace(.3,1.6,20) # our bond length, in angstrom.\n",
-    "amp_arrays = []\n",
-    "state_preps = []\n",
-    "for i in bond_lengths:\n",
-    "    # the line below initializes a tequila molecule object for H2 at a specific bond length.\n",
-    "    # see the quantum chemistry tutorial for more details.\n",
-    "    molecule = tq.chemistry.Molecule(geometry = \"H 0.0 0.0 0.0\\n H 0.0 0.0 {}\".format(str(i)), basis_set=\"sto-3g\")\n",
-    "    amplitude = molecule.compute_amplitudes(method='ccsd') # get the state prep amplitudes\n",
-    "    amp_arrays.append(np.asarray([v for v in amplitude.make_parameter_dictionary().values()]))\n",
-    "    state_preps.append(molecule.make_uccsd_ansatz(trotter_steps=1,initial_amplitudes=amplitude))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### Next, we create the pytorch `DataSet` and `DataLoader` to load data from. To do so, we must implement our own inheritor from the basic pytorch `DataSet`  class\n",
-    "\n",
-    "Our `Dataset` inheritor, named `AngleData`, needs to define `__len__` and `__getitem__` methods to function properly."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "class AngleData(torch.utils.data.Dataset):\n",
-    "    \n",
-    "    def __init__(self,data_list):\n",
-    "        self.data_list=data_list\n",
-    "    \n",
-    "    def __len__(self):\n",
-    "        return len(self.data_list)\n",
-    "    \n",
-    "    def __getitem__(self,idx):\n",
-    "        return torch.from_numpy(self.data_list[idx]).to(torch.device('cuda:0'))\n",
-    "        \n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### We now construct a `DataLoader`. We will enable batching, so that we train over random subsets over the data when we finally train the model."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "my_data = AngleData(amp_arrays)\n",
-    "my_loader = torch.utils.data.DataLoader(my_data,batch_size=4,shuffle=True) ### here's our data loader!"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## 2: Create an Ansatz `Objective`.\n",
-    "\n",
-    "Our autoencoder ansatz must be a circuit that both constructs the hydrogen wavefunction, and then compresses it. Furthermore, the autoencoder cost function must be encoded into the objective. The cost function can be defined as a hamiltonian which projects all the non-latent, or 'trash' qubits, onto the all zero state."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "combined state prep, encoder circuit:  \n",
-      " circuit: \n",
-      "X(target=(0,))\n",
-      "X(target=(1,))\n",
-      "Trotterized(target=(0, 1, 2, 3), control=(), angles=[(1, 0, 1, 0), (1, 0, 1, 0), Objective with 0 unique expectation values\n",
-      "variables = [(1, 0, 1, 0)]\n",
-      "types     = [], Objective with 0 unique expectation values\n",
-      "variables = [(1, 0, 1, 0)]\n",
-      "types     = []], generators=[+0.1250X(0)X(1)Y(2)X(3)-0.1250Y(0)X(1)X(2)X(3)-0.1250Y(0)Y(1)Y(2)X(3)-0.1250X(0)Y(1)X(2)X(3)+0.1250Y(0)X(1)Y(2)Y(3)+0.1250X(0)X(1)X(2)Y(3)+0.1250X(0)Y(1)Y(2)Y(3)-0.1250Y(0)Y(1)X(2)Y(3), -0.1250Y(0)Y(1)Y(2)X(3)+0.1250Y(0)X(1)Y(2)Y(3)+0.1250X(0)X(1)Y(2)X(3)+0.1250X(0)Y(1)Y(2)Y(3)-0.1250Y(0)X(1)X(2)X(3)-0.1250Y(0)Y(1)X(2)Y(3)-0.1250X(0)Y(1)X(2)X(3)+0.1250X(0)X(1)X(2)Y(3)])\n",
-      "Rx(target=(0,), parameter=a)\n",
-      "Rx(target=(1,), parameter=b)\n",
-      "X(target=(3,), control=(1,))\n",
-      "X(target=(2,), control=(0,))\n",
-      "X(target=(1,), control=(0,))\n",
-      "\n"
-     ]
-    }
-   ],
-   "source": [
-    "encoder = tq.gates.Rx('a',0) +tq.gates.Rx('b',1) +tq.gates.CNOT(1,3) +tq.gates.CNOT(0,2)+tq.gates.CNOT(0,1)\n",
-    "state_prep = state_preps[0] # every member of this list is the same object; it doesn't matter which we pick.\n",
-    "combined = state_prep + encoder\n",
-    "print('combined state prep, encoder circuit:  \\n', combined)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "H2 autoencoder:  Objective with 1 unique expectation values\n",
-      "variables = [(1, 0, 1, 0), a, b]\n",
-      "types     = not compiled\n"
-     ]
-    }
-   ],
-   "source": [
-    "# we decide that the 3rd and 4th qubits will be trash qubits. The hamiltonian below projects onto zero.\n",
-    "hamiltonian = tq.hamiltonian.paulis.Qm(2)*tq.hamiltonian.paulis.Qm(3)\n",
-    "h2_encoder = tq.ExpectationValue(U=combined,H=hamiltonian)\n",
-    "print('H2 autoencoder: ', h2_encoder)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## 3: Convert the Tequila `Objective` into a PyTorch `Module`.\n",
-    "\n",
-    "in order for pytorch to interact with Tequila objectives, we need to build wrappers which allow the classes of pytorch and tequila to work together. For user convenience, this can be done with the class `TorchLayer`. \n",
-    "This class takes an `Objective`, a dict of compilation args (optional), and a list of `Variable`s of the objective which should be treater as input (I.e, loaded from the `DataLoader`), and will treat all the remaining variables as internal weights of the quantum neural network layer that the objective constitutes. If not specified in the compile_args dictionary, random values (between 0 and $2 \\pi$) will be used for the weights."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "input_variable=h2_encoder.extract_variables()[0]\n",
-    "inits={'a':1.5, 'b':1.5}\n",
-    "compile_args={'backend':'qulacs', 'initial_values':inits} # dict. allowed keys: backend, samples, noise, device, initial_values"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "WARNING:absl:No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "TorchLayer(\n",
-      "  Tequila TorchLayer. Represents: \n",
-      "  Objective with 1 unique expectation values\n",
-      "  variables = [(1, 0, 1, 0), a, b]\n",
-      "  types     = not compiled \n",
-      "  Current Weights: {'b': Parameter containing:\n",
-      "  tensor(1.5000, dtype=torch.float64, requires_grad=True), 'a': Parameter containing:\n",
-      "  tensor(1.5000, dtype=torch.float64, requires_grad=True)}\n",
-      ")\n"
-     ]
-    }
-   ],
-   "source": [
-    "my_torch_encoder = tq.ml.interface_torch.TorchLayer(h2_encoder,compile_args,input_vars=[input_variable])\n",
-    "print(my_torch_encoder)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## 4: Optimize using PyTorch and plot the results.\n",
-    "\n",
-    "Once converted to a PyTorch layer, Tequila `Objective`'s can be optimized with the inbuilt tools of PyTorch. Do note that `TorchLayer` objects cannot be optimized with the tequila optimizers."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "*** Epoch 0 ***\n",
-      "0.2866195387587957\n",
-      "0.28661953875879626\n",
-      "0.2866195387587953\n",
-      "0.28661953875879653\n",
-      "0.28130235607019866\n",
-      "0.2813023560701979\n",
-      "0.28130235607019843\n",
-      "0.2813023560701981\n",
-      "0.27603301556135906\n",
-      "0.2760330155613586\n",
-      "0.2760330155613589\n",
-      "0.2760330155613585\n",
-      "0.27081289963294786\n",
-      "0.270812899632948\n",
-      "0.27081289963294825\n",
-      "0.2708128996329484\n"
-     ]
-    }
-   ],
-   "source": [
-    "optim = torch.optim.Adam(my_torch_encoder.parameters(),lr=0.01)\n",
-    "loss_values = []\n",
-    "for epoch in range(30):\n",
-    "    print('*** Epoch {} ***'.format(epoch))\n",
-    "    batch = 0\n",
-    "    batched_loss = []\n",
-    "    for point in my_loader:\n",
-    "        batch += 1\n",
-    "        optim.zero_grad()\n",
-    "        loss = my_torch_encoder(point)\n",
-    "        loss = loss.mean()\n",
-    "        batched_loss.append(loss)\n",
-    "        loss.backward()\n",
-    "\n",
-    "        optim.step()\n",
-    "    bv = np.mean([l.detach().numpy() for l in batched_loss])\n",
-    "    loss_values.append(bv)\n",
-    "    print('Batched Average Loss: ', bv)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "plt.plot(loss_values, label='loss per epoch')\n",
-    "plt.legend()\n",
-    "plt.xlabel('Epoch', fontsize=18)\n",
-    "plt.ylabel('Autoencoder Loss', fontsize=16)\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## This concludes our tutorial. We hope you've enjoyed it!\n"
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.7.9"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 4
-}
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-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Exploring the application of quantum circuits in convolutional neural networks"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "This tutorial will guide you through implementing a hybrid quantum-classical convolutional neural network using Tequila along with other packages such as Tensorflow. We will then train the model on the MNIST dataset, which contains images of handwritten numbers classifed according to the digit they represent. Finally, we will compare the accuracy and loss of models with and without the quantum preprocessing.\n",
-    "\n",
-    "Inspriation for this tutorial comes from [Pennylane: Quanvolutional Neural Networks](https://pennylane.ai/qml/demos/tutorial_quanvolution.html). We will similarly follow the method proposed in the reference paper used for this tutorial, [Henderson at al (2020)](https://doi.org/10.1007/s42484-020-00012-y)."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Background"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "#### Convolutional Neural Nets"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "An excellent high-level explanation of convolutional neural networks can be found [here](https://www.youtube.com/watch?v=FmpDIaiMIeA). Alternatively, an excellent written explanation can be found [here](http://neuralnetworksanddeeplearning.com/chap6.html) and for more information, the wikipedia article can be found [here](https://en.wikipedia.org/wiki/Convolutional_neural_network).\n",
-    "\n",
-    "In summary, a convolutional neural network includes preprocessing layers prior to optimisation layers so that features in the input (which are often images) are extracted and amplified. The result is a model with greater predictive power. This processing also improves classification of images as it extracts features even if they are translocated between images. This means that searching for a particular pixel distribution (for example the shape of a curve or line may be a useful feature when classifying digits) is not dependant on the distribution being in an identical location in each image where it is present. The convolutional process extracts this information even if it is slightly rotated or translocated.\n",
-    "\n",
-    "The implementation of the convolutional layer involves a grid for each feature being passed over the entire image. At each location, a score is calculated representing how well the feature and the section of the image match, and this becomes the value of the corresponding pixel in the output image. As a guide, a large score represents a close match, generally meaning that the feature is present at that location of the image, and a low score represents the absence of a match."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "#### Our Approach"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Our general approach is similar to that used in a conventional convolutional neural network however the initial processing occurs by running the images through a quantum circuit instead of a convolutional filter. Each simulation of a circuit represents one 3x3 filter being applied to one 3x3 region of one image. The construction of the circuit is randomised (see below), however this construction only occurs once per filter such that each region of the image being transformed by the same filter gets run through the same circuit. A single, scalar output is generated from the circuit which is used as the pixel strength of the output image, and the remainder of the neural net uses only classical processing, specifically two further convolutional layers, max pooling and two fully connected layers. This architecture has been chosen to closely mimic the structure used in our reference paper (Henderson et al, 2020), however as they note, \"The QNN topology chosen in this work is not fixed by nature ... the QNN framework was designed to give users complete control over the number and order of quanvolutional layers in the architecture. The topology explored in this work was chosen because it was the simplest QNN architecture to use as a baseline for comparison against other purely classical networks. Future work would focus on exploring the impact of more complex architectural variations.\""
-   ]
-  },
-  {
-   "attachments": {},
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "<img src=\"Quanv_Neural_Net/Our_approach.jpg\" width=\"700\" />"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "#### Quantum Processing"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Henderson et al summarise the use of quantum circuits as convolutional layers: \"Quanvolutional layers are made up of a group of N quantum filters which operate much like their classical convolutional layer counterparts, producing feature maps by locally transforming input data. The key difference is that quanvolutional filters extract features from input data by transforming spatially local subsections of data using quantum circuits.\" Our approach to the circuit design is based on the paper and is as follows:\n",
-    "\n",
-    "1) The input images are iterated over and each 3x3 region is embedded into the quantum circuit using the threshold function: \n",
-    "$$|\\psi \\rangle = \\begin{cases} \n",
-    "                      |0\\rangle & if & strength\\leq 0 \\\\\n",
-    "                      |1\\rangle & if & strength > 0\n",
-    "                   \\end{cases}$$ \n",
-    "\n",
-    "As the pixel strengths are normalised to values between -0.5 and 0.5, it is expected that brighter regions of the image will intialise their corresponding qubit in the state $|1\\rangle$ and darker regions will intitialise the state $|0\\rangle$. Each pixel is represented by one qubit, such that 9 qubits are used in total, and this quantum circuit is reused for each 3x3 square in the filter.\n",
-    "\n",
-    "2) We next apply a random circuit to the qubits. To implement this, a random choice from Rx, Ry and Rz gates is applied to a random qubit, and the total number of gates applied in each layer is equal to the number of qubits. With a set probability (which we set to 0.3), a CNOT gate will be applied instead of the rotation to two random qubits. We have chosen to set the parameters of rotation with random numbers between (0,2π) however futher optimisation of the model could be found from using a variational circuit and optimising these parameters.\n",
-    "\n",
-    "3) Further layers could be applied of the random gates. To simplify, we only apply one layer.\n",
-    "\n",
-    "4) A scalar is outputted from the circuit and used as the corresponding pixel in the output image. We generate this number using the following method. The state vector of the final state of the circuit is simulated and the state corresponding to the most likely output (largest modulus) is selected. We then calculate the number of qubits for this state which are measured as a $|1\\rangle$. \n",
-    "\n",
-    "5) A total of four filters are applied to each image, and for each filter steps 1-3 are repeated with a different randomised circuit. The output image therefore contains a third dimension with four channels representing the four different outputted values which each filters produced."
-   ]
-  },
-  {
-   "attachments": {},
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "<img src=\"Quanv_Neural_Net/Quantum_circuit.jpg\" width=\"700\" />"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Code and Running the Program"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The following code cell is used to import the necessary packages and to set parameters."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import math\n",
-    "import matplotlib.pyplot as plt\n",
-    "import numpy as np\n",
-    "import tensorflow as tf\n",
-    "import tequila as tq\n",
-    "\n",
-    "from operator import itemgetter\n",
-    "from tensorflow import keras\n",
-    "\n",
-    "n_filters = 4               # Number of convolutional filters\n",
-    "filter_size = 3             # Size of filter = nxn (here 3x3)\n",
-    "pool_size = 2               # Used for the pooling layer\n",
-    "n_qubits = filter_size ** 2 # Number of qubits\n",
-    "n_layers = 1                # Number of quantum circuit layers\n",
-    "n_train = 1000              # Size of the training dataset\n",
-    "n_test = 200                # Size of the testing dataset\n",
-    "n_epochs = 100              # Number of optimization epochs\n",
-    "\n",
-    "SAVE_PATH = \"quanvolution/\" # Data saving folder\n",
-    "PREPROCESS = False          # If False, skip quantum processing and load data from SAVE_PATH\n",
-    "tf.random.set_seed(1)       # Seed for TensorFlow random number generator"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We start by creating the Dataset class. Here, we load the images and labels of handwritten digits from the MNIST dataset. We then reduce the number of images from 60,000 and 10,000 (for the training and testing sets respectively) down to the variables n_train and n_test, normalise the pixel values to within the range (-0.5,0.5) and reshape the images by adding a third dimension. Each image's shape is therefore transformed from (28, 28) to (28, 28, 1) as this is necessary for the convolutional layer."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "class Dataset:\n",
-    "\n",
-    "    def __init__(self):\n",
-    "        # Loading the full dataset of images from keras\n",
-    "        # Shape of self.train_images is (60000, 28, 28), shape of self.train_labels is (60000,)\n",
-    "        # For self.test_images and self.test_labels, shapes are (10000, 28, 28) and (10000,)\n",
-    "        mnist_dataset = keras.datasets.mnist\n",
-    "        (self.train_images, self.train_labels), (self.test_images, self.test_labels) = mnist_dataset.load_data()\n",
-    "\n",
-    "        # Reduce dataset size to n_train and n_test\n",
-    "        # First dimension of shapes are reduced to n_train and n_test\n",
-    "        self.train_images = self.train_images[:n_train]\n",
-    "        self.train_labels = self.train_labels[:n_train]\n",
-    "        self.test_images = self.test_images[:n_test]\n",
-    "        self.test_labels = self.test_labels[:n_test]\n",
-    "\n",
-    "        # Normalize pixel values within -0.5 and +0.5\n",
-    "        self.train_images = (self.train_images / 255) - 0.5\n",
-    "        self.test_images = (self.test_images / 255) - 0.5\n",
-    "\n",
-    "        # Add extra dimension for convolution channels\n",
-    "        self.train_images = self.train_images[..., tf.newaxis]\n",
-    "        self.test_images = self.test_images[..., tf.newaxis]"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The next code cell contains the class used to generate the quantum circuit. In theory, the circuit could be either structured or random. We form a randomised circuit to match the reference paper (Henderson et al, 2020), however for simplicity, our implementation differs in some ways. We choose to use only use single qubit Rx($\\theta$), Ry($\\theta$) and Rz($\\theta$) gates and the two qubit CNOT gate compared to the choice of single qubit X($\\theta$), Y($\\theta$), Z($\\theta$), U($\\theta$), P, T, H and two qubit CNOT, SWAP, SQRTSWAP, or CU gates used in the paper. Furthermore, we chose to assign a two qubit gate to any random qubits with a certain probability (labelled ratio_imprim, set to 0.3) rather than setting a connection probabiltiy between each pair of qubits (this approach follows the Pennylane tutorial). The seed is used for reproducability and its value is set depending on which filter the circuit represents (see QuantumModel below).\n",
-    "\n",
-    "The parameters used for the rotation gates have the potential to be optimised using a cost function. For simplicity, and to mirror the paper, here we will use random parameters and we will not include these in the optimisation of the model. This means that the quantum processing only needs to happen once, prior to creating the neural net."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "class QuantumCircuit:\n",
-    "    \n",
-    "    def __init__(self, seed=None):\n",
-    "        # Set random seed for reproducability\n",
-    "        if seed: np.random.seed(seed)\n",
-    "        \n",
-    "        # Encode classical information into quantum circuit\n",
-    "        # Bit flip gate is applied if the pixel strength > 0\n",
-    "        self.circ = tq.QCircuit()\n",
-    "        for i in range(n_qubits):\n",
-    "            self.circ += tq.gates.X(i, power='input_{}'.format(i))\n",
-    "\n",
-    "        # Add random layers to the circuit\n",
-    "        self.circ += self.random_layers()\n",
-    "    \n",
-    "    def random_layers(self, ratio_imprim=0.3):\n",
-    "        # Initialise circuit\n",
-    "        circuit = tq.QCircuit()\n",
-    "\n",
-    "        # Iterate over the number of layers, adding rotational and CNOT gates\n",
-    "        # The number of rotational gates added per layer is equal to the number of qubits in the circuit\n",
-    "        for i in range(n_layers):\n",
-    "            j = 0\n",
-    "            while (j < n_qubits):\n",
-    "                if np.random.random() > ratio_imprim:\n",
-    "                    # Applies a random rotation gate to a random qubit with probability (1 - ratio_imprim)\n",
-    "                    rnd_qubit = np.random.randint(n_qubits)\n",
-    "                    circuit += np.random.choice(\n",
-    "                        [tq.gates.Rx(angle='l_{},th_{}'.format(i,j), target=rnd_qubit),\n",
-    "                         tq.gates.Ry(angle='l_{},th_{}'.format(i,j), target=rnd_qubit),\n",
-    "                         tq.gates.Rz(angle='l_{},th_{}'.format(i,j), target=rnd_qubit)])\n",
-    "                    j += 1\n",
-    "                else:\n",
-    "                    # Applies the CNOT gate to 2 random qubits with probability ratio_imprim\n",
-    "                    if n_qubits > 1:\n",
-    "                        rnd_qubits = np.random.choice(range(n_qubits), 2, replace=False)\n",
-    "                        circuit += tq.gates.CNOT(target=rnd_qubits[0], control=rnd_qubits[1])\n",
-    "        return circuit"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "As an example to show the circuit used in this program, an instance of a circuit is drawn below. This will differ between calls if you remove the seed variable due to the random nature of forming the circuit."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "circuit = QuantumCircuit(seed=2)\n",
-    "tq.draw(circuit.circ, backend='qiskit')"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We next show the QuantumModel class, used to generate the neural network for the images which undergo pre-processing through the quantum convolutional layer. If PREPROCESSING is set to True, each image from the dataset undergoes processing through a number of quantum circuits, determined by n_filters. The embedding used, the structure of the circuit and the method of extracting the output are described in the background of this tutorial. \n",
-    "\n",
-    "We use tensorflow to construct the neural net. The implementation we use contains two conventional convolutional layers, each followed by max pooling, and then one fully connected with 1024 nodes before the softmax output layer. We use a Relu activation function for the convolutional and fully connected layers. See the background section of this tutorial for some context on this choice of neural net."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "class QuantumModel:\n",
-    "\n",
-    "    def __init__(self, dataset, parameters):\n",
-    "        # Initialize dataset and parameters\n",
-    "        self.ds = dataset\n",
-    "        self.params = parameters\n",
-    "        \n",
-    "        # The images are run through the quantum convolutional layer\n",
-    "        self.convolutional_layer()\n",
-    "\n",
-    "        # The model is initialized\n",
-    "        self.model = keras.models.Sequential([\n",
-    "            keras.layers.Conv2D(n_filters, filter_size, activation='relu'),\n",
-    "            keras.layers.MaxPooling2D(pool_size=pool_size),\n",
-    "            keras.layers.Conv2D(n_filters, filter_size, activation='relu'),\n",
-    "            keras.layers.MaxPooling2D(pool_size=pool_size),\n",
-    "            keras.layers.Flatten(),\n",
-    "            keras.layers.Dense(1024, activation=\"relu\"),\n",
-    "            keras.layers.Dense(10, activation=\"softmax\")\n",
-    "        ])\n",
-    "\n",
-    "        # Compile model using the Adam optimiser\n",
-    "        self.model.compile(\n",
-    "            optimizer=keras.optimizers.Adam(learning_rate=0.00001),\n",
-    "            loss=\"sparse_categorical_crossentropy\",\n",
-    "            metrics=[\"accuracy\"]\n",
-    "        )\n",
-    "    \n",
-    "    def convolutional_layer(self):\n",
-    "        if PREPROCESS == True:\n",
-    "            # Initate arrays to store processed images\n",
-    "            self.q_train_images = [np.zeros((28-2, 28-2, n_filters)) for _ in range(len(self.ds.train_images))]\n",
-    "            self.q_test_images = [np.zeros((28-2, 28-2, n_filters)) for _ in range(len(self.ds.test_images))]\n",
-    "            \n",
-    "            # Loop over the number of filters, applying a different randomised quantum circuit for each\n",
-    "            for i in range(n_filters):\n",
-    "                print('Filter {}/{}\\n'.format(i+1, n_filters))\n",
-    "                \n",
-    "                # Construct circuit\n",
-    "                # We set the seed to be i+1 so that the circuits are reproducable but the design differs between filters\n",
-    "                # We use i+1 not i to avoid setting the seed as 0 which sometimes produces random behaviour\n",
-    "                circuit = QuantumCircuit(seed=i+1)\n",
-    "                \n",
-    "                # Apply the quantum processing to the train_images, analogous to a convolutional layer\n",
-    "                print(\"Quantum pre-processing of train images:\")\n",
-    "                for j, img in enumerate(self.ds.train_images):\n",
-    "                    print(\"{}/{}        \".format(j+1, n_train), end=\"\\r\")\n",
-    "                    self.q_train_images[j][...,i] = (self.filter_(img, circuit, self.params[i]))\n",
-    "                print('\\n')\n",
-    "\n",
-    "                # Similarly for the test_images\n",
-    "                print(\"Quantum pre-processing of test images:\")\n",
-    "                for j, img in enumerate(self.ds.test_images):\n",
-    "                    print(\"{}/{}        \".format(j+1, n_test), end=\"\\r\")\n",
-    "                    self.q_test_images[j][...,i] = (self.filter_(img, circuit, self.params[i]))\n",
-    "                print('\\n')\n",
-    "\n",
-    "            # Transform images to numpy array\n",
-    "            self.q_train_images = np.asarray(self.q_train_images)\n",
-    "            self.q_test_images = np.asarray(self.q_test_images)\n",
-    "            \n",
-    "            # Save pre-processed images\n",
-    "            np.save(SAVE_PATH + \"q_train_images.npy\", self.q_train_images)\n",
-    "            np.save(SAVE_PATH + \"q_test_images.npy\", self.q_test_images)\n",
-    "        \n",
-    "        # Load pre-processed images\n",
-    "        self.q_train_images = np.load(SAVE_PATH + \"q_train_images.npy\")\n",
-    "        self.q_test_images = np.load(SAVE_PATH + \"q_test_images.npy\")\n",
-    "\n",
-    "    def filter_(self, image, circuit, variables):\n",
-    "        # Initialize output image\n",
-    "        output = np.zeros((28-2, 28-2))\n",
-    "\n",
-    "        # Loop over the image co-ordinates (i,j) using a 3x3 square filter\n",
-    "        for i in range(28-2):\n",
-    "            for j in range(28-2):\n",
-    "\n",
-    "                # Extract the value of each pixel in the 3x3 filter grid\n",
-    "                image_pixels = [\n",
-    "                    image[i,j,0],\n",
-    "                    image[i,j+1,0],\n",
-    "                    image[i,j+2,0],\n",
-    "                    image[i+1,j,0],\n",
-    "                    image[i+1,j+1,0],\n",
-    "                    image[i+1,j+2,0],\n",
-    "                    image[i+2,j,0],\n",
-    "                    image[i+2,j+1,0],\n",
-    "                    image[i+2,j+2,0]\n",
-    "                ]\n",
-    "\n",
-    "                # Construct parameters used to embed the pixel strength into the circuit\n",
-    "                input_variables = {}\n",
-    "                for idx, strength in enumerate(image_pixels):\n",
-    "                    # If strength > 0, the power of the bit flip gate is 1\n",
-    "                    # Therefore this qubit starts in state |1>\n",
-    "                    if strength > 0:\n",
-    "                        input_variables['input_{}'.format(idx)] = 1\n",
-    "                    # Otherwise the gate is not applied and the initial state is |0>\n",
-    "                    else:\n",
-    "                        input_variables['input_{}'.format(idx)] = 0\n",
-    "\n",
-    "                # Find the statevector of the circuit and determine the state which is most likely to be measured\n",
-    "                wavefunction = tq.simulate(circuit.circ, variables={**variables, **input_variables})\n",
-    "                amplitudes = [(k,(abs(wavefunction(k)))) for k in range(2**n_qubits) if wavefunction(k)]\n",
-    "                max_idx = max(amplitudes,key=itemgetter(1))[0]\n",
-    "                \n",
-    "                # Count the number of qubits which output '1' in this state\n",
-    "                result = len([k for k in str(bin(max_idx))[2::] if k == '1'])\n",
-    "                output[i,j] = result\n",
-    "        return output\n",
-    "\n",
-    "    def train(self):\n",
-    "        # Train the model on the dataset\n",
-    "        self.history = self.model.fit(\n",
-    "            self.q_train_images,\n",
-    "            self.ds.train_labels,\n",
-    "            validation_data=(self.q_test_images, self.ds.test_labels),\n",
-    "            batch_size=4,\n",
-    "            epochs=n_epochs,\n",
-    "            verbose=2\n",
-    "        )"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We also create a ClassicalModel class to run the images through a conventional convolutional neural network. The design of the neural net used here is identical to the QuantumModel class, however the images used are directly from the dataset and therefore have not been processed through the quantum layer. We include this as a control to compare the results from the quantum model."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "class ClassicalModel:\n",
-    "\n",
-    "    def __init__(self, dataset):\n",
-    "        # Initialize dataset and parameters\n",
-    "        self.ds = dataset\n",
-    "\n",
-    "        # The model is initialized\n",
-    "        self.model = keras.models.Sequential([\n",
-    "            keras.layers.Conv2D(n_filters, filter_size, activation='relu'),\n",
-    "            keras.layers.MaxPooling2D(pool_size=pool_size),\n",
-    "            keras.layers.Conv2D(n_filters, filter_size, activation='relu'),\n",
-    "            keras.layers.MaxPooling2D(pool_size=pool_size),\n",
-    "            keras.layers.Flatten(),\n",
-    "            keras.layers.Dense(1024, activation=\"relu\"),\n",
-    "            keras.layers.Dense(10, activation=\"softmax\")\n",
-    "        ])\n",
-    "\n",
-    "        # Compile model using the Adam optimiser\n",
-    "        self.model.compile(\n",
-    "            optimizer=keras.optimizers.Adam(learning_rate=0.00005),\n",
-    "            loss=\"sparse_categorical_crossentropy\",\n",
-    "            metrics=[\"accuracy\"]\n",
-    "        )\n",
-    "    \n",
-    "    def train(self):\n",
-    "        # Train the model on the dataset\n",
-    "        self.history = self.model.fit(\n",
-    "            self.ds.train_images,\n",
-    "            self.ds.train_labels,\n",
-    "            validation_data=(self.ds.test_images, self.ds.test_labels),\n",
-    "            batch_size=4,\n",
-    "            epochs=n_epochs,\n",
-    "            verbose=2\n",
-    "        )"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We are now able to run our program! The following code does this using the quantum_model and classical_model functions. Although the implementations are similar, quantum_model additionally defines the parameters used for the rotational gates in the circuit. We have limited the value of each parameter to the range (0,2π).\n",
-    "\n",
-    "Running the program takes some time. Our results are plotted below, so if you would rather not wait, either reduce the numbers in n_train and n_test or skip ahead!"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "scrolled": true
-   },
-   "outputs": [],
-   "source": [
-    "def quantum_model():\n",
-    "    # Generating parameters, each maps to a random number between 0 and 2*π\n",
-    "    # parameters is a list of dictionaries, where each dictionary represents the parameter\n",
-    "    # mapping for one filter\n",
-    "    parameters = []\n",
-    "    for i in range(n_filters):\n",
-    "        filter_params = {}\n",
-    "        for j in range(n_layers):\n",
-    "            for k in range(n_qubits):\n",
-    "                filter_params[tq.Variable(name='l_{},th_{}'.format(j,k))] = np.random.uniform(high=2*np.pi)\n",
-    "        parameters.append(filter_params)\n",
-    "        \n",
-    "    # Initalise the dataset\n",
-    "    ds = Dataset()\n",
-    "    \n",
-    "    # Initialise and train the model\n",
-    "    model = QuantumModel(ds, parameters=parameters)\n",
-    "    model.train()\n",
-    "    \n",
-    "    # Store the loss and accuracy of the model to return\n",
-    "    loss = model.history.history['val_loss']\n",
-    "    accuracy = model.history.history['val_accuracy']\n",
-    "\n",
-    "    return model\n",
-    "\n",
-    "def classical_model():\n",
-    "    # Initialise the dataset\n",
-    "    ds = Dataset()\n",
-    "    \n",
-    "    # Initialise and train the model\n",
-    "    model = ClassicalModel(ds)\n",
-    "    model.train()\n",
-    "    \n",
-    "    # Store the loss and accuracy of the model to return\n",
-    "    loss = model.history.history['val_loss']\n",
-    "    accuracy = model.history.history['val_accuracy']\n",
-    "    \n",
-    "    return model\n",
-    "\n",
-    "model_q = quantum_model()\n",
-    "model_c = classical_model()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Plotting the Results"
-   ]
-  },
-  {
-   "attachments": {},
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The graphs showing the accuracy and loss of our models are included in this text box. These were generated using the function plot, available below. As shown, the results from the quantum processing lead to a model comparable to the classical control in both accuracy and loss. After running for 100 epochs, the quantum model results in a validation set accuracy of 0.9350, compared to the fully classical model which has a validation set accuracy of 0.9150.\n",
-    "<img src=\"Quanv_Neural_Net/Plots.png\" />"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def plot(model_q, model_c):\n",
-    "\n",
-    "    plt.style.use(\"seaborn\")\n",
-    "    fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(6, 9))\n",
-    "\n",
-    "    # Plotting the graph for accuracy\n",
-    "    ax1.plot(model_q.history.history['val_accuracy'], color=\"tab:red\", label=\"Quantum\")\n",
-    "    ax1.plot(model_c.history.history['val_accuracy'], color=\"tab:green\", label=\"Classical\")\n",
-    "    ax1.set_ylabel(\"Accuracy\")\n",
-    "    ax1.set_ylim([0,1])\n",
-    "    ax1.set_xlabel(\"Epoch\")\n",
-    "    ax1.legend()\n",
-    "\n",
-    "    # Plotting the graph for loss\n",
-    "    ax2.plot(model_q.history.history['val_loss'], color=\"tab:red\", label=\"Quantum\")\n",
-    "    ax2.plot(model_c.history.history['val_loss'], color=\"tab:green\", label=\"Classical\")\n",
-    "    ax2.set_ylabel(\"Loss\")\n",
-    "    ax2.set_xlabel(\"Epoch\")\n",
-    "    ax2.legend()\n",
-    "    \n",
-    "    plt.tight_layout()\n",
-    "    plt.show()\n",
-    "\n",
-    "plot(model_q, model_c)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Evaluating the Model"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let us now compare the behaviour of the two models. We do this by running the test images through each with the optimised weights and biases and seeing the results of the classification. This process is implemented using the Classification class, shown below."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Overall, our quantum model misclassified images 34, 37, 42, 54, 67, 74, 120, 127, 143, 150, 152, 166, and 185. The classical model misclassified images 8, 16, 21, 23, 54, 60, 61, 67, 74, 93, 113, 125, 134, 160, 168, 178, and 196. This means that in total, the quantum model misclassified 13 images and the classical model misclassified 17 images. Of these, only images 54, 67, and 74 were misclassified by both."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from termcolor import colored\n",
-    "\n",
-    "class Classification:\n",
-    "    \n",
-    "    def __init__(self, model, test_images):\n",
-    "        # Initialising parameters\n",
-    "        self.model = model\n",
-    "        self.test_images = test_images\n",
-    "        self.test_labels = model.ds.test_labels\n",
-    "\n",
-    "    def classify(self):\n",
-    "        # Create predictions on the test set\n",
-    "        self.predictions = np.argmax(self.model.model.predict(self.test_images), axis=-1)\n",
-    "\n",
-    "        # Keep track of the indices of images which were classified correctly and incorrectly\n",
-    "        self.correct_indices = np.nonzero(self.predictions == self.test_labels)[0]\n",
-    "        self.incorrect_indices = np.nonzero(self.predictions != self.test_labels)[0]\n",
-    "    \n",
-    "    def print_(self):\n",
-    "        # Printing the total number of correctly and incorrectly classified images\n",
-    "        print(len(self.correct_indices),\" classified correctly\")\n",
-    "        print(len(self.incorrect_indices),\" classified incorrectly\")\n",
-    "        print('\\n')\n",
-    "\n",
-    "        # Printing the classification of each image\n",
-    "        for i in range(n_test):\n",
-    "            print(\"Image {}/{}\".format(i+1, n_test))\n",
-    "            if i in self.correct_indices:\n",
-    "                # The image was correctly classified\n",
-    "                print('model predicts: {} - true classification: {}'.format(\n",
-    "                    self.predictions[i], self.test_labels[i]))\n",
-    "            else:\n",
-    "                # The image was not classified correctly\n",
-    "                print(colored('model predicts: {} - true classification: {}'.format(\n",
-    "                    self.predictions[i], self.test_labels[i]), 'red'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "print('Quantum Model')\n",
-    "q_class = Classification(model_q, model_q.q_test_images)\n",
-    "q_class.classify()\n",
-    "q_class.print_()\n",
-    "\n",
-    "print('\\n')\n",
-    "\n",
-    "print('Classical Model')\n",
-    "c_class = Classification(model_c, model_c.ds.test_images)\n",
-    "c_class.classify()\n",
-    "c_class.print_()"
-   ]
-  },
-  {
-   "attachments": {},
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Lastly, we can see the effect that the quantum convolutional layer actually has on the images by plotting images after they have been run through the quantum filters, and to do this we use the function visualise, shown below. Included in this text box is a plot showing four images which have been run through our filters. The top row shows images from the original dataset, and each subsequent row shows the result from each of the four filters on that original image. It can be seen that the processing preserves the global shape of the digit while introducing local distortion.\n",
-    "<img src=\"Quanv_Neural_Net/Filters.png\" />"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def visualise(model):\n",
-    "    # Setting n_samples to be the number of images to print\n",
-    "    n_samples = 4\n",
-    "    \n",
-    "    fig, axes = plt.subplots(1 + n_filters, n_samples, figsize=(10, 10))\n",
-    "    \n",
-    "    # Iterate over each image\n",
-    "    for i in range(n_samples):\n",
-    "        \n",
-    "        # Plot the original image from the dataset\n",
-    "        axes[0, 0].set_ylabel(\"Input\")\n",
-    "        if i != 0:\n",
-    "            axes[0, i].yaxis.set_visible(False)\n",
-    "        axes[0, i].imshow(model.ds.train_images[i, :, :, 0], cmap=\"gray\")\n",
-    "\n",
-    "        # Plot the images generated by each filter\n",
-    "        for c in range(n_filters):\n",
-    "            axes[c + 1, 0].set_ylabel(\"Output [ch. {}]\".format(c))\n",
-    "            if i != 0:\n",
-    "                axes[c, i].yaxis.set_visible(False)\n",
-    "            axes[c + 1, i].imshow(model.q_train_images[i, :, :, c], cmap=\"gray\")\n",
-    "\n",
-    "    plt.tight_layout()\n",
-    "    plt.show()\n",
-    "    \n",
-    "visualise(model_q)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "#### Resources used to make this tutorial:\n",
-    "\n",
-    "1. [Pennylane: Quanvolutional Neural Networks](https://pennylane.ai/qml/demos/tutorial_quanvolution.html)\n",
-    "2. Henderson, M., Shakya, S., Pradhan, S. et al. Quanvolutional neural networks: powering image recognition with quantum circuits. Quantum Mach. Intell. 2, 1–9 (2020). https://doi.org/10.1007/s42484-020-00012-y\n",
-    "3. [Keras for Beginners: Implementing a Convolutional Neural Network. Victor Zhou](https://victorzhou.com/blog/keras-cnn-tutorial/).\n",
-    "4. [CNNs, Part 1: An Introduction to Convolutional Neural Networks. Victor Zhou](https://victorzhou.com/blog/intro-to-cnns-part-1/).\n",
-    "5. [How Convolutional Neural Networks work](https://www.youtube.com/watch?v=FmpDIaiMIeA)\n",
-    "6. [Neural Networks and Deep Learning, chapter 6. Michael Nielsen](http://neuralnetworksanddeeplearning.com/chap6.html)"
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.6.10"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 4
-}
diff --git a/tutorials/ReducedDensityMatrices.ipynb b/tutorials/ReducedDensityMatrices.ipynb
deleted file mode 100644
index 44c338eb..00000000
--- a/tutorials/ReducedDensityMatrices.ipynb
+++ /dev/null
@@ -1,480 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Reduced Density Matrices in Tequila\n",
-    "\n",
-    "This notebook serves as a tutorial to the computation and usage of the one- and two-particle reduced density matrices."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import tequila as tq\n",
-    "import numpy"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## The 1- and 2-RDM\n",
-    "\n",
-    "First, look at the definition of the reduced density matrices (RDM) for some state $ |\\psi\\rangle$:\n",
-    "\n",
-    "1-RDM: $ \\gamma^p_q \\equiv \\langle \\psi | a^p a_q | \\psi\\rangle$\n",
-    "\n",
-    "2-RDM $ \\gamma^{pq}_{rs} \\equiv \\langle \\psi | a^p a^q a_s a_r | \\psi\\rangle$ (we mainly use the standard physics ordering for the second-quantized operators, i.e. $p,r$ go with particle 1 and $q,s$ with particle 2)\n",
-    "\n",
-    "The operators $ a^p = a_p^\\dagger $ and $a_p$ denote the standard fermionic creation and annihilation operators.\n",
-    "\n",
-    "Since we work on a quantum computer, $|\\psi\\rangle$ is represented by some unitary transformation $U$: $|\\psi\\rangle = U |0\\rangle^{\\otimes N_q}$, using $N_q$ qubits. This corresponds to $N_q$ spin-orbitals in Jordan-Wigner encoding. Obtaining the RDMs from a quantum computer is most intuitive when using the Jordan-Wigner transformation, since the results directly correspond to the ones computed classically in second quantized form.\n",
-    "\n",
-    "It is worth mentioning that since we only consider real orbitals in chemistry applications, the implementation also expects only real-valued RDM's.\n",
-    "The well-known anticommutation relations yield a series of symmetry properties for the reduced density matrices, which can be taken into consideration to reduce the computational cost:\n",
-    "\\begin{align} \\gamma^p_q &= \\gamma^q_p \\\\ \\gamma^{pq}_{rs} &= -\\gamma^{qp}_{rs} = -\\gamma^{pq}_{sr} = \\gamma^{qp}_{sr} = \\gamma^{rs}_{pq}\\end{align}\n",
-    "\n",
-    "In chemistry applications, solving the electronic structure problem involves the electronic Hamiltonian (here in Born-Oppenheimer approximation)\n",
-    "$$ H_{el} = h_0 + \\sum_{pq} h^q_p a^p_q + \\frac{1}{2}\\sum_{pqrs} h^{rs}_{pq} a^{pq}_{rs}$$\n",
-    "with the one- and two-body integrals $h^q_p, h^{rs}_{pq}$ that turn out to be independent of spin.\n",
-    "\n",
-    "Therefore, we introduce the spin-free RDMs $\\Gamma^P_Q$ and $\\Gamma^{PQ}_{RS}$, obtained by spin-summation (we write molecular orbitals in uppercase letters $P,Q,\\ldots\\in\\{1,\\ldots,N_p\\}$ in opposite to spin-orbitals $p,q,\\ldots\\in\\{1,\\ldots,N_q\\}$):\n",
-    "\n",
-    "\\begin{align} \\Gamma^P_Q &= \\sum_{\\sigma \\in \\{\\alpha, \\beta\\}} \\gamma^{p\\sigma}_{q\\sigma} = \\langle \\psi |\\sum_{\\sigma} a^{p\\sigma} a_{q\\sigma} | \\psi\\rangle \\\\\n",
-    " \\Gamma^{PQ}_{RS} &= \\sum_{\\sigma,\\tau \\in \\{\\alpha, \\beta\\}} \\gamma^{p\\sigma q\\tau}_{r\\sigma s\\tau} = \\langle \\psi | \\sum_{\\sigma,\\tau}  a^{p\\sigma} a^{q\\tau} a_{s\\tau} a_{r\\sigma} | \\psi \\rangle.  \\end{align}\n",
-    " \n",
-    "Note, that by making use of linearity, we obtain the second equality in the two expressions above. Performing the summation before evaluating the expected value means less expected values and a considerable reduction in computational cost (only $N_p=\\frac{N_q}{2}$ molecular orbitals vs. $N_q$ spin-orbitals).\n",
-    "\n",
-    "Due to the orthogonality of the spin states, the symmetries for the spin-free 2-RDM are slightly less than for the spin-orbital RDM:\n",
-    "\\begin{align} \\Gamma^P_Q &= \\Gamma^Q_P\\\\\n",
-    " \\Gamma^{PQ}_{RS} &= \\Gamma^{QP}_{SR} = \\Gamma^{RS}_{PQ} \\end{align}"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Optimizer: <class 'tequila.optimizers.optimizer_scipy.OptimizerSciPy'> \n",
-      "backend         : qulacs\n",
-      "device          : None\n",
-      "samples         : None\n",
-      "save_history    : True\n",
-      "noise           : None\n",
-      "\n",
-      "Method          : BFGS\n",
-      "Objective       : 1 expectationvalues\n",
-      "gradient        : 12 expectationvalues\n",
-      "\n",
-      "active variables : 3\n",
-      "\n",
-      "E=-1.64501793  angles= {a1: 0.9750975289027688, a2: 0.9195439775408228, a3: 3.49947562895891}  samples= None\n",
-      "E=-2.71423735  angles= {a1: 0.027272521865900456, a2: 0.5712705986200453, a3: 3.520294120034508}  samples= None\n",
-      "E=-2.83675244  angles= {a1: -0.32223270411892413, a2: -0.04569099158289358, a3: 3.5188489289335756}  samples= None\n",
-      "E=-2.86970164  angles= {a1: -0.13709848313691403, a2: 0.02172805360757754, a3: 3.5204102536245103}  samples= None\n",
-      "E=-2.86981377  angles= {a1: -0.13088348290012078, a2: 0.008088333832009013, a3: 3.519022680895903}  samples= None\n",
-      "E=-2.86981636  angles= {a1: -0.13079375632116388, a2: 0.007733482556698751, a3: 3.5173894007616413}  samples= None\n",
-      "E=-2.86982553  angles= {a1: -0.13043485000533636, a2: 0.006314077455457701, a3: 3.510856280224594}  samples= None\n",
-      "E=-2.86984780  angles= {a1: -0.13007285288854895, a2: 0.004740925916254425, a3: 3.494264102407214}  samples= None\n",
-      "E=-2.86988975  angles= {a1: -0.12972368573501192, a2: 0.0029648395618087795, a3: 3.4613580852617147}  samples= None\n",
-      "E=-2.86996535  angles= {a1: -0.12942551842632163, a2: 0.0008468777208130323, a3: 3.394945842601524}  samples= None\n",
-      "E=-2.87008241  angles= {a1: -0.12941852758214206, a2: -0.001404284566265573, a3: 3.2550600292581557}  samples= None\n",
-      "E=-2.87014838  angles= {a1: -0.13025095945928908, a2: -0.0011199665930895575, a3: 3.0890426632635295}  samples= None\n",
-      "E=-2.87015769  angles= {a1: -0.1309236921681526, a2: 0.0010325708853818772, a3: 3.0701586033329873}  samples= None\n",
-      "E=-2.87016207  angles= {a1: -0.13164011434830297, a2: 0.003920028405061652, a3: 3.0733549062345684}  samples= None\n",
-      "Optimization terminated successfully.\n",
-      "         Current function value: -2.870162\n",
-      "         Iterations: 12\n",
-      "         Function evaluations: 14\n",
-      "         Gradient evaluations: 14\n"
-     ]
-    }
-   ],
-   "source": [
-    "# As an example, let's use the Helium atom in a minimal basis\n",
-    "mol = tq.chemistry.Molecule(geometry='He 0.0 0.0 0.0', basis_set='6-31g')\n",
-    "\n",
-    "# We want to get the 1- and 2-RDM for the (approximate) ground state of Helium\n",
-    "# For that, we (i) need to set up a unitary transformation U(angles)\n",
-    "#             (ii) determine a set of angles using VQE s.th. U(angles) |0> = |psi>, where H|psi> = E_0|psi>\n",
-    "#            (iii) compute the RDMs using compute_rdms\n",
-    "\n",
-    "# (i) Set up a circuit\n",
-    "# This can be done either using the make_uccsd-method (see Chemistry-tutorial) or by a hand-written circuit\n",
-    "# We use a hand-written circuit here\n",
-    "U = tq.gates.X(target=0)\n",
-    "U += tq.gates.X(target=1)\n",
-    "U += tq.gates.Ry(target=3, control=0, angle='a1')\n",
-    "U += tq.gates.X(target=0)\n",
-    "U += tq.gates.X(target=1, control=3)\n",
-    "U += tq.gates.Ry(target=2, control=1, angle='a2')\n",
-    "U += tq.gates.X(target=1)\n",
-    "U += tq.gates.Ry(target=2, control=1, angle='a3')\n",
-    "U += tq.gates.X(target=1)\n",
-    "U += tq.gates.X(target=2)\n",
-    "U += tq.gates.X(target=0, control=2)\n",
-    "U += tq.gates.X(target=2)\n",
-    "\n",
-    "# (ii) Run VQE\n",
-    "H = mol.make_hamiltonian()\n",
-    "O = tq.objective.objective.ExpectationValue(H=H, U=U)\n",
-    "result = tq.minimize(objective=O, method='bfgs')\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "The spin-free matrices:\n",
-      "1-RDM:\n",
-      "[[ 1.99134915 -0.00391427]\n",
-      " [-0.00391427  0.00865085]]\n",
-      "2-RDM:\n",
-      "[[[[ 1.99134029e+00 -4.19031562e-03]\n",
-      "   [-4.19031562e-03 -1.31183605e-01]]\n",
-      "\n",
-      "  [[-4.19031562e-03  8.85898841e-06]\n",
-      "   [ 8.77611396e-06  2.76045591e-04]]]\n",
-      "\n",
-      "\n",
-      " [[[-4.19031562e-03  8.77611396e-06]\n",
-      "   [ 8.85898841e-06  2.76045591e-04]]\n",
-      "\n",
-      "  [[-1.31183605e-01  2.76045591e-04]\n",
-      "   [ 2.76045591e-04  8.64198765e-03]]]]\n",
-      "\n",
-      "The spin-ful matrices:\n",
-      "1-RDM has not been computed. Return None for 1-RDM.\n",
-      "1-RDM is None now: None\n",
-      "2-RDM has been determined:\n",
-      "[[[[ 0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00]]\n",
-      "\n",
-      "  [[ 0.00000000e+00  9.95670147e-01  0.00000000e+00 -2.23878547e-03]\n",
-      "   [-9.95670147e-01  0.00000000e+00  1.95153015e-03  0.00000000e+00]\n",
-      "   [-0.00000000e+00 -1.95153015e-03  0.00000000e+00 -6.55918025e-02]\n",
-      "   [ 2.23878547e-03 -0.00000000e+00  6.55918025e-02  0.00000000e+00]]\n",
-      "\n",
-      "  [[ 0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00]\n",
-      "   [-0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00]\n",
-      "   [-0.00000000e+00 -0.00000000e+00  0.00000000e+00  0.00000000e+00]\n",
-      "   [-0.00000000e+00 -0.00000000e+00 -0.00000000e+00  0.00000000e+00]]\n",
-      "\n",
-      "  [[ 0.00000000e+00 -2.23878547e-03  0.00000000e+00  5.03395665e-06]\n",
-      "   [ 2.23878547e-03  0.00000000e+00 -4.38805698e-06  0.00000000e+00]\n",
-      "   [-0.00000000e+00  4.38805698e-06  0.00000000e+00  1.47484561e-04]\n",
-      "   [-5.03395665e-06 -0.00000000e+00 -1.47484561e-04  0.00000000e+00]]]\n",
-      "\n",
-      "\n",
-      " [[[ 0.00000000e+00 -9.95670147e-01 -0.00000000e+00  2.23878547e-03]\n",
-      "   [ 9.95670147e-01  0.00000000e+00 -1.95153015e-03 -0.00000000e+00]\n",
-      "   [ 0.00000000e+00  1.95153015e-03  0.00000000e+00  6.55918025e-02]\n",
-      "   [-2.23878547e-03  0.00000000e+00 -6.55918025e-02  0.00000000e+00]]\n",
-      "\n",
-      "  [[ 0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00]]\n",
-      "\n",
-      "  [[ 0.00000000e+00  1.95153015e-03  0.00000000e+00 -4.38805698e-06]\n",
-      "   [-1.95153015e-03  0.00000000e+00  3.82503176e-06  0.00000000e+00]\n",
-      "   [-0.00000000e+00 -3.82503176e-06  0.00000000e+00 -1.28561031e-04]\n",
-      "   [ 4.38805698e-06 -0.00000000e+00  1.28561031e-04  0.00000000e+00]]\n",
-      "\n",
-      "  [[ 0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00]\n",
-      "   [-0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00]\n",
-      "   [-0.00000000e+00 -0.00000000e+00  0.00000000e+00  0.00000000e+00]\n",
-      "   [-0.00000000e+00 -0.00000000e+00 -0.00000000e+00  0.00000000e+00]]]\n",
-      "\n",
-      "\n",
-      " [[[ 0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00 -0.00000000e+00 -0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 -0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00]]\n",
-      "\n",
-      "  [[ 0.00000000e+00 -1.95153015e-03 -0.00000000e+00  4.38805698e-06]\n",
-      "   [ 1.95153015e-03  0.00000000e+00 -3.82503176e-06 -0.00000000e+00]\n",
-      "   [ 0.00000000e+00  3.82503176e-06  0.00000000e+00  1.28561031e-04]\n",
-      "   [-4.38805698e-06  0.00000000e+00 -1.28561031e-04  0.00000000e+00]]\n",
-      "\n",
-      "  [[ 0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00]]\n",
-      "\n",
-      "  [[ 0.00000000e+00 -6.55918025e-02  0.00000000e+00  1.47484561e-04]\n",
-      "   [ 6.55918025e-02  0.00000000e+00 -1.28561031e-04  0.00000000e+00]\n",
-      "   [-0.00000000e+00  1.28561031e-04  0.00000000e+00  4.32099382e-03]\n",
-      "   [-1.47484561e-04 -0.00000000e+00 -4.32099382e-03  0.00000000e+00]]]\n",
-      "\n",
-      "\n",
-      " [[[ 0.00000000e+00  2.23878547e-03 -0.00000000e+00 -5.03395665e-06]\n",
-      "   [-2.23878547e-03  0.00000000e+00  4.38805698e-06 -0.00000000e+00]\n",
-      "   [ 0.00000000e+00 -4.38805698e-06  0.00000000e+00 -1.47484561e-04]\n",
-      "   [ 5.03395665e-06  0.00000000e+00  1.47484561e-04  0.00000000e+00]]\n",
-      "\n",
-      "  [[ 0.00000000e+00 -0.00000000e+00 -0.00000000e+00 -0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00 -0.00000000e+00 -0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 -0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00]]\n",
-      "\n",
-      "  [[ 0.00000000e+00  6.55918025e-02 -0.00000000e+00 -1.47484561e-04]\n",
-      "   [-6.55918025e-02  0.00000000e+00  1.28561031e-04 -0.00000000e+00]\n",
-      "   [ 0.00000000e+00 -1.28561031e-04  0.00000000e+00 -4.32099382e-03]\n",
-      "   [ 1.47484561e-04  0.00000000e+00  4.32099382e-03  0.00000000e+00]]\n",
-      "\n",
-      "  [[ 0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00]]]]\n",
-      "1-RDM is also here now:\n",
-      "[[ 0.99567518  0.         -0.00180405  0.        ]\n",
-      " [ 0.          0.99567397  0.         -0.00211022]\n",
-      " [-0.00180405  0.          0.00432482  0.        ]\n",
-      " [ 0.         -0.00211022  0.          0.00432603]]\n"
-     ]
-    }
-   ],
-   "source": [
-    "# (iii) Using the optimal parameters out of VQE, we know have a circuit U_opt |0> ~ U|0> = |psi> \n",
-    "mol.compute_rdms(U=U, variables=result.angles, spin_free=True, get_rdm1=True, get_rdm2=True)\n",
-    "rdm1_spinfree, rdm2_spinfree = mol.rdm1, mol.rdm2\n",
-    "print('\\nThe spin-free matrices:')\n",
-    "print('1-RDM:\\n' + str(rdm1_spinfree))\n",
-    "print('2-RDM:\\n' + str(rdm2_spinfree))\n",
-    "\n",
-    "\n",
-    "# Let's also get the spin-orbital rdm2\n",
-    "# We can select to only determine one of either matrix, but if both are needed at some point, it is \n",
-    "# more efficient to compute both within one call of compute_rdms\n",
-    "print('\\nThe spin-ful matrices:')\n",
-    "mol.compute_rdms(U=U, variables=result.angles, spin_free=False, get_rdm1=False, get_rdm2=True)\n",
-    "rdm1_spin, rdm2_spin = mol.rdm1, mol.rdm2\n",
-    "print('1-RDM is None now: ' + str(rdm1_spin))\n",
-    "print('2-RDM has been determined:\\n' + str(rdm2_spin))\n",
-    "\n",
-    "# We can compute the 1-rdm still at a later point\n",
-    "mol.compute_rdms(U=U, variables=result.angles, spin_free=False, get_rdm1=True, get_rdm2=False)\n",
-    "rdm1_spin = mol.rdm1\n",
-    "print('1-RDM is also here now:\\n' + str(rdm1_spin))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Consistency of spin summation:\n",
-      "1-RDM: True\n",
-      "2-RDM: True\n"
-     ]
-    }
-   ],
-   "source": [
-    "# To check consistency with the spin-free rdms, we can do spin-summation afterwards \n",
-    "# (again, if only the spin-free version is of interest, it is cheaper to get it right from compute_rdms) \n",
-    "rdm1_spinsum, rdm2_spinsum = mol.rdm_spinsum(sum_rdm1=True, sum_rdm2=True)\n",
-    "print('\\nConsistency of spin summation:')\n",
-    "print('1-RDM: ' + str(numpy.allclose(rdm1_spinsum, rdm1_spinfree, atol=1e-10)))\n",
-    "print('2-RDM: ' + str(numpy.allclose(rdm2_spinsum, rdm2_spinfree, atol=1e-10)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Psi4-RDMs:\n",
-      "1-RDM:\n",
-      "[[ 1.9913455  -0.00385072]\n",
-      " [-0.00385072  0.0086545 ]]\n",
-      "2-RDM:\n",
-      "[[[[ 1.99133696e+00 -4.12235350e-03]\n",
-      "   [-4.12235350e-03 -1.31213704e-01]]\n",
-      "\n",
-      "  [[-4.12235350e-03  8.53386376e-06]\n",
-      "   [ 8.53386376e-06  2.71631211e-04]]]\n",
-      "\n",
-      "\n",
-      " [[[-4.12235350e-03  8.53386376e-06]\n",
-      "   [ 8.53386376e-06  2.71631211e-04]]\n",
-      "\n",
-      "  [[-1.31213704e-01  2.71631211e-04]\n",
-      "   [ 2.71631211e-04  8.64596819e-03]]]]\n",
-      "\n",
-      "FCI energy: -2.870162138900821\n",
-      "VQE-Energy: -2.870162072561385\n"
-     ]
-    }
-   ],
-   "source": [
-    "# We can also compute the RDMs using the psi4-interface.\n",
-    "# Then, psi4 is called to perform a CI-calculation, while collecting the 1- and 2-RDM\n",
-    "# Let's use full CI here, but other CI flavors work as well\n",
-    "mol.compute_rdms(psi4_method='fci')\n",
-    "rdm1_psi4, rdm2_psi4 = mol.rdm1, mol.rdm2\n",
-    "print('\\nPsi4-RDMs:')\n",
-    "print('1-RDM:\\n' + str(rdm1_psi4))\n",
-    "print('2-RDM:\\n' + str(rdm2_psi4))\n",
-    "\n",
-    "# Comparing the results to the VQE-matrices, we observe a close resemblance,\n",
-    "# also suggested by the obtained energies\n",
-    "fci_energy = mol.logs['fci'].variables['FCI TOTAL ENERGY']\n",
-    "vqe_energy = result.energy\n",
-    "print('\\nFCI energy: ' + str(fci_energy))\n",
-    "print('VQE-Energy: ' + str(vqe_energy))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "pycharm": {
-     "name": "#%% md\n"
-    }
-   },
-   "source": [
-    "## Consistency checks\n",
-    "\n",
-    "At this point, we can make a few consistency checks.\n",
-    "\n",
-    "We can validate the trace condition for the 1- and 2-RDM:\n",
-    "\n",
-    "\\begin{align}\\mathrm{tr}(\\mathbf{\\Gamma}_m)&=N!/(N-m)!\\\\ \\mathrm{tr} (\\mathbf{\\Gamma}_1) &= \\sum_P \\Gamma^P_P = N \\\\\n",
-    " \\mathrm{tr} (\\mathbf{\\Gamma}_2) &= \\sum_{PQ} \\Gamma^{PQ}_{PQ} = N(N-1), \\end{align}\n",
-    "\n",
-    "$N$ describes the number of particles involved, i.e. in our case using a minimal basis this corresponds to $N_p$ above. For the Helium atom in Born-Oppenheimer approximation, $N_p=2$.\n",
-    "In the literature, one can also find the $m$-particle reduced density matrices normalized by a factor $1/m!$, which in that case would be inherited by the trace conditions.\n",
-    "\n",
-    "Also, the (in our case, as we use the wavefunction from VQE, ground-state) energy can be computed by\n",
-    "\n",
-    "\\begin{equation} E = \\langle H_{el} \\rangle = h_0 + \\sum_{PQ} h^Q_P \\Gamma^P_Q + \\frac{1}{2}\\sum_{PQRS} h^{RS}_{PQ} \\Gamma^{PQ}_{RS}, \\end{equation}\n",
-    "\n",
-    "where $h_0$ denotes the nuclear repulsion energy, which is 0 for Helium anyways.\n",
-    "\n",
-    "Note, that the expressions above also hold true for the spin-RDMs, given that the one- and two-body integrals are available in spin-orbital basis.\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {
-    "pycharm": {
-     "name": "#%%\n"
-    }
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "1-RDM: N_true = 2, N_spin = 2.0000000000000004, N_spinfree = 2.0000000000000004.\n",
-      "2-RDM: N*(N-1)_true = 2, spin = 2.0000000000000004, spinfree = 2.000000000000001.\n",
-      "h0 is zero: 0.0\n",
-      "\n",
-      "VQE-Energy is:      -2.870162072561385\n",
-      "RDM-energy matches: -2.870162072561384\n"
-     ]
-    }
-   ],
-   "source": [
-    "# Computation of consistency checks\n",
-    "#todo: normalization of rdm2 *= 1/2\n",
-    "# Trace\n",
-    "tr1_spin = numpy.einsum('pp', rdm1_spin, optimize='greedy')\n",
-    "tr1_spinfree = numpy.einsum('pp', rdm1_spinfree, optimize='greedy')\n",
-    "\n",
-    "tr2_spin = numpy.einsum('pqpq', rdm2_spin, optimize='greedy')\n",
-    "tr2_spinfree = numpy.einsum('pqpq', rdm2_spinfree, optimize='greedy')\n",
-    "\n",
-    "print(\"1-RDM: N_true = 2, N_spin = \" + str(tr1_spin) + \", N_spinfree = \" + str(tr1_spinfree)+\".\")\n",
-    "print(\"2-RDM: N*(N-1)_true = 2, spin = \" + str(tr2_spin) + \", spinfree = \" + str(tr2_spinfree)+\".\")\n",
-    "\n",
-    "# Energy\n",
-    "# Get molecular integrals\n",
-    "h0 = mol.molecule.nuclear_repulsion\n",
-    "print(\"h0 is zero: \" + str(h0))\n",
-    "h1 = mol.molecule.one_body_integrals\n",
-    "h2 = mol.molecule.two_body_integrals\n",
-    "# Reorder two-body-integrals according to physics convention\n",
-    "h2 = tq.chemistry.qc_base.NBodyTensor(elems=h2, ordering='openfermion')\n",
-    "h2.reorder(to='phys')\n",
-    "h2 = h2.elems\n",
-    "# Compute energy\n",
-    "rdm_energy = numpy.einsum('qp, pq', h1, rdm1_spinfree, optimize='greedy') + 1/2*numpy.einsum('rspq, pqrs', h2, rdm2_spinfree, optimize='greedy')\n",
-    "print('\\nVQE-Energy is:      ' + str(vqe_energy))\n",
-    "print('RDM-energy matches: ' + str(rdm_energy))\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "pycharm": {
-     "name": "#%% md\n"
-    }
-   },
-   "source": [
-    "## References \n",
-    "... for the definition of the reduced density matrices, spin-free formulation, symmetries:\n",
-    "1. Kutzelnigg, W., Shamasundar, K. R. & Mukherjee, D. Spinfree formulation of reduced density matrices, density cumulants and generalised normal ordering. Mol. Phys. 108, 433–451 (2010).\n",
-    "2. Helgaker, T., Jørgensen, P. & Olsen, J. Molecular Electronic-Structure Theory (John Wiley & Sons, Ltd, 2000). \n",
-    "\n",
-    "## Possible applications\n",
-    "So far, the content of this notebook is comparably trivial, and misses some interesting applications. An interesting possilibity on how to make use of the RDM's obtained by a quantum computer is given by a technique that has been named quantum subspace expansion, which e.g. can be used to approximate excited states [3], decode quantum errors [4] or improve the accuracy of results [5]. \n",
-    "References herefore:\n",
-    "3. McClean, J. R., Kimchi-Schwartz, M. E., Carter, J. & De Jong, W. A. Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states. Phys. Rev. A 95, 1–10 (2017).\n",
-    "4. McClean, J. R., Jiang, Z., Rubin, N. C., Babbush, R. & Neven, H. Decoding quantum errors with subspace expansions. Nat. Commun. 11, 1–9 (2020).\n",
-    "5. Takeshita, T. et al. Increasing the Representation Accuracy of Quantum Simulations of Chemistry without Extra Quantum Resources. Phys. Rev. X 10, 11004 (2020).\n",
-    "\n",
-    "Everybody is invited to enrich this notebook by implementing one of the techniques mentioned, or some other application of the 1- and 2-RDM!\n"
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "tequila-chemistry",
-   "language": "python",
-   "name": "tequila-chemistry"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.7.7"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}
diff --git a/tutorials/SingleQubitClassifier_tutorial.ipynb b/tutorials/SingleQubitClassifier_tutorial.ipynb
deleted file mode 100644
index 74dfe003..00000000
--- a/tutorials/SingleQubitClassifier_tutorial.ipynb
+++ /dev/null
@@ -1,682 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Single-qubit classifier with data re-uploading tutorial\n",
-    "\n",
-    "This tutorial shows:\n",
-    "- How to construct a fidelity cost function for an optimization problem\n",
-    "- How to construct a quantum classifier with one qubit\n",
-    "\n",
-    "Based on [Data re-uploading for a universal quantum classifier](https://quantum-journal.org/papers/q-2020-02-06-226/), A. Pérez-Salinas, A. Cervera-Lierta, E. Gil-Fuster, and J. I. Latorre, *Quantum **4**, 226 (2020)*."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import tequila as tq\n",
-    "import numpy as np\n",
-    "import matplotlib.pyplot as plt\n",
-    "from numpy import random\n",
-    "import time"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Introduction\n",
-    "\n",
-    "Single-qubit operations are just rotations on the Bloch sphere. A collection of single-qubit rotations can be reduced to a single one by combining their angles: you can always move from one point to another on the Bloch sphere with a single operation. \n",
-    "\n",
-    "Because of this property, a single-qubit classifier with simple parameterized rotations can not treat complex data. Even if it succeeds to classify one data point, it will probably misclassify the others since rotational angles have been only adapted to one particular point. To circumvent this limitation one can introduce the data points into these angles, so each rotation will be data point-dependent. This methodology is called data re-uploading and it can be shown that a single-qubit classifier can be universal using this technique.\n",
-    "\n",
-    "The strategy to train this single-qubit classifier is the following. Given a problem with 𝑛n classes, we choose 𝑛n vectors on the Bloch sphere. Then, we train the classifier by constructing a cost function that adds penalties if the final state of the classifier is far from the target state that corresponds to its class.\n",
-    "\n",
-    "The single-qubit classifier circuit is divided into layers. Each layer comprises single-qubit rotations that encode a data training point and parameters to be optimized. $$ L\\left(\\vec{x};\\vec{\\theta}_{i}\\right) = U\\left(\\vec{x}\\right)U\\left(\\vec{\\theta}_{i}\\right) $$\n",
-    "By considering more layers, the final state of the classifier will have a richer structure in terms of the data point $\\vec{x}$.\n",
-    "\n",
-    "$$ \\mathcal{U}_{class}\\left(\\vec{x};\\vec{\\theta}_{1},\\vec{\\theta}_{2},...,\\vec{\\theta}_{l}\\right) = L\\left(\\vec{x};\\vec{\\theta}_{1}\\right)L\\left(\\vec{x};\\vec{\\theta}_{2}\\right)\\cdots L\\left(\\vec{x};\\vec{\\theta}_{l}\\right)$$\n",
-    "\n",
-    "We will run a $\\mathcal{U}_{class}$ for each training point $\\vec{x}$, but the parameters $\\vec{\\theta}$ are the same. These are the variables to be optimized classically through the cost function."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Model"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Let's define the model that we would like to classify. Let's start with a simple model with two classes: a circle of radius $r =\\sqrt{2/\\pi}$ centered at (0,0). Data points will be distributed in a square of length 2 centered at (0,0). The particular choice of the circle radius implies that a random classification will have a $\\sim 50$% accuracy.\n",
-    "\n",
-    "`circle` function will have two parts:\n",
-    "- `random = True`: generate and label random points according to their position inside or outside the circle (used for training)\n",
-    "- `random = False`: computes the label of a given point `x_input` (used for testing)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "np.random.seed(42)\n",
-    "\n",
-    "def circle(samples = False, random = True, x_input = False, center=[0.0, 0.0], radius=np.sqrt(2 / np.pi)):   \n",
-    "    \"\"\"\n",
-    "    Args:\n",
-    "        samples (int): number of samples to generate\n",
-    "        random = True: generates and labels sample random points\n",
-    "        random = False: labels x_input point\n",
-    "        x_input (array[tuple]): given point to be labeled if random = False\n",
-    "        center (tuple): center of the circle\n",
-    "        radius (float): radius of the circle\n",
-    "\n",
-    "    Returns:\n",
-    "        if random = True:\n",
-    "            xvals (array[tuple]): data points coordinates \n",
-    "            yvals (array[int]): corresponding data labels\n",
-    "        if random = False:\n",
-    "            y (int): label of x_input point\n",
-    "    \"\"\"\n",
-    "    xvals, yvals = [], []\n",
-    "\n",
-    "    if random == True:\n",
-    "        for i in range(samples):\n",
-    "            x = 2 * (np.random.rand(2)) - 1\n",
-    "            y = 0\n",
-    "            if np.linalg.norm(x - center) < radius:\n",
-    "                y = 1\n",
-    "            xvals.append(x)\n",
-    "            yvals.append(y)        \n",
-    "        return np.array(xvals), np.array(yvals)\n",
-    "    \n",
-    "    if random == False:\n",
-    "        y = 0\n",
-    "        if np.linalg.norm(x_input - center) < radius:\n",
-    "            y = 1\n",
-    "        return y"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Target states\n",
-    "\n",
-    "Next step is to fix the classes states. The classifier will be trained to return these states depending on the data point. To reduce the uncertanty, target states should be as much distanced as possible. With a single qubit, that means to choose points in the Bloch sphere as much separated as possible.\n",
-    "For a two-class problem, an easy choice is $|0\\rangle$ and $|1\\rangle$ states."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# |0> : points inside the circle\n",
-    "# |1> : points outside the circle\n",
-    "def targ_wfn(y, nclass):\n",
-    "    \"\"\"\n",
-    "    Arg:\n",
-    "        - y (int): class label\n",
-    "        - nclass: number of classes\n",
-    "    Returns:\n",
-    "        - wfn: wavefunction of the target state\n",
-    "    \"\"\"\n",
-    "    if nclass == 2:\n",
-    "        if y==0:\n",
-    "            wfn = tq.QubitWaveFunction.from_array(np.asarray([1,0]))\n",
-    "        if y==1:\n",
-    "            wfn = tq.QubitWaveFunction.from_array(np.asarray([0,1]))\n",
-    "    else:\n",
-    "        raise Exception(\"nclass = {} is not considered\".format(nclass))\n",
-    "    return wfn"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Single-qubit classifier circuit\n",
-    "\n",
-    "The single-qubit classifier has a layer structure, i.e. we have to decide how to design one layer and then how many layers we would like to consider. \n",
-    "We will consider the following structure: each layer is a collection of rotational gates which angles are a linear function of a data point with the free parameters to be optimized. In particular,\n",
-    "$$L\\left(\\vec{x};\\vec{\\theta}_{i}\\right) = R_{z}\\left(x^{2}+\\theta_{i}^{2}\\right) R_{y}\\left(x^{1}+\\theta_{i}^{1}\\right).$$\n",
-    "Then, each layer adds 2 parameters to be optimized. The data points $(x^1,x^2)$ are re-uploaded in each layer."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# single-qubit quantum classifier circuit\n",
-    "def qcircuit(xval, param):\n",
-    "    \"\"\"\n",
-    "    Arg:\n",
-    "        - xval (array[tuple]): data point\n",
-    "        - param (dict): parameters dictionary\n",
-    "    Returns:\n",
-    "        - qc: quantum circuit\n",
-    "    \"\"\"\n",
-    "    layers = int((len(param))/2) # 2 parameters/layer\n",
-    "    # initialize the circuit \n",
-    "    qc = tq.gates.Rz(0.0,0)\n",
-    "    for p in range(0,2*layers-1):\n",
-    "        # add layers to the circuit\n",
-    "        qc += tq.gates.Ry(xval[0] + param[p],0) + tq.gates.Rz(xval[1] + param[p+1],0) \n",
-    "    return qc"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Cost function\n",
-    "\n",
-    "The cost function for this quantum classifier model will be constructed from the fidelity of the classifier final state respect to the target state of its corresponding class. It will penalize that the output state is far from its label state.\n",
-    "\n",
-    "First, we define the fidelity between two states as an objective (see State Preparation Tutorial). Then, we construct the simplest cost function of this kind: average of squared infidelities for all training points $M$: $$ \\chi^2 = \\sum_{i=1}^{M}\\left(1-|\\langle\\psi_{target}|\\psi_{circuit}\\rangle|^2\\right)^2$$ "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# Fidelity objective\n",
-    "def fid(wfn_targ, qc):\n",
-    "    \"\"\"\n",
-    "    Arg:\n",
-    "        - wfn_targ: target wavefunction\n",
-    "        - qc : quantum circuit \n",
-    "    Returns:\n",
-    "        - O: objective\n",
-    "    \"\"\"  \n",
-    "    rho_targ =  tq.paulis.Projector(wfn=wfn_targ)\n",
-    "    O = tq.Objective.ExpectationValue(U=qc, H=rho_targ)\n",
-    "    # fidelity = tq.simulate(O)\n",
-    "    return O \n",
-    "\n",
-    "# cost function: sum of all infidelities for each data point respect the label state\n",
-    "def cost(x, y, param, nclass):\n",
-    "    \"\"\"\n",
-    "    Arg:\n",
-    "        - x (array[tuple]): training points\n",
-    "        - y (array[int]): labels of training points\n",
-    "        - param (dict): parameters dictionary\n",
-    "        - nclass (int): number of classes\n",
-    "    Returns:\n",
-    "        - loss/ len(x): loss objective\n",
-    "    \"\"\"  \n",
-    "    loss = 0.0\n",
-    "    # M = len(y): number of training points\n",
-    "    for i in range(len(y)):\n",
-    "        \n",
-    "        # state generated by the classifier\n",
-    "        qc = qcircuit(x[i], param)\n",
-    "        # fidelity objective respect to the label state\n",
-    "        f = fid(targ_wfn(y[i],nclass), qc)\n",
-    "        \n",
-    "        loss = loss + (1 - f)**2\n",
-    "        \n",
-    "    return loss / len(x)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Training\n",
-    "\n",
-    "We have now all the ingredients to train a single-qubit classifier with data re-uploading.  \n",
-    "If a gradient based optimization is chosen for this type of optimization problems, numerical gradients are adviced since analytical ones become quite expensive."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Optimizer: <class 'tequila.optimizers.optimizer_gd.OptimizerGD'> \n",
-      "backend         : qulacs\n",
-      "samples         : None\n",
-      "save_history    : True\n",
-      "noise           : None\n",
-      "\n",
-      "Objective       : 400 expectationvalues\n",
-      "Gradient        : 2400 expectationvalues\n",
-      "gradient instr  : {'method': '2-point', 'stepsize': 0.0001}\n",
-      "active variables : 6\n",
-      "Iteration: 1 , Energy: +0.23346574, angles: {th_3: 4.946478475226956, th_1: -1.984857687022879, th_5: 6.094228093092652, th_0: -1.7808298315353657, th_2: 2.0305330159430013, th_4: 8.89720462977007}\n",
-      "Iteration: 2 , Energy: +0.24568509, angles: {th_3: 5.177458750101836, th_1: -1.5046410048962369, th_5: 6.094228093092652, th_0: -1.9668793788050198, th_2: 0.25366461000251084, th_4: 9.429982384992186}\n",
-      "Iteration: 3 , Energy: +0.34273167, angles: {th_3: 2.610709683911139, th_1: -4.11965271230925, th_5: 6.094228093092652, th_0: -3.990162105280362, th_2: -0.837018339540754, th_4: 12.077363592549728}\n",
-      "Iteration: 4 , Energy: +0.41100568, angles: {th_3: 4.081797701231221, th_1: -4.1998105692556384, th_5: 6.094228092741568, th_0: -2.9373123644616017, th_2: -1.5325493513295756, th_4: 13.399512918875173}\n",
-      "Iteration: 5 , Energy: +0.31916175, angles: {th_3: 2.391303024200917, th_1: -6.472994601839014, th_5: 6.094228092566027, th_0: -1.469593533147448, th_2: -2.518924236681155, th_4: 16.237487146769446}\n",
-      "Iteration: 6 , Energy: +0.18903087, angles: {th_3: 0.6054755106135814, th_1: -4.350076845031609, th_5: 6.094228092566027, th_0: -1.1529563858416918, th_2: -0.7674481295413216, th_4: 18.32308007272708}\n",
-      "Iteration: 7 , Energy: +0.24706587, angles: {th_3: 1.4170489917460554, th_1: -4.558366452437925, th_5: 6.094228092653798, th_0: -2.1858732633280455, th_2: -0.9235025623782028, th_4: 18.780993200577786}\n",
-      "Iteration: 8 , Energy: +0.18957480, angles: {th_3: 1.9605822789058145, th_1: -5.527640916329952, th_5: 6.094228092917111, th_0: -0.6687996002617134, th_2: -0.6889772782590158, th_4: 18.081389154242707}\n",
-      "Iteration: 9 , Energy: +0.28645830, angles: {th_3: 1.5788772007046856, th_1: -5.638779777627052, th_5: 6.094228092917111, th_0: -1.4139949979544377, th_2: -1.1512637374432393, th_4: 18.302153905481166}\n",
-      "Iteration: 10 , Energy: +0.27527401, angles: {th_3: 1.9429922146972913, th_1: -3.3228180477941693, th_5: 6.094228092917111, th_0: -0.24408389064543945, th_2: -0.4065263357136326, th_4: 18.028189277072833}\n",
-      "Iteration: 11 , Energy: +0.35620661, angles: {th_3: 1.0124985821386665, th_1: -2.7198954044125903, th_5: 6.094228092917111, th_0: -1.1758665832184727, th_2: 0.5522929556759827, th_4: 18.22237564643069}\n",
-      "Iteration: 12 , Energy: +0.44487047, angles: {th_3: 1.1112520918477444, th_1: -3.9067179067828812, th_5: 6.094228092566027, th_0: -0.18357759524889428, th_2: 0.03411429510428532, th_4: 16.46264976481032}\n",
-      "Iteration: 13 , Energy: +0.42685449, angles: {th_3: 1.2325104045554103, th_1: -4.072692525957542, th_5: 6.094228092566027, th_0: 0.10939902088916315, th_2: -0.055096351638694016, th_4: 16.59816347483484}\n",
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-      "Iteration: 86 , Energy: +0.11940878, angles: {th_3: 4.877862694635358, th_1: -7.775972933772485, th_5: 6.094228091600548, th_0: 1.089702868111344, th_2: 1.3006803513536878, th_4: 13.301262280304371}\n",
-      "Iteration: 87 , Energy: +0.11931291, angles: {th_3: 4.751449909069185, th_1: -7.872482881481733, th_5: 6.094228091468891, th_0: 0.9547160773764097, th_2: 1.1754461172227222, th_4: 13.257799635361732}\n",
-      "Iteration: 88 , Energy: +0.11932194, angles: {th_3: 4.876228931321227, th_1: -7.776499588387041, th_5: 6.094228091468891, th_0: 1.089508152012567, th_2: 1.3003314453781933, th_4: 13.29919918789301}\n",
-      "Iteration: 89 , Energy: +0.11922583, angles: {th_3: 4.753156137983769, th_1: -7.872513225910726, th_5: 6.0942280914250055, th_0: 0.9554848835207264, th_2: 1.1757050503207387, th_4: 13.259965039065278}\n",
-      "Iteration: 90 , Energy: +0.11923677, angles: {th_3: 4.8746187693106355, th_1: -7.777005191986608, th_5: 6.094228091468891, th_0: 1.0892790084573687, th_2: 1.2999112763831913, th_4: 13.2972356492063}\n",
-      "Iteration: 91 , Energy: +0.11914147, angles: {th_3: 4.754794575817218, th_1: -7.87248016907876, th_5: 6.0942280914250055, th_0: 0.956275074286904, th_2: 1.175970091098098, th_4: 13.262057668253918}\n",
-      "Iteration: 92 , Energy: +0.11915424, angles: {th_3: 4.87303704355402, th_1: -7.777489105946069, th_5: 6.0942280914250055, th_0: 1.0890300050203252, th_2: 1.2994489272748093, th_4: 13.295346908453466}\n",
-      "Iteration: 93 , Energy: +0.11906051, angles: {th_3: 4.756375150067583, th_1: -7.872406323966117, th_5: 6.094228091293349, th_0: 0.9570690282549251, th_2: 1.1762338622509514, th_4: 13.264093843856315}\n",
-      "Iteration: 94 , Energy: +0.11907502, angles: {th_3: 4.871485636822082, th_1: -7.777951401614059, th_5: 6.094228091337235, th_0: 1.0887723263826419, th_2: 1.2989661028445254, th_4: 13.293511878161997}\n",
-      "Iteration: 95 , Energy: +0.11898339, angles: {th_3: 4.757907284619115, th_1: -7.872309011877777, th_5: 6.094228091205578, th_0: 0.9578541074513943, th_2: 1.1764908260543958, th_4: 13.266088617903543}\n",
-      "Iteration: 96 , Energy: +0.11899951, angles: {th_3: 4.869964041233722, th_1: -7.778392617357314, th_5: 6.094228091293349, th_0: 1.0885145485795444, th_2: 1.2984788025406138, th_4: 13.291712100323416}\n",
-      "Iteration: 97 , Energy: +0.11891037, angles: {th_3: 4.759400082059777, th_1: -7.872201464734745, th_5: 6.094228091337235, th_0: 0.9586214868729757, th_2: 1.1767367967149163, th_4: 13.268056305973213}\n",
-      "Iteration: 98 , Energy: +0.11892795, angles: {th_3: 4.868469819065048, th_1: -7.7788136009269655, th_5: 6.094228091337235, th_0: 1.088263268133242, th_2: 1.2979987019104118, th_4: 13.289930888644408}\n",
-      "Iteration: 99 , Energy: +0.11884157, angles: {th_3: 4.760862504007687, th_1: -7.87209380933516, th_5: 6.094228091293349, th_0: 0.9593652123465327, th_2: 1.1769685695678753, th_4: 13.270010920694222}\n"
-     ]
-    }
-   ],
-   "source": [
-    "layers = 3\n",
-    "nclass = 2\n",
-    "training_set = 400\n",
-    "\n",
-    "# generate the training set and its corresponding labels\n",
-    "xdata, ydata = circle(training_set)\n",
-    "\n",
-    "# generate the variational parameters\n",
-    "param = [tq.Variable(name='th_{}'.format(i)) for i in range(0,2*layers)]\n",
-    "\n",
-    "# initialize the variational parameters\n",
-    "# note that due to the random initialization the result can be different from time to time\n",
-    "# With gradient based optimization you might get stuck\n",
-    "inval = {key : random.uniform(0, 2*np.pi) for key in param}\n",
-    "\n",
-    "grad = '2-point' # numerical gradient (= None: analytical gradient)\n",
-    "mthd = 'rmsprop' # scipy minimization method\n",
-    "mthd_opt = {'eps':1.e-4} # method options (that's the stepsize for the gradients)\n",
-    "\n",
-    "obj = cost(xdata, ydata, param, nclass) # objective to be optimized: cost function\n",
-    "\n",
-    "t0 = time.time()\n",
-    "# depending on the optimizer this will take a while\n",
-    "test = tq.minimize(objective=obj, initial_values=inval, method = mthd,\n",
-    "                                   gradient = grad, method_options = mthd_opt, silent=False)\n",
-    "t1 = time.time()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Extract the results:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "loss =  0.11884156841701687\n",
-      "method:  rmsprop\n",
-      "method parameters:  {'eps': 0.0001}\n",
-      "execution time =  35.648783659935  min\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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Xl+8/vYVrp5czb0wJF4yMn5ZSKBSKUNIq0Hf60cdPbzy55Hx8EgbmZaR8HVoOPlKgv3xcKRUFmRFtlL0Bw7KCLAs+CUYBHS4Pq7YeZ1ZlAc0dbhrbnQwrykpocIlCoTi3Sa9AH1DbOHXIK0ty/QG+2e6mxe5mSEHsTtpEKMnN4PtXjmZkcfexf8OLsxke4XXw2xzsu28hMvAzdDZ/WUwG/v7+IR5+ZS8f3bcQs1EFeoVCoY+0ytHrbZhqtrv5zWt72XOilQde2sU1f1yb0nWU5du47dJREW8erQ43b+2tp77VGfFah8fH/vq24CQp7btYjH73StD3xKJQKBQaaRXoDQbB5PI8irJj59yPN9v5zWsfsa+ujdwMc8rllU0dLmqb7PgieMcfPWXni3/+kI2HT3U7dqrdxSUPvcGC37zDwYZ2ICTQmwyYArt85WCpUCgSIa0CPcDzt10Yt8v1VJsL8OfCc21mnB4fTk/qZrH+84MjzHlgTUQpZF4MB8tT7S4aAmvrcHVKPktzrWRnmBKqQSgUCoVG2gV6PTS2+4NpYbYlKIFsTaGWvsXhxmI0YI1QcM2LMXwkdPB3u9P/86jSHD744eXMG1OCyeB/P9U0pVAoEiHtAv2X//Ihv3ltb8xzTrV37ug1iWMq0zctdg+5NlNEZUyWxYjRIGjqiB3oQ3f0GrOGDeC+T048I7bKCoUifUm7iPFRXRsD4tgON7a7EAIGZFqYOiSfexdNiHtNIkTyotcQQgSbprpij7Cj31bTzK9e3cOPrh7HyJIcRpbkdLsuWaL53ysUivQi7QK9xWTAGSeH/a3LRvHlCyoxGgSVRVlUFmWldA0tdje5MZqhHv3sNEpzu3vKaymZL8weyvShAwA42eLgjT31fPvy0TTb3Rxp7GBkSTY2S89slWP536tgr1CkF+kX6I2GuPJKo0EwINAN6/L42FfXRmmuNWUDPb44uzJmwXT2iMKIr88bW8KhB64Oey1UR//+gUa++veNvHD7hUwsy+vRGmP536tAr1CkF2mXo7eY4lv5Lnt7P0+tPwJAQ5uTq373ji5/HL1cPr6UhZOi2zBsPHya12J83uajTcG5t6HySq1JyhNBtpkosfzvFQpFepF2gX5KeT6jS2PnsZdvqOHNPfVAp01BKo3NttU0U9fqiHr8b2sP8bNVO7u9/tbeer67fDOLH32Pv607BIQ3TGk++54UyCtj+d/3V1ZW1zLngTUMu3MVcx5Yw8rq2t5ekkLRJ0i71M29iyfGPUdzrgS/CsYgOh0ne8qKTTV8Z/kWINxqOJRoxdg9J1p4dlMt2VZTUHWTaTUyvCgLm8UYlFemwqp46fwxYTl66PS/74+omoNCEZ2029HHw+uTnO5wBR0rhRDk2sy0pmBHv7K6lrtWdE6P0oJN152lFui7ds463P4AXpBlCapuPjZ5MGu+fwlF2dbO1E0KdPSLq8pYMnd48PeyfBv3XzOp3wbFWDUHheJcJ+0C/Y+f286X//Jh1ONNHS6kJLijB8jJMKVk+MhDq/cEg7VGpGCTZzPjk9DWRStvd3sxG0XYjj6UYUVZ/OYzUxkzMDUSS03Zc++iCRH97/sTquagUERHV6AXQiwQQuwRQuwTQtwZ4fgiIcRWIcRmIcQGIcSFIccOCSG2acdSufhINLS7OHyqI+rxZru/a7UgRGFz99Xj+fz5Q3v82XqDTbA7tkvTlMPtJcNsJMtqDO7ol68/ynWPr8PnkxRmW1lcVUZpbmqslbUdcFXFgJS8X2+SjjUHhSJVxM3RCyGMwKPAFUANsF4I8byUMrSa+DrwvJRSCiEmA8uBsSHH50kpG1K47qhY48grhxdns+dnCwgd8HTlhIEp+ezB+TZqIwT7rsHmsnElrPrmhZR00dJbjAZKczP43pVjgjbFh0+1s/HwaQwG/xCSLTVNjCjOpjin51JQrRN3z4nWHss1e5t0qzkoFKlEz45+FrBPSnlASukCngQWhZ4gpWyTnbPxsoBeM2OxmOLr6IUQGAyd9gT769tYf6i7m2SiLJ0/hgxz+B9ppGBTmG1lwuA8rKbwpqe7rhrHa9+9mPOHFzKzsgDwq240++UTLQ6uX/Y+7+6r7/FaAZyBNNOv41hG9AcWV5Vx/zWTgv5C/b3moFCkEj2Bvgw4GvJ7TeC1MIQQnxRC7AZWATeFHJLAK0KIjUKIJT1ZrB4sJkNMVcobe+r4/n+20O7szIH/4Y39fOvf1T3+7MVVZTxwzWTK8m0IogebFoebf7x/mH11bRHfZ19dK2/v9Qdzl8cXdK1MtU1x+QD/k4bRkB5DTM4fXogz8OfV32sOCkUq0SOvjBQFukUaKeUKYIUQYi5wL3B54NAcKeUxIUQJ8KoQYreU8u1uH+K/CSwBqKio0Lv+bowblBs0LevKyupa7n5uO60OD2v3N/CD+WNZXFVGri01xViAqUPy+eV1U5hVWRD21BDKMxtr+Ol//ZmvUAnmr17di8vjw+H2sqK6li0/vhKXtzPQd+roUxPoLxhZxNWTB7HreEtK3q+3abL7/3//9XVTe3klCkXfQk+grwGGhPxeDhyLdrKU8m0hxAghRJGUskFKeSzwep0QYgX+VFC3QC+lXAYsA5gxY0bSkeyGWRXcMKv7jaKrzvpYkyOos87NMNPm9OD1yR7vbp/eWMMf39rPvvsWRjy+srqWB1/eHfw9VO/94cFGfBJmDB0QVN0MyrMxKZA/1+SVqfSjzzQb6XD2zIu/r5ijacXtvCiGcgrFuYqe1M16YJQQYpgQwgJcDzwfeoIQYqQIePIKIaYBFqBRCJElhMgJvJ4FXAlsT+UX0EssnbXWHduWgl19k91Fns0cdXh3LAmm3e0LqG5MuL0Sl8fHNy8bxZ+/NBMg5aMEf/Hybv6zsSailFMv2g20tsmOJHrvwNlAa0L76t/PuLhLoehXxA30UkoPcBuwGtgFLJdS7hBC3CqEuDVw2qeA7UKIzfgVOp8JFGdLgXeFEFuAD4FVUsqXz8QX0Xhi3SFm/OzVMG93iC191PzdU2GD0NThJj/GjjLWOpxuLzazgcyAM2XXAJxlMbLsxulcOT41KqEOl//P6PEbZyT9Hn2pUUkL9O2u1E0LUyjSAV0WCFLKF4EXu7z2WMjPDwIPRrjuADClh2tMCJfHR0ObC5fXvzvWiCV9vGhUEX/98kwK48ya1UOz3R0cFxiJWOuwazp6i///lnaXl4df2UaH08uvPjMVk9GQMiko+OWVJTnWqG6aeuhLjUplSjOvUEQk7TpjtYJlV4nl0vljsJnD5Yya9HFQno1LxpSQaem59U+8HX2sdZTmZDAwL4OLxxTz76+cT2GWhQP17RwJaQBbs/sk++pae7xO8O+869ucPL/lWLcnIL30pUalC0YW8Z3LRwN+qwuFQuEn7QJ9tAHams46kvSx3elh9Y4TEXfaiXLPogl854rRUY/HWsfyW2dz18JxlOZmMHtEIRlmY5i8EmDJExt5dlNq8t8Otxcp4Zv/rg7O0U2UWDeus42UMtjHkMph7wpFfyft3CstUXb04A+yz2851k0V0tjm4qt/38jDn57CtdPLe/T5euwEFleVkWkxcrLFwY2zK7sdP93u4p19DcyqLMDl9ZEdMiPWbIzvt6+XuaOLOdzYwe4TrdiTLMhqf47ffmozEN2x82zwnac2s3LzMS4cWaR29ApFCGm3o68symTx1MFh+XkNp8fLmt113XbuubZAMbaHA8K9Pslzm2s52NAe99yXt59g2TsHgr/7fJLrHl/HyupaapvsfPPf1WyrbQ7rjAUwGUXKGqY+d97Q4M67vQcSy9Cg/u4d83qtUanJ7mZSWR7/uOW84NB3hUKRhoF++tACfnN9VUTjr9aAfDInI/xBJtuaGtVNq8PNt57czBu76+Kem51hCq4HwOHx8uHBU5xscYSpbiaX5zF+cG7wPIvRgMeXmh290+MNpl06eqhUGZyXEXjP1Gn8E6XZ7iY/RiFcoThXSbvUTSyiBXqT0UC2NTzwJkNToGFHT7DJtppoc3iQUiKECGrrNR09+HfZv7g2XLRkMgrcHv+OvqeNSp945L2gD39PtPQAt1w0nHte2InT44v4NHU2aLa7OdjQzoUPruEvX5rJqDiTxhSKc4W029G/f6CRsXe/xIcHu5uUaUEtx9o9EOdkmHqcummyJxDoM0x4fDIY4DUtekYMHT3AHz43jSUXD09Jo5LD42ViWR4rvn4BMwImaskgpWTKkHye+dpssiy9E+TBn3rLspioOW2nzZkaSwuFIh1Iu0BvNPh3x9FUFyOKsyiIoJd/7PPT+eZlo3r02U0dfuVKni2+Hl/LIbc6/TcHu0sL9MagzLPN6eGq377D717/KHjd9KEFjCjOTkmjkt3lpTDbQlXFgB7ZBnS4vHzqj2vZcOh0sHu3N7h2+hAuG1cC0K37WKE4l0m71E0s1c3k8nxe/94l3V5PlVdLcwI7+munlbN46uBgfcBoEEwqy6Mo24rRIHjuG3MYlJ/B428dCBtz+OaeOjLMxpQ0KtndXowGwfL1R5lYFl4LSAQtv798w1E+PWNI2PSus8mdC8ey6chpnlh3GIeSVyoUQdIv0JuiB/pIpHKo9MWji3n26xfo6tC0WYxAZ5pjWFEW/709OJiLKUPyAcLcKwF+8fIeBufbdA85iYXT7cNqMvKDZ7aydP6YHgR6f5pkf307x5rsvRLovT6Jw+0N+tE7k2wAUyjSkbRL3QQ7YyNozZ/bXMt1j60Ly9+m0qslP9PCtIoBuoqRtU12fv7irqhdrqu2HueN3XV4fTJsQInZKHB7fT1uVJJScstFw5g7uhiTQfSoGBuq2Okt1c3ek61M+PFqPjhwiivHl1KU3fMJXApFupB2O/oBmWY+e14FFQWZ3Y4daujgw0Ongrs+SK1Xy7r9jdS1Olg0Nf6TQHOHm2VvH2BaxQBGluSwbn8j9724k99eX8WI4mweWfNRcFxg6I7eHJBXak8bP1u1k4Y2V8KNSkIIfrDAP+3RZjH2SEcfHuh7Zyetpc3GDszhpguH9coaFIq+StoF+sJsKz//5KSIx1odbmxmY3DXD/rnvOrhPxuP8sGBU7oCvSbx1PLvje1Otte24At0dGZajHS4vMyfUMrwoqzgdaHyysVVZSyuKuN4sx23R1JR2P3mFg2vT9Jsd5NtNZFlMfVoRz9kgI1rppXx7KbaXtvRa4E+V3nRKxTdSLvUDfi7TCO1wLc6PN009Kn0ammxu3WrV7QirJZGClXdAGRZTfik5PEbZ4Q5VpqNBtwhDVO7jrdwyUNvcs8LobPa43OixcG0e19lRXVN8KaSLCW5Gdxy4XCgcw7t2UYL9FaTgWn3vspf3jvYK+tQKPoiabejb3d6mPDj1dy1cCxfvXhE2LFWp7tboNdSHf/73HZaHB4G5WVwx4KxSalumjr0d2ZmB3f0/kDvcIcH+kyLkfpWZ7frfvqJCWFzHO94ZitOj4+a0x3dzo1F6I3lz1+aSaY1ef17Y5sTt9fHmu9dzKC83rEK1qZLFWVbOdXuosWudPQKhUbaBXpzjClMQwZkRiyULq4q46JRRTTZ3VQWZiU9TrDJ7mZ0abbudWaYDcGddGdnrH/9WRYTu0+0UnXPK9x/zSQWTBwEwPDi8PfXhpzXnk6sphB6Y6kMSQ0lw8s7TvCjFdt5/67LAmqis09VRT63zRtJns2MySCUvFKhCCENA70/SEeSV9511bio1xVmWynsoVKjqcOtq1lKY9tP5gdvTCW5VmYNKwjeiO5cOJaPTxnMl/+6ntAs1Np9DdS3OYN1AK2I2ur0+Iee6EwdhQb613ae5HSHi0/PGBLnqshoTwd/XXuIBRMHMjUgDT2bzKgsCHb3ZpiNvZZCUij6ImkX6IUQWEwGnAla+R5p7GD1jhMsqhpMSU53QzQ9PH/bHEwJPA2EFoUXTS0LK+KW5GZwosUBEOZeuXzDUTYdaQoJ9B5Kc62cbHFSc7qDPFuers/WniBsZiPL1x9lz8nWpAO99lTy2Fv7Kcq29Eqgr291YjYK8jMtZJgNakevUISQlsVYq9EQcUd/7R/XhtkJhHKgoY37XtzF0VOJ5bpDGZxvoySCa2Y0Hn9rP8ve3h/x2OajTZGKG/IAACAASURBVPzmNf9aQ+WVJqMBT+AmJqWk3eVh7qhifnv9VAYnkB+vKMhk6fwxDCmwYbMY6eiBN0x7iGKnt1Q33//PFr745w8B+PiUwUwtP/s3G4Wir6Ir0AshFggh9ggh9gkh7oxwfJEQYqsQYrMQYoMQ4kK9154JvnzhMGYP7z4HdcexlqjGZZq/TLLqk6YOF79f81FCY/7e2lvPKztOAvDgy7u59o9rg8c2HDrFmoDdcVcdvSvgRy+l3+TslouGs2hqGQMS6EitKMzkG/NGMijPRpbFSEcPOkntLi+5geJyb8orNWnljz8+getmJvd0olCkI3EDvRDCCDwKLATGAzcIIcZ3Oe11YIqUcipwE/CnBK5NOd+9YnS3Idpurw+72xt1IEWnY2RyAe9Yk4OHX9nLvro23ddkW01BeeWJZgcnWx0h6/EHzgtGFIZ565uNIuhHbzAIFkwcxJiBOVQfOc322mbdn93icHP0VAden8RmMdHRg4apa6eXc/81k7GaDL3WMJWItFWhONfQs6OfBeyTUh6QUrqAJ4FFoSdIKduklFrJMAuCCsC4154J2p2ebja1bVG86DU0tYg92R29Xb9zpUbo8BGH20tGiNVBVkDueO/iiQwLUcWYjQY8gR19m9PDm3vqaGhzsvTprTyyJnJaKhLPVddy0S/e4FS7iyyLEZfXl/SIwsnl+Vw9eVCvFkGbQgL9Dcve58b/+6BX1qFQ9EX0FGPLgKMhv9cA53U9SQjxSeB+oAS4OpFrA9cvAZYAVFRU6FhWdBY9+h6jS7P5w+emB1+LNnREo6c7+uYEho5o5GaYg52xdrc3TPoZTCV12Wl/7ZIR3Hj+UAAONbTzpb+s5/Ebp1MWpcM3GqFyzi/NqeSG8yoSKiSHsr22GaNB8Mb3Lwn+OZ5NpJRhiiMhkr9hKxTpiJ4dfaR//d3aTqWUK6SUY4HFwL2JXBu4fpmUcoaUckZxcbGOZUXHEqEYazDAvDHFDInggQNQkpPBursu5Zppyc071TozE0kf5NnMmI0GpPQ7L4Z26GoDPD7++3fDCsRF2dag7l3T0GdZTJQPsFGTgJbeHiKvzMkwU5RtRYjkAv09L+zkx8/voCDL0ivTpXwSfvzx8Vw2rhTwfyelulEoOtET6GuA0MpWOXAs2slSyreBEUKIokSvTRVmk6FbUbB8QCZ/+fIszo9QpAW/H/ygPFvSgSqR6VIa37liNBvvvgIhBFUVA5g1rHPK0/TKAUEbBpOxMwBXHznNY2/tx+eTQbVLltVI2QAbTR3uYPCPh8PtxWQQmI0GPjrZyi9f2ROxE1cPdpeXLIuRv7x3kGc21iT1Hj3BaBB8YXYl04cOAPxPKWrwiELRiZ5Avx4YJYQYJoSwANcDz4eeIIQYKQLbQSHENMACNOq59kxgNRqSyjc/+sY+3twTf7B3JG6+cBgb/ufybr45erljwVi+H+KvYzUZg344oTr6tfsbeeCl3bi8PtoCaZ1sq4nyAf4nFb3pG4e7c7brocYOHlmzjxPNjjhXRabD5SHTYuLpjTW8tP14Uu/RE9qdHnYdbwmma6wmY7AhTKFQ6Aj0UkoPcBuwGtgFLJdS7hBC3CqEuDVw2qeA7UKIzfhVNp+RfiJeeya+SCgWU/fUzQtbj3H+z1+P6Qnz+Fv7eXNPfdz3X1ldy5wH1jDszlXMeWANK6trMRsNCac/qo+c5mv/2BhxTW1OD/e9uCv4fTS0zl+PTwa171lWExeMKGT5V2dTPkCfln7BxIH8MNApHGtGrR46XF5sFmNAdXP2d9JbappY+Nt3qD56GvAPgLlmWvlZX4dC0VfR1RkrpXwReLHLa4+F/Pwg8KDea880n55R3i3gnGp3caLFETM1k6nDrjfaRKp1BxoYPyiPL15QqXudpztcvLT9BEvmDufmv25g7ugifnS1X33q8fqCN6uwhimDIXj8kjEl/PXLMynMtmA1GRMatjFrWEEwVdTTQnRHIHVjNfWO6qalS30kGUM6hSKdSTsLBCCiH3w81Q2gy6432kSqldXH2F/XnlCg1zT9bU4PJ1ocYU8hmuoGwlM3ZlPnBK2BeRkMzOvU2L+8/Th5NguzR0SuQ4RypLEDn5RUFmWRZe1Zs9gjN1RRkmvlgZd2c7rdldR79ISmjvBA7/NJnB5frxmsKRR9jbS0QGjucHO8OTxX3eJwYzEZwsbydcVmMcaV5UWbPOX0+BIqxEKIJ73D45dXhgQmi8mAxWjg65eMCEsHmQMSSI9Xsq2mmVd2nAgee/DlPfzjg8O6Pvsn/93B7f+uBjp39O1Jpm7mji5m7MDcXkvddFU8/W7NR4z735cjziRQKM5F0nJHf88LO3n/QCPv3Xlp8LVWh4cca+yvq2dHH20ilVGIhJqloPPposXhxuXxhTVMgT8f39zFsuETUwdz6bgSCrOsPPrGPl7efoIrJwxkZXUtx5rsHGxoZ/ORNXHHCtpdnXLOwXk2dt4zv9vn68Hp8fLmnnomDM7lkRumJa3F7wnNdjdGgwjeOLWbuUvt6hUKIE139JYIO8uJg/O4evKgmNf99cuz+OtNM2OeE2kildkoMBoSk1aCP3UzMDcj6F3TtX7Q7vLyzw+OhL2WaTFRkpOB0SBod3rIspqCdQPtO2t1g5XVtVE/2+HxYg143xsMgkyLCUMSQfp0u5uv/n0jb+9twGIyJPUePeWqSYN46NrJwScfzdNfKW8UCj9pGeitJgOuLg0znz2vgnsWTYx5XZbVFDO1A/5C3/3XTAqaeJmNAgG4vJL/e/dgUIWjhzybmfd/eBmfmlbGNdPKGDsoJ3hsZXVt8IYS+p776lr51St7qGt10Ob0kmU1Ra0bPLR6T9TPtrvCO3F//uKusDSQXrTidabFyKqtx7lvVWIjDVPBxLK8MJWN9r1U05RC4SctA73FZMCVhI7+ha3H+NWre+Oet7iqjBtmVWA1Gfjq3OHBHTno2013JdNi4lfXTWXemBIgurJnZXUtBxs6+N2afdS1OOlweci2GqPWDaK9Dv6aQuiTyb8+OML7B07pXrOGlurKtBjZdOQ0//7waJwrUsvK6lpm3vdamNRV29Gr4SMKhZ/0DPQRLBCu/t07fPepzTGvW7e/kX++r6+Y2er0DxpfUd290TfebjqU7z61mT++Ge5JH2uHrnXJury+YOpmcH5k7Xy018E/wepz53V6CvnrE4kXYzsDvemsuVdqfQyVd67iO09tpr7ViaTzhnisycFt80YG5/IqFOc6afkvYd7YEoqyLUgpg3nb0+2uuPljPcVYDaMQDMzLYEdtS8TjsXbToWyuaWLz0SZ+/epe/vC5aVw+vjTmDt0c1NFLfnndFECwvbY57AkA/JOjloZ02nZlfhcb50S+eyjazcEW0NG7vRKvTyY9dzceXZ92uupq7G4v//rgSFghXqE410nLQD996ICg74lGq8MTU0MPYLOYsLu9+Hwy7k3h3sX+fP+cB9ZEVOHE2k2HkpNh5kBdGy6vL6iRj6bsGZxvC3bGur0+Rpb4c/ojS/wDwx98eTfHmx2U5Fj54VXjYqpuPjx4irIBNsoC69TTLBaJqiEDeHLJ+YwuzWb9IX/q50yqXSI97XTlWJOdhjYn2VZTr5isKRR9jbRM3TR3uNl9oiU4cs/nk7S5PFGHjmhoevJ4gSSUSCqceLvpUHKsJloDVgYZgUAf6z1NgeYpt9fHkx8eYWtNE+CvGzx32xwAbr9sVFiQ72rZsGJTDdc9vo6n1nfm07Os/t14ouRlmjl/eCE5GWZsZiM2szHiGMdUoedJqTDbyoyfvcb7BxrP2DoUiv5EWgb657ceY8Fv3uFUh79Ls93lQUp06eiNBqEr0P9oxTb+9M6BoAqnLN+GAMrybdx/zSTdbfihTxna7jPWe04dks/Oe+Zz0ahifrhiG6/uPBm8XmsYau7o7E7VUh21TfbOPPaKbYHPCxk6/tXZ/O2mWbrWHMpHJ1tZWV2L0+PlixdUsuveBeQlKDNNhHhPSjazkS/N8fv1KwdLhcJPWqZuLMH0RucO9QuzhzKxLC/mdTeeP5QvzK7U9Rlrdtdx4cgiwB+Yk/VXCZ0eFZruiPaexoDmvcPlwScJ2heAv1Eo02IMWgJA5FSHFgBDnxqS9aJfs7uO+1/azRXj5xPnPpoSvnnpSO58dltYbl7gz9WX5dtYOn8ME8vyeHj13l4ba6hQ9DXSM9BrfjCBFEJOhjmuhh4SC3b+nH/Pd64/WDCWBRMHsnzDUQp0DPduaHPyxzf3B28yWV2ia77NHNZNGyvVEZq//s+Go+w41sJPPjEhofVrBVyb2ciWo0385b2DLF0wNpj7TzVun0QCRdkWGttcDA4E99CbouYGquSVCoWf9Az0xs4WePA7PfpkuAtkJD462cqytw/w9Xkjw3baXfH6JG3O+MVdvUwuz2dyeb6uc9udHv7v3YPBAJ/VpeiZazMHh6BA9MIuhKduttY088LWY0kEeg82sxGDQVDX6mTl5mPcfOHwMxLopZQ8se4QEwbn8sLtF0a9MauGKYUinLTM0Xfd0b/zUQOj/+clqo+cjnldY7uL/2ysiVvw08y/UhHoX9h6jPm/frubp000tGKslofvuqN/csn5PHJDVfD3pfPHdPOfyTAbuPnCYZw3rNPlMtNipD0peaU3WMS2Bv7cz0TKRGuM2nuyjdomO89tjj6oLNtq4gcLxlA1ZEDUcxSKc4m0DPQTBufyi2snMzjfb+HbEhjAHS8w6/Vld7p9DCvKojhHv/97NFodHvacbGXKT1/RNRVLk1cOLcxizfcuZk4ghaORnxk+t3VxVRlzR3WeU5Zv44FrJnP3x8aHFTYzLSZcHl9QqaQXe2DoCIQG+tSmTLSCckOb/+bW1OGO2X2cYTby9UtGMqk8dk1GoThXSMvUzeB8G9fN6BxV2+lFH09eqfmyx9aTF+dYeeP7l/RskQGyQ3bkZmP8+67WMCUEDC/O7nb81Z0n2VrTxPeu7JR3FgQGkswdXcwTN82ioc3J67tOMmNoQVAhE7zJub3k6liHxtIFY2ix+/+8rIEbTKp39LE6haMVwY+e6sBmSWwYi0KRrqTljr7d6WHj4dM0BdIbeoaOQIiOPskBHMmQaPpHs0DYdbyFZW/v75by2XDoFMvePhD22qnAMJCTgZmwW2uauPlvGzjY2B48J89mpjDLknABc1CejTED/Y1bmRYjRdkW/DZvqSMZL58Fv3m7m7WEQnGuoivQCyEWCCH2CCH2CSHujHD8c0KIrYH/rRVCTAk5dkgIsU0IsVkIsSGVi4/Ggfp2PvXHtaw/5M/Jtzn9fuXxBndnWUxxtfYA6w+d4vpl6zhQ39bjtSYa6LOtJg7efxVVFQP4+Yu7aXeGP33kZZpxenxhFr0TB+cCkGvzf1YkeeV1M4ew8e4rEk5H/XfLMdbs9mv5R5fmsOF/rmDe2JKE3iMeyXj5ZJjVgHCFQiNulBFCGPEP/L4CqAHWCyGel1KG+tEeBC6WUp4WQiwElgHnhRyfJ6VsSOG6Y9K1GDuzsgCDEHHlk3mZZrb9dH7c9z/WZOf9A6dIxQCjwqzEAqv2HdpDBoOHkh8YftLU4WZgnj+Qf/fKMXw3JJWjPbGEqm6S5Q9v7qcsP4NLx5b2+L2isXT+GJY+vSWsLyJe93GG2dgr064Uir6Inn/ps4B9UsoDUkoX8CSwKPQEKeVaKaUmaXkfKKcXCQZ6rz+gXTKmJCxnrZeu1gFa8a8lkArKTYHqprIoi99/toq7Fo7Vfc1dz27jmU3+tXSVV2rDT5rs0We3arLD0KLt3pOtLHliA7tPRDZpi4bd5QnWNlodbr7yxAZeC+nWTQWLq8q4fJz/RqK3+9hqMqgdvUIRQE+kKgNCTcZrCN+td+Vm4KWQ3yXwihBCAo9LKZdFukgIsQRYAlBRURHpFN1oyhSXx8fK6loefHk3J5odEZtrurL0P1uYNnQANrMxoic8+AMaxC/u6uVjkwcndP4zm2pweXxYTYag3FIj32ZGiM66hMPtZcbPXmPR1MHsOdHK3R8bH7Kj7wz0bU4Pr+w8yQ3nVTB2YK7utYTKK4UQvLrzJLMqCxL6PnoYkGWhMMvCxruv0HW+1WxUFggKRQA9gT5SviNi0kIIMQ9/oL8w5OU5UspjQogS4FUhxG4p5dvd3tB/A1gGMGPGjB4lRbQd/fpDp1m19XjEYB0t2L+1tx6jQfDORw1RlR6Lpg7GZBApSX2s2FTD9/6zBZ/sbOGPZ6eg+e1nR6gnnDe8kH33XRW0CT7V7qLN6cFqMrLh8GkOn+rg6smDGDcoN+z6ZAvRkeWVqd9Jn2h2UJqbofv82+aNJNOqnCsVCtCXuqkBhoT8Xg5061YRQkwG/gQsklIGbQOllMcC/60DVuBPBZ1R8mxmHv3sNN75qD7hEXuaL3sspUdBloVpQwck7Q+jsbK6lh+u2B7M9eudTmUyCq6dXs5L376o2zGjQYR5wWuKm/GBguzJZgeD8mzMGVkUdt57+/wllK//c5PucYhSSjrcXrICqRuTQWAQqdfRgz/QD8zTH+ivnjwoOLFLoTjX0RPo1wOjhBDDhBAW4Hrg+dAThBAVwLPAjVLKvSGvZwkhcrSfgSuB7alafDSsJiNXTx5EXYsz4vFYsjybxUSHyxtT6XHLRcNZ/tXZPV5nMrNeAUwGA2ajgZKc7oHP7fWFuVo2tPn/DCoLM7GZjZxocbDlaBMvbz8evGZldW3YZyYyDvHtH8zj5guHAf7UjdV0Zoqg9y6ewO2XjtR9/tFTHew92ZrydSgU/ZG4gV5K6QFuA1YDu4DlUsodQohbhRC3Bk77X6AQ+EMXGWUp8K4QYgvwIbBKSvlyyr9FBN75qJ6S3MiKlliyvEyLEbvb02OfeT0kow8HyLOZeHrjUf6zoft8VpNBsHz90aDdg7ajL8iyMDAvg5MtDv6z8Sg/XNF5v31o9Z5u+Ww9NxwhBGX5NgaEmLENL87SJVFNlOlDC6iq0G9pcN+qXdz2r00xz4lWbFco0g1d/yKllC8CL3Z57bGQn28Bbolw3QFgStfXzwZf+st6xpRmc7LLrj5esC7Lt+Hx+YJ58p/+dwenO9wUZFn434+NZ3FVGd99ajM2i5H7PjmpR2uMNUkqFq9/7xIW/f5dVm07zqdnDAk7JoQgP7PT2Kws38anppVTnGNlVqW/E/ZUuys45ASSv+E0d7h5Yt0hrpwwMNg0teqb3dNJPaW5w807++o5b1ihbp1/htkQsxgbbQA7RK/fKBT9lbTsjF1ZXYvPJ9l5vJUcq9GvREGfLO93N1Txh89NB/z/4E1GA9fNKGfT3VcEr9t5vKXbDSQZevLU0Ob0BHPjXcm1mWkOeNKfN7yQX143hZwMMw9eO5kfXjUOu9tLRogsM5mGJID6Nge/fHXvGU+R7D7Rwm3/qk5I+hmtYUrbxX/7qc1Jpc0Uiv5I2gV6baemyXZanV6cHh+//sxU3rvz0oR2a16fpLHN2S0X3urwpERDn+x0qvtf2sX++nayoqhKQj3pnR4vUoaLmJxuLxmmzmuTveG0O/2BMjPkpnHH01t5OMXB8kSL37phYAKqm0g6+tBpW9HQO9RdoehPpJ2pWTIGWKE8se4Q7+1r4PEbZ9DY7sQn4fdv7ONEi4OHP+3PQrU63Cnzok9mOpWmkOnaFatRkpMRtFL+xj83Udfq5PnbLuS/W47xwEu7ybOZw6Sh2udrqQy9Ms/g0JGQQL/jeDMlbfoDsh5OBgJ9aQKqmwyzEUeXorCeweJ6h7orFP2JtAv0yeabNQ43dvDOR/5AGqra2V7bDPglhf6hI2duLmo8TAEHy0g6eoDHbpwe/Lmx3RW8KRmEoLbJzt0fG8fIknDny8VVZWyvbeafHxzh3Tvm6ZKO2t3+m0lmSArJr7pJrY7+eLODLIsxoSLvx6cMZkKX0ZHx/g6kutiuUPQV0i51k2y+WcOvuvGnO+pb/YF+7MAc6gI/u7w+LhxV3C1Qnk0sRgOzKgu4TYfc8FS7K+inMzDP/98Ms5GRJTndzi3NzcDu9tLqjG3TrBEpdWM1GYIeQ6niZIuD0ryMhPoWJpbl8Ykp4R3HMU3QTIaEhrorFP2JtAv0PZVF2ixGpPQ7PE6vHMDTt85m7uhiTrW7ArYDRp64aVavBgSTUSCRWE2Rc/Srd5zg5r+ux+31carNFZxFq9UaHn/rAGv3d/eY0+SodYFUSTwWThxI9d1XMDxk7KLVZIioo++JlPF/rh7P72+Ypvt88H+Htfsawm46S+ePCVMbgf/vxoyh+QzIsqggr0hb0i7QJ1vg1Mg0a1OmPORmmJlRWRCcH6s1H/U2QvjtHbR0UldONDt4fXcdDW1OWp0eCgOBXrMQWHegkWc2dg+0FQWZVFXk49Fpy2kyGhiQZQnz2xlenM3QwvB5u6FFUEliDVng34lrnb16eXXXST77pw+CfQTg/7vxwKcmd/u7MX/CII43O8LOVSjSibTL0UNyBU6N0twMxg3KxeuTvLevgWa7mxHF2Vw8uhivT7K1pomv/WMTv7l+KjPPgHmXHu5aOI6PPfIutU12JpZ1H5eXZ/PXDxrbXHxj3ghmDfOv02Iy8LHJg3hh63Fslu73+KqKAaz4+hzd63jno3rW7m/ke1eMDgb7uz82vtt5PSmQe32SP797kAtHFTFukP5gr6mKQpU3LQ43JqNg9XfmhtU3dh5r4TuXj9b93gpFfyPtdvQ9ZeGkQbz0rYsoyc3g7+sO86tX9zJrWAF/u2kWQwoyOdXuorbJjiG1Q5QSQvOij1aM1cYDurw+ls4fy3nDO4eA//6z08i0GMPklcnywYFTPP7W/jDPnEj0pEDe2Obkvhd3seHQqYTWlhEca9iZunlrTz23/auaPSfCdf/jB+fyrctHBVNcCkW6oQJ9DOpaHZR06cTUO3/2TPKrV/12QtHklfmBHf2JZgen2134QlIxUkrsbm+YJDKUTz+2ll+9ok8H77coNoUVSZe9vZ/PPL4u7LyeFMiPB8YfDsxLTPaoyUdDd/RrdtdRkGVh6pD8buc3dbjYV6e8cRTpiQr0XdhxrJlFv3+XzUebqG9zUpJjxeeTzP3FG/x+zUe0OfXNnz2TbAr42GRHaZgqyLIwpMDG6h0nqLr3VQ40dM6GveeFnUgZ7kUfSmO7i/317RGPhbKyupYn1x+hzekJK67WtzrZ1qV2EKkIKvDn6uMVZpNploLO7+dwe1lZXcsFD7zOiupa7C4v/93SzXyV7y3fwjf+WZ3QZygU/QUV6Lvg8Uq21DTT2OakrsVJSW4GBoOgw+Wl5rQ95UNHkkFrdI22ox9amMU7P7iUyeX+nWthSEpCW/enZ0QeAlaakxFsUIqGVlzVGqZCi6uR3CtDi6DgD/LaM0a8wqy2lkQsigHGDcrlT1+Ywb66Nu56dhvHmvzvY3d7I37e+MG57KtvU1OpFGmJCvRd0DThJ1ucOD2+YOqmJMdKXauTioJM5k8o7TbC72yxsro2OFjl2j+ujbkbPtXuxGgQweIswIlmf178vPtej7ibLs21crI1dqCPVVy1mAx4fRKPtzPYH2poJ9tq4s2ll1CWb+s2tSaWx8zxZgdmowi7WemhIMvC5eNL+cOb+3V52owPFOA/Otnzge8KRV8jLVU3PUHLXRsEvHvHvKBxWEmulbpWBwsmDmLBxEG9srbujouOqI6Lt/59Iy/vOEFRtgVDoFi6srqWFYHAHipzDL2+NDeDky1OpJRRG5RiFVc7p0z5eGHrcR5avSfoLXPf4okJF2a/ddkoPndeRfA76KXD5WHtvkbdn6cpenYeb2ZSeXclk0LRn1E7+i5o7fwOt5fyAZlBr/WSHGvUQSZni0QGlew47s+Ta12x2vVub/h+uuv1k8vzuXxcSczhIbGKq0MKMpk9vJD/buluIPazVbuCw8v1vmeG2Uj5gMyoa4lGY5uLW57YEFQgxfu86sOnEcAdz2xT3vSKtEMF+i5kWoxMHzqAY80O/vDmvmBOfvaIQi4fX8o3/rWpm6rkbJHIbjjf5r9BfWXu8ISuv3ryIP7wuelRi7XgL65aI3SYLp0/hqsmDeLfS87nkTWRUyZSortzeWV1LZN/sprKJLpptfVfPrYEizHyWkM/54crt+uuGygU/Q0V6LuQYTbyzNcuoDjbyi9e3hOc5/rJqnJ+/slJNLY58ckezS5PmkRkivmZZqoq8rl2ennM86K93tXaOJTFVWVcFyjmRus+jnZTaba7g53LGkvnj+6WevKnqbbSEpCzJhp8NXnl2EG5nDe8IOZakx3pqFD0F1SOPgp1rQ6sJkOY77zPJ2m2exgYZUThmWbp/DFhOXqIvhvOtZl556MGmjvcwfSFnuuPN9tZ+Nt3+NFV47pNrwolw2zEajKw46fzwywQ3t5bz/8+t53iQPG6K4PzbcHO5cY2J6c7XIwo7m4Q5w++kccb6ul6toZ0xp5scXDRqCL+fvN5Ec/tqeOpQtHX0bWjF0IsEELsEULsE0LcGeH454QQWwP/WyuEmKL32r7IZx5fx/975yAludZgQXJbTTNj7n6JXcdbek1amYiPz4iAP89f1x5K6PoBmRaaOtwRg3Qo22tbGDswJyzIg384+aHGDj5/fkXcFE1htpWRJTkRi749Db5mo8AgoOa0nb0n27hgRFHUc3vqeKpQ9HXi7uiFEEbgUeAKoAZYL4R4Xkq5M+S0g8DFUsrTQoiFwDLgPJ3X9jm0bszQyVL5meZgIbM3m6X0+PisrK5l+YYaAP783kGGFmYGr4l3fYbZSG6GKaaDpZSS7cea+XgXG2Do3EnPHlFERUEWD63ew7EmO4OjDDPZcOgUK6pruXfRxDBlTbLzdDWEEPzrK+cHm8suGFEY9dxEnpQUiv6Inh39LGCflPKAlNIFPAksCj1BSrlWSnk68Ov7QLnea/simpY+1P4gdCh1qHdMX0OTxJ2fzwAAD2BJREFUYGodpc12d8KFRU1iGY1mu5shAzIjWglYA7lxp9vHwkkDmT2ikH8vOT/qGMfDjR3884Mj7OoyD3bp/DGYjeE7/USD7/nDCynLtzF1SH5E8zeNzicd/409y2pU3vSKtEJPoC8Djob8XhN4LRo3Ay8leW2fwGYxct6wAh68dnLwtQyzkTybmRvPH9ptoEVfIhWFxdLcjJhNU/mZFl781kVcFyGH36mj93KsycHTG2uoOR093dLq9Kuarv7du2HKmsVVZTx07RQG52UkZTcN8OrOkwzOt7HyG3PiGq8trirjvTsvY8LgXGZWFqggr0gr9OQgIv0LiSjJEELMwx/oL0zi2iXAEoCKigodyzpzZFqM2F1ecrvk4otzrMG0Tl8lFYXF+RNKaepwJ/X5AzItXD6uhPxMC7WBAF8+IHK6ZWV1LQ++1HkD6trA1RO76ZXVtXxv+Ra8UuqegQswrCiLrTWRff4Viv6Knh19DRC6dSsHurlCCSEmA38CFkkpGxO5FkBKuUxKOUNKOaO4uFjP2s8YlYVZbDrSxM5j4emE84cX8NqukzwfwRSrr5CKwuKNsyu5/bJRUY9/41+buPOZrRGPDSnI5E9fnMn0oQOoOd0BECalDCXe08cf39zPY2/t171uDS195Q1IRBORZv5g/lieXHJ+wp+pUPRl9AT69cAoIcQwIYQFuB54PvQEIUQF8Cxwo5RybyLX9kWumeYvMYSmL1ZW17J6+0kAfvr8jj7bTNPTUYoaDrcXb4RJU1JK3t/fGPFYV2qb7BgNgkFRDMniPX28tP046/Y3RjwnFj1JX1UUZiq1jSLtiBvopZQe4DZgNbALWC6l3CGEuFUIcWvgtP8FCoE/CCE2CyE2xLr2DHyPlLGyupavPLEegB88vZWV1bXBHWJ9YJRgY7urz3ZO9nSUIvhnzo69++VuAzrAb/bW2O6KWtxs7nAz877X+PeHR3C4vQwtyOwmwdSI9/RxotlBaRI9Cz1JXzXb3Tz21v6oYxoViv6ILp2glPJF4MUurz0W8vMtwC16r+2rdDUNq291ctez28gwG5Iehdcb9CS3DQRTVlf97p2w/PbK6lruecGvjH1kzUfk2czdPsdkFNS3Oml1uPnR1eP54VXjon5OLFmjx+ujoc0ZnHObCD2VZj7w0m7uWjg2plJHoehPqM7YEKI98nd9TSMdOydXVteG5cW1/PaGw6d4ZmNt8M+ioc0V0TkzqLoJdLVGc8AMvU5zuMy2mvjZ4oksrirjZIsDnySpQN8TXXyezUxRtoWDDfGHrygU/QXldRNCooE7HXO5D63e08250u728u8PjurKe5uMBowGQZvLw+f/9AGrd5yI+Xl+WeOlzKosYPyg3GDwb7a7Kcq2JDxZSnvPnqSvhhVlhU3lUij6O2pHH0K0R/58mxmnx3dOdE5Gu9l5o5icRTrfajJwpLGDd/c18PEp+rz7hxRksnZ/Q/D30aU5bPifK3RdG4mepK+GFWWxZnd90p+tUPQ11I4+hGiKlZ98YkKPC5z9hWhPKcYoGZhI5y+aOjjYg6DXS76iIJMTLY4+McpvWFE2pztctAfmAysU/R21ow8hNGccyZ8lHQN7VyLltwG8ETb00Z5q7r9mMv/ZcJSnNhyNqqHvSkWhDSn9NYERxdn884PDrN3XyO8/WxUzz38m+OIFQ7nlomGYo6iFFIr+hgr0XeipYqW/07VA2hVtsHe8btPaJjtCwKB8fTn2USU5zBlZiCdwR9l0uIlNR06f9SAPnVPGFIp0Qf2NVnRDu9nNeWBNt2CvBfn37rw06vWLHn2PLUebmD50QNDNMh4Ty/L45y2dHal1rY6kFDepQErJPS/sZFJZXrB5TqHoz6hnU0VUkm08klIyb0wxz3ztgqQ/+2RLcs1SqUAIwWu7TvLGHlWQVaQHKtAropKsb47VZIg5XDwaN/11Pbf/uxrwd8UmI61MBSura6lrcfLfLcfUoHBFWqACvSIqyfrmmAwG1u5vZPn6ozHPi8S+ujbcXh8VhZmMKOk+YvBMo3VHazcqNShckQ6oHL0iKvFUSNFosvstjt2+xHb1FQWZrD94CpNB8MLtFyW36B4SyxDtXC7SK/o3KtArYpKoCmlldS2HAl2lv3plL1kWk+7rhxRk0ur00NThZkCWJan19hQ1KFyRjqjUjSJldDWFS9Tls6LA31z15/cOsuj373KiF4a8qEHhinREBXpFyujpGMPRpdlcO72cE80OttQ0k2XVJ81MJZHqEhlmQ1raXSjOHVSgV6SMnqY9hhZm8fCnp5CTYSbTYiTbevYzi10N0SxGA8MKs1R+XtGvUTl6RcroqQ88+DX4BxraGJib0StdsRBel/jqE+tZvbOOYXeu0l2MVij6GmpHr0gZqRhj+Jll7/PmnnpKeqlZKpSV1bW8udfvqClRUktF/0UFekXKSMUYQ61JatawwjO0Sv1E8+bXW3NQKPoKKnWjSCk9NYWzu/zWwI+8/hHPbKzp1VSJkloq0gVdO3ohxAIhxB4hxD4hxJ0Rjo8VQqwTQjiFEN/vcuyQEGJb6NBwhSIS/lSJ31+mL6RKlNRSkS7EDfRCCCPwKLAQGA/cIIQY3+W0U8A3gYejvM08KeVUKeWMnixWkd48tHoP7i7G972ZKklFzUGh6Avo2dHPAvZJKQ9IKV3Ak8Ci0BOklHVSyvWA+wysUXGO0NdSJV1rDtlWE1+9eLhS3Sj6HXoCfRkQ6k5VE3hNLxJ4RQixUQixJNpJQoglQogNQogN9fXKHvZcpC+mSrTh5TvvWYDXJ2loc/baWhSKZNET6COJmSNPio7MHCnlNPypn28IIeZGOklKuUxKOUNKOaO4uDiBt1ekC305VWKzGLl0bAkvbz+J15fIX3+FovfRE+hrgCEhv5cDx/R+gJTyWOC/dcAK/KkghaIbqZBnnkkWThpIQ5uTDYdO9fZSFIqE0COvXA+MEkIMA2qB64HP6nlzIUQWYJBStgZ+vhK4J9nFKtKfvjyzd96YEowCbvrbejqcXtUpq+g3xA30UkqPEOI2YDVgBP4spdwhhLg1cPwxIcRAYAOQC/iEEN/Gr9ApAlYEWtlNwL+klC+fma+iUJxZXt15EhC0O/3GbZr8E1DBXtGn0dUwJaV8EXixy2uPhfx8An9KpystwJSeLFCh6Cs8tHoPXhlZ/qkCvaIvoywQFAqd9DX5p0KhFxXoFQqd9EX5p0KhBxXoFQqdRJJ/gj9XP+eBNcrVUtFnUaZmCoVOQoeld/XdV4VZRV9G7egVigTQOmXL8jO6HbO7vXz7qc1qd6/oc6gdvUKRBMeaog8ur22y852nNvPtpzaTbzMjBDR1uJXuXtFrqECvUCRBtLGJGpoIs8ne6fMX7QaQp24GijOMkLLv+XbMmDFDbtigrOsVfZeV1bXc9ew27G5vyt9b4L9RRLsZ6Pl5cL6NeWOLeWN3Pcea7Alff6Z/TmZ96iYYGyHExmhW8CrQKxRJsrK6NmJhVnHmSMVNsK/fNJO9oalAr1CcQc7k7l5xbmIzGxM29IsV6JXqRqHoIaGumxDZ11uhSIRUT1ZTxViFIgWEum5qKZ3Qx/zTHe5g2kGh0EMqrTVUoFcoUkw0q+VIN4DQ/Ky6GShCSaW1hgr0CsVZQo/XfrybQV8tIJ7p9Z1rN8FUT1ZTgV6h6EP05cErvU2qboJ9/aZ5JmSkKtArFIp+gboJJo9S3SgUCkWaowK9QqFQpDkq0CsUCkWaowK9QqFQpDkq0CsUCkWa0ye9boQQ9cDhJC8vAhpSuJyzhVr32UWt++yi1n3mGSqlLI50oE8G+p4ghNgQzdinL6PWfXZR6z67qHX3Lip1o1AoFGmOCvQKhUKR5qRjoF/W2wtIErXus4ta99lFrbsXSbscvUKhUCjCSccdvUKhUChCUIFeoVAo0py0CfRCiAVCiD1CiH1CiDt7ez2xEEL8WQhRJ4TYHvLaT4QQtUKIzYH/XdWba+yKECJDiP/f3t2EWFWHcRz//hwMUhDNMqQpeiEkcDFJTEQwSCb0IpZBoBBIRERkKC2K2lQ7i4J2LhqLiWLCbFG4KIToDXqRSsM3skTyls0EFjG1mCZ/Lc7/xs3uqUai//8cng9czj3/mcXD75557jnPnMvVx5L2STog6fG0fo6k3ZKOpO2i3LX2I2lA0meSdqX9ovPukrRQ0k5JhyUdknRN6ZlLWtaT615JP0na0oTMJW2WtD8d41vSWtF5/xutmNFLGgC+AFYDHWAPsMH2wayF1ZA0AkwBL9hentYeA6ZsP5WztjqSBMy3PSVpLvA+sBm4DThpe2t6g11k+6GctfYj6QHgKmCB7TWl590laQx4z/aopLOAecAjNCBz+ONv8xvgauBOCs5c0nLgZWAYmAbeAO4F7qYheddpyxn9MPCl7aO2p6lerFsy11TL9rvAydx1zIYrU2l3bnqYKuextD4G3JqhvL8laRC4GRjNXctsSFoAjADbAWxP2/6RBmTeYxXwle0z/aT7/+kK4EPbv9ieAd4B1tGsvPtqS6O/ADjes99Ja02zSdLnabRT3OVhGn/sBSaB3bY/As63fQIgbZfkrLHGM8CDwKnT1ovOG7gU+B54Po2dRiXNpxmZd60Hxnv2S858PzAiabGkecBNwIU0K+++2tLo1WetaTOpbcBlwBBwAng6bzl/Zfs320PAIDCcLnWLJmkNMGn7k9N+VHzeVN8AtwLYZvtK4Geg6P8/9UqjprXAK2mp6MxtHwKeAHZTjW32ATNZi/qPtKXRd6jeebsGgW8z1XJGbE+kRnoKeJZqHFWkND54G7gBmJC0FCBtJzOW1s+1wFpJx6hGetdJerEheXeATrpyAthJ1fhLz7zrRuBT2xPQjGPc9nbbK2yPUI1Xj9CcvGu1pdHvAS6XdEk6i1gPvJ65plnpHkjJOqrLyGJIOk/SwvT8bOB64DBVzhvTr20EXstTYX+2H7Y9aPtiquPiLdt3lJ43gO3vgOOSlqWlVcBBCs+8xwZ6xjZNyFzSkrS9iOpGg3Gak3etVnw5uO0ZSZuAN4EB4DnbBzKXVUvSOLASOFdSB3gUWClpiGrkdAy4J1uB/S0FxtJdFHOAHbZ3SfoA2CHpLuBr4PacRc7Ck4Xn3XU/8FI6gTlKdefKHArPPM24V/PnXJuQ+auSFgO/AvfZ/kHSVgrP+5+04vbKEEII9doyugkhhFAjGn0IIbRcNPoQQmi5aPQhhNBy0ehDCKHlotGHEELLRaMPIYSW+x3ZgyiVFGd8TAAAAABJRU5ErkJggg==\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "None\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "None\n"
-     ]
-    }
-   ],
-   "source": [
-    "print(\"loss = \", test.energy)\n",
-    "print(\"method: \", mthd)\n",
-    "print(\"method parameters: \", mthd_opt)\n",
-    "print(\"execution time = \", (t1-t0)/60, \" min\")\n",
-    "\n",
-    "print(test.history.plot('energies', label='loss'))\n",
-    "print(test.history.plot('angles', label=\"\"))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Test\n",
-    "\n",
-    "Once trained, we have the optimal parameters for the classifier stored in `test.angles`. We run again the classifier with the test data set and with these parameters fixed."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "success %:  90.5 %\n",
-      "random success %:  49.1 %\n"
-     ]
-    }
-   ],
-   "source": [
-    "test_set = 1000\n",
-    "\n",
-    "# initialize\n",
-    "xval_test, yval_test, yval_rand, yval_real = [], [], [], []\n",
-    "suc = 0 # success\n",
-    "suc_rand = 0 # random success\n",
-    "\n",
-    "for i in range(test_set):\n",
-    "    \n",
-    "    # random test point\n",
-    "    x = 2 * (np.random.rand(2)) - 1\n",
-    "    \n",
-    "    # state generated by the trained classifier\n",
-    "    qc = qcircuit(x, param)\n",
-    "    wfn_qc = tq.simulate(qc, variables=test.angles) \n",
-    "        \n",
-    "    if nclass == 2:\n",
-    "        \n",
-    "        # compute the fidelity respect to one of the label states, the |0>\n",
-    "        f = abs(wfn_qc.inner(targ_wfn(0,nclass)))**2\n",
-    "\n",
-    "        y = 1\n",
-    "        # if fidelity is >= 0.5, we conclude that this state belongs to |0> class\n",
-    "        # (|1> class otherwise)\n",
-    "        if f >= 0.5:\n",
-    "            y = 0\n",
-    "            \n",
-    "        # check the real class of the data point\n",
-    "        y_real = circle(random=False, x_input=x)\n",
-    "        \n",
-    "    else:\n",
-    "        raise Exception(\"nclass = {} is not considered\".format(nclass))\n",
-    "    \n",
-    "    # compute success rate \n",
-    "    if y == y_real:\n",
-    "        suc = suc + 1\n",
-    "        \n",
-    "    # compute random success rate \n",
-    "    yrand = np.random.randint(0, nclass-1)\n",
-    "    if yrand == y_real:\n",
-    "        suc_rand = suc_rand + 1\n",
-    "        \n",
-    "    xval_test.append(x)\n",
-    "    yval_test.append(y)\n",
-    "    yval_real.append(y_real)\n",
-    "    \n",
-    "print(\"success %: \", 100*suc/test_set,\"%\")\n",
-    "print(\"random success %: \", 100*suc_rand/test_set,\"%\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Print results:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def plot_data(x, y, nclass, fig=None, ax=None):\n",
-    "    \"\"\"\n",
-    "    Arg:\n",
-    "        - x (array[tuple]): data points\n",
-    "        - y (array[int]): data labels\n",
-    "        - nclass (int): number of classes\n",
-    "    Returns:\n",
-    "        - Plot\n",
-    "    \"\"\"    \n",
-    "    if fig == None:\n",
-    "        fig, ax = plt.subplots(1, 1, figsize=(5, 5))\n",
-    "     \n",
-    "    # colors and labels\n",
-    "    col = [\"red\",\"blue\",\"green\",\"yellow\"]\n",
-    "    lab = [0,1,2,3]\n",
-    "    \n",
-    "    for i in range(nclass):\n",
-    "        ax.scatter(x[y == lab[i], 0], x[y == lab[i], 1], c=col[i], s=20, edgecolor=\"k\")\n",
-    "    ax.set_xlabel(\"$x_1$\")\n",
-    "    ax.set_ylabel(\"$x_2$\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x216 with 2 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Total execution time:  36.01548974911372  min.\n"
-     ]
-    }
-   ],
-   "source": [
-    "xval_test = np.array(xval_test)\n",
-    "yval_test = np.array(yval_test)\n",
-    "yval_real = np.array(yval_real)\n",
-    "\n",
-    "fig, axes = plt.subplots(1, 2, figsize=(6, 3))\n",
-    "\n",
-    "plot_data(xval_test, yval_test, nclass, fig, axes[0])\n",
-    "plot_data(xval_test, yval_real, nclass, fig, axes[1])\n",
-    "\n",
-    "axes[0].set_title(\"Single-qubit class. {} layers\".format(layers))\n",
-    "axes[1].set_title(\"True test data\")\n",
-    "fig.tight_layout(pad=0.5)\n",
-    "plt.show()\n",
-    "\n",
-    "t2 = time.time()\n",
-    "print(\"Total execution time: \", (t2-t0)/60,\" min.\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Improvements and customization\n",
-    "\n",
-    "This tutorial just shows a simple classification example. It is constructed in a way that one can easily change the classification model and try more sophisticated problems comprising more classes. To do so, one should define the target states for >2 classes, i.e. include more vectors in the Bloch sphere.\n",
-    "\n",
-    "The single-qubit classifier circuit can also be modified to include higher dimensional data or to increase/reduce the number of parameters per layer.\n",
-    "\n",
-    "The cost function can also be improved. See for instance the weigthed fidelity cost function proposed in the main reference.\n",
-    "\n",
-    "Finally, the core of any variational algorithm is the minimization method. Tequila provides many methods besides the scipy ones. See the [optimizers tutorial](https://github.com/aspuru-guzik-group/tequila/blob/master/tutorials/Optimizer_Tutorial.ipynb) for more information.\n",
-    "Notice also that the algorithm starts with a random initialization. It is well-known that random initialization in variational circuits leads to a barren-plateaus problem when computing the gradients. This problem can be avoided by providing a good initialization guess. \n",
-    "\n",
-    "Another possibility to play with expoloiting other Tequila modules is to use Phoenics for initial exploration and a gradient based optimizer with the best Phoenics results as starting point (see Phoenics documentation)."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "tqenv",
-   "language": "python",
-   "name": "tqenv"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.7.4"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 4
-}
diff --git a/tutorials/StatePreparation_tutorial.ipynb b/tutorials/StatePreparation_tutorial.ipynb
deleted file mode 100644
index 44951380..00000000
--- a/tutorials/StatePreparation_tutorial.ipynb
+++ /dev/null
@@ -1,720 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# State preparation algorithm tutorial\n",
-    "\n",
-    "This tutorial shows:\n",
-    "- How to define a quantum gate not included in Tequila's gate set\n",
-    "- How to construct a parametrized quantum circuit\n",
-    "- How to compute the fidelity between two states\n",
-    "- How to train a parametrized quantum circuit"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# Import everthing you need\n",
-    "import tequila as tq\n",
-    "import numpy as np\n",
-    "import random\n",
-    "import time"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Quantum gate construction\n",
-    "\n",
-    "Sometimes, one may need to use a particular quantum gate that is not included in the basic gate set. If we know the decomposition of this gate in terms of Tequila's gates, we can define a function that runs a small quantum circuit that constructs this particular gate.  \n",
-    "  \n",
-    "As an example, let's define the general one-qubit unitary gate  \n",
-    "$$ U(\\theta,\\phi,\\lambda) = \\left( \\begin{array}{cc}\n",
-    " e^{-\\frac{1}{2} i (\\lambda +\\phi )} \\cos \\left(\\frac{\\theta }{2}\\right) & -e^{\\frac{1}{2} i (\\lambda -\\phi )} \\sin \\left(\\frac{\\theta }{2}\\right) \\\\\n",
-    " e^{-\\frac{1}{2} i (\\lambda -\\phi )} \\sin \\left(\\frac{\\theta }{2}\\right) & e^{\\frac{1}{2} i (\\lambda +\\phi )} \\cos \\left(\\frac{\\theta }{2}\\right) \\end{array} \\right) = R_{z}\\left(\\phi\\right) R_{y}\\left(\\theta\\right) R_{z}\\left(\\lambda\\right) $$"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "0: ───Rz(0.25π)───Ry(π)───Rz(0.5π)───\n"
-     ]
-    }
-   ],
-   "source": [
-    "# q0 = target qubit\n",
-    "def U(th,phi,lam,q0):\n",
-    "    ugate = tq.gates.Rz(target=q0,angle=phi) + tq.gates.Ry(target=q0,angle=th) + tq.gates.Rz(target=q0,angle=lam)\n",
-    "    return ugate\n",
-    "# draw the circuit for some (th,phi,lam) for qubit \"0\"\n",
-    "tq.draw(U(np.pi, np.pi/4.0, np.pi/2.0, 0))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Similarly, we can construct a multi-qubit gate. For instance, the controlled-phase gate:  \n",
-    "$$ CPh\\left(\\varphi \\right) = \\left(\n",
-    "\\begin{array}{cccc}\n",
-    " 1 & 0 & 0 & 0 \\\\\n",
-    " 0 & 1 & 0 & 0 \\\\\n",
-    " 0 & 0 & 1 & 0 \\\\\n",
-    " 0 & 0 & 0 & e^{i \\varphi } \\\\\n",
-    "\\end{array}\n",
-    "\\right)  = e^{i\\phi/4} \\left(R_{z}\\left(\\varphi/2\\right)\\otimes\\mathbb{I}\\right)CR_{z}\\left(\\phi/2\\right)$$"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "0: ───Rz(0.25π)───@───────────\n",
-      "                  │\n",
-      "1: ───────────────Rz(0.25π)───\n"
-     ]
-    }
-   ],
-   "source": [
-    "# q0 = control qubit\n",
-    "# q1 = target qubit\n",
-    "def CPh(phi,q0,q1):\n",
-    "    cph = tq.gates.Rz(target=q0, angle=phi/2) + tq.gates.CRz(control=q0, target=q1, angle=phi/2)\n",
-    "    return cph\n",
-    "# draw the circuit for some varphi for qubits \"0\" and \"1\"\n",
-    "tq.draw(CPh(np.pi/2,0,1))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The gate defined is equal to $CPh(\\varphi)$ gate up to a global phase."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Compute the fidelity\n",
-    "\n",
-    "Let's compute the fidelity between two states, one constructed from a string (target state $|\\tilde{\\psi}\\rangle$) and other obtained from a given quantum circuit, $|\\psi\\rangle$."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "target state:  +0.7071|00> +0.7071|11> \n"
-     ]
-    }
-   ],
-   "source": [
-    "# Target state example: Bell state\n",
-    "wfn_targ = tq.QubitWaveFunction.from_string(string=\"1.0*|00> + 1.0*|11>\")\n",
-    "wfn_targ = wfn_targ.normalize() # Remember to normalize the state!!! \n",
-    "print(\"target state: \", wfn_targ) # Print the wavefunction"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "circuit state:  +0.9641e^(-0.3614πi)|00> +0.0247e^(+0.8932πi)|10> +0.2462e^(-0.3614πi)|01> +0.0967e^(-0.1068πi)|11> \n",
-      "circuit diagram: \n",
-      "0: ───Rz(0.5π)───Ry(0.064π)───Rz(0.159π)───@───Rz(0.064π)───@─────────────────────────\n",
-      "                                           │                │\n",
-      "1: ────────────────────────────────────────X────────────────Rz(0.064π)───Ry(0.159π)───\n"
-     ]
-    }
-   ],
-   "source": [
-    "# Quantum circuit\n",
-    "q0 = 0\n",
-    "q1 = 1\n",
-    "qc = U(0.2, np.pi/2.0, 0.5, q0) + tq.gates.CNOT(target=q1,control=q0) + CPh(0.4,q0,q1) + tq.gates.Ry(target=q1,angle=0.5)\n",
-    "wfn_qc = tq.simulate(qc) # Simulate the wavefunction \n",
-    "print(\"circuit state: \", wfn_qc) \n",
-    "print(\"circuit diagram: \")\n",
-    "tq.draw(qc)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "There are two ways to compute the fidelity of these two states. The natural way to do it, in case we have both wavefunctions, is just by computing the inner product of these two states:\n",
-    "$$ F\\left(|\\psi\\rangle, |\\tilde{\\psi}\\rangle\\right) = |\\langle \\psi | \\tilde{\\psi} \\rangle|^2 $$"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "fidelity =  0.5343666886804502\n"
-     ]
-    }
-   ],
-   "source": [
-    "fidelity = abs(wfn_targ.inner(wfn_qc))**2\n",
-    "print('fidelity = ', fidelity)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The second method consists on computing the expected value of the target state density matrix operator $\\rho = |\\tilde{\\psi}\\rangle\\langle\\tilde{\\psi}|$, i.e. \n",
-    "$$ F\\left(|\\psi\\rangle, |\\tilde{\\psi}\\rangle\\right) = \\langle \\psi | \\rho |\\psi\\rangle = \\langle \\psi |\\tilde{\\psi}\\rangle \\langle \\tilde{\\psi} |\\psi\\rangle = |\\langle \\psi | \\tilde{\\psi} \\rangle|^2$$\n",
-    "\n",
-    "To do so, we need to write the density operator in terms of pauli matrices:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "+0.2500+0.2500Z(0)Z(1)+0.2500X(0)X(1)-0.2500Y(0)Y(1)\n"
-     ]
-    }
-   ],
-   "source": [
-    "# construct the density operator of target state\n",
-    "rho_targ =  tq.paulis.Projector(wfn=wfn_targ)\n",
-    "print(rho_targ)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Then, we trait this operator as a Hamiltonian and compute the objective expectation value:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "fidelity =  0.5343666886804503\n"
-     ]
-    }
-   ],
-   "source": [
-    "O = tq.Objective.ExpectationValue(U=qc, H=rho_targ)\n",
-    "fidelity= tq.simulate(O)\n",
-    "print('fidelity = ', fidelity)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Construct a parametrized quantum circuit \n",
-    "\n",
-    "Parametrized quantum circuits (PQC) are usually defined with a small gate set. Same gates are used along the circuit with different parameters, which makes more natural to define them as vectors. In the following example, we construct a parametrized quantum circuit of two qubits using the $U(\\theta,\\phi,\\lambda)$ (defined above) and a CNOT gate. Parameters are identified with the vectors $\\vec{\\theta}$, $\\vec{\\phi}$ and $\\vec{\\lambda}$. The circuit ansatz consist on applying general unitary gates on both qubits, then entangle them with the CNOT gate, and finally apply another unitary gate."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "#qubits\n",
-    "q0=0\n",
-    "q1=1\n",
-    "\n",
-    "#define variables\n",
-    "th = [tq.Variable(name='theta_{}'.format(i)) for i in range(0,4)]\n",
-    "phi = [tq.Variable(name='phi_{}'.format(i)) for i in range(0,4)]\n",
-    "lam = [tq.Variable(name='lam_{}'.format(i)) for i in range(0,4)]\n",
-    "\n",
-    "# PQC\n",
-    "pqc  = U(th[0],phi[0],lam[0],q0) + U(th[1],phi[1],lam[1],q1) \n",
-    "pqc += tq.gates.CNOT(control = q0, target = q1)\n",
-    "pqc += U(th[2],phi[2],lam[2],q0) + U(th[3],phi[3],lam[3],q1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "0: ───Rz(0.318309886183791*pi*f((phi_0,))_0)───Ry(0.318309886183791*pi*f((theta_0,))_1)───Rz(0.318309886183791*pi*f((lam_0,))_2)───@───Rz(0.318309886183791*pi*f((phi_2,))_6)───Ry(0.318309886183791*pi*f((theta_2,))_7)────Rz(0.318309886183791*pi*f((lam_2,))_8)────\n",
-      "                                                                                                                                   │\n",
-      "1: ───Rz(0.318309886183791*pi*f((phi_1,))_3)───Ry(0.318309886183791*pi*f((theta_1,))_4)───Rz(0.318309886183791*pi*f((lam_1,))_5)───X───Rz(0.318309886183791*pi*f((phi_3,))_9)───Ry(0.318309886183791*pi*f((theta_3,))_10)───Rz(0.318309886183791*pi*f((lam_3,))_11)───\n"
-     ]
-    }
-   ],
-   "source": [
-    "# Draw the circuit \n",
-    "n_th = len(th)\n",
-    "n_phi = len(phi)\n",
-    "n_lam = len(lam)\n",
-    "\n",
-    "tq.draw(pqc)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# initialize random values for the variables\n",
-    "th0 ={key : random.uniform(0, np.pi) for key in th}\n",
-    "phi0 = {key: random.uniform(0, np.pi) for key in phi}\n",
-    "lam0 = {key: random.uniform(0, np.pi) for key in lam}\n",
-    "all_values = {**th0, **phi0, **lam0}"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "{theta_0: 1.9400742456012434,\n",
-       " theta_1: 0.18708644852210973,\n",
-       " theta_2: 1.6718785378724963,\n",
-       " theta_3: 2.9210555160438036}"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "th0"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "0: ───Rz(0.318309886183791*pi*f((phi_0,))_0)───Ry(0.318309886183791*pi*f((theta_0,))_1)───Rz(0.318309886183791*pi*f((lam_0,))_2)───@───Rz(0.318309886183791*pi*f((phi_2,))_6)───Ry(0.318309886183791*pi*f((theta_2,))_7)────Rz(0.318309886183791*pi*f((lam_2,))_8)────\n",
-      "                                                                                                                                   │\n",
-      "1: ───Rz(0.318309886183791*pi*f((phi_1,))_3)───Ry(0.318309886183791*pi*f((theta_1,))_4)───Rz(0.318309886183791*pi*f((lam_1,))_5)───X───Rz(0.318309886183791*pi*f((phi_3,))_9)───Ry(0.318309886183791*pi*f((theta_3,))_10)───Rz(0.318309886183791*pi*f((lam_3,))_11)───\n"
-     ]
-    }
-   ],
-   "source": [
-    "# in case you want to look at the circuit with specific values\n",
-    "tq.draw(pqc, variables=all_values)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We can now compute the fidelity of the output state of this PQC with some two-qubit random state:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "random state:  +0.5890e^(-0.1420πi)|00> +0.4439e^(-0.2940πi)|01> +0.5727e^(-0.7747πi)|10> +0.3577e^(-0.4773πi)|11> \n"
-     ]
-    }
-   ],
-   "source": [
-    "# 2-qubit random state wavefunction from array\n",
-    "rand_array = np.asarray([random.uniform(-1, 1)+1j*random.uniform(-1, 1) for x in range(1,5)])\n",
-    "wfn_rand = tq.QubitWaveFunction.from_array(rand_array)\n",
-    "wfn_rand = wfn_rand.normalize()\n",
-    "print(\"random state: \", wfn_rand)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "And now we can compute the fidelity of these two states:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "fidelity =  0.18646916747892608\n",
-      "fidelity =  0.18646916747892608\n"
-     ]
-    }
-   ],
-   "source": [
-    "# Fidelity method 1: using inner product\n",
-    "wfn_pqc = tq.simulate(pqc, variables=all_values) # compute the PQC wavefunction\n",
-    "fid_rand = abs(wfn_rand.inner(wfn_pqc))**2\n",
-    "print(\"fidelity = \", fid_rand)\n",
-    "\n",
-    "# Fidelity method 2: using the the density matrix as objective\n",
-    "rho_rand = tq.paulis.Projector(wfn=wfn_rand) # density operator target state\n",
-    "fid_pqc = tq.Objective.ExpectationValue(U=pqc, H=rho_rand)\n",
-    "print(\"fidelity = \", tq.simulate(fid_pqc, variables = all_values))"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## State preparation algorithm\n",
-    "\n",
-    "This algorithm minimizes the fidelity between a PQC and a the target state. Since the optimizer only minimizes, we will minimize the infidelity, i.e. $ 1 - F(|\\tilde{\\psi}\\rangle,|\\psi\\rangle)$.\n",
-    "\n",
-    "We can use any of the two methods to compute the infidelity, but it will be more convenient to use the second one.\n",
-    "\n",
-    "The goal of this example is to obtain a quantum circuit that generates the Bell state\n",
-    "$$ |\\tilde{\\psi}\\rangle = \\frac{1}{\\sqrt{2}}\\left(|00\\rangle + |11\\rangle\\right) $$"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Bell state:  +0.7071|00> +0.7071|11> \n"
-     ]
-    }
-   ],
-   "source": [
-    "# Bell state wavefunction from array\n",
-    "bell_array = np.asarray([1,0,0,1])\n",
-    "wfn_bell = tq.QubitWaveFunction.from_array(bell_array)\n",
-    "wfn_bell = wfn_targ.normalize()\n",
-    "print(\"Bell state: \", wfn_bell)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Optimizer: <class 'tequila.optimizers.optimizer_scipy.OptimizerSciPy'> \n",
-      "backend         : qulacs\n",
-      "samples         : None\n",
-      "save_history    : True\n",
-      "noise           : None\n",
-      "\n",
-      "Method          : TNC\n",
-      "Objective       : 1 expectationvalues\n",
-      "bounds          : {theta_0: [0, 6.283185307179586], theta_1: [0, 6.283185307179586], theta_2: [0, 6.283185307179586], theta_3: [0, 6.283185307179586], phi_0: [0, 6.283185307179586], phi_1: [0, 6.283185307179586], phi_2: [0, 6.283185307179586], phi_3: [0, 6.283185307179586], lam_0: [0, 6.283185307179586], lam_1: [0, 6.283185307179586], lam_2: [0, 6.283185307179586], lam_3: [0, 6.283185307179586]}\n",
-      "gradient        : 36 expectationvalues\n",
-      "\n",
-      "active variables : 12\n",
-      "\n",
-      "E=+0.97978838  angles= {theta_1: 0.18708644852210973, phi_2: 0.814058741440068, theta_2: 1.6718785378724963, phi_0: 0.2345203432452239, lam_2: 1.4159205992271224, lam_3: 0.13148303719773408, lam_1: 2.2681484065626556, lam_0: 2.3054575437873366, theta_0: 1.9400742456012434, phi_3: 1.535128381817424, theta_3: 2.9210555160438036, phi_1: 0.3289124675729237}  samples= None\n",
-      "E=+0.97978833  angles= {theta_1: 0.18708646000189555, phi_2: 0.814058833791607, theta_2: 1.6718785383234156, phi_0: 0.23452034324522408, lam_2: 1.415920500429734, lam_3: 0.13148293840034553, lam_1: 2.2681483849790918, lam_0: 2.305457636138876, theta_0: 1.9400743288187945, phi_3: 1.5351284785470272, theta_3: 2.92105543325136, phi_1: 0.3289124675729238}  samples= None\n",
-      "E=+0.85149465  angles= {theta_1: 0.2023641517385193, phi_2: 0.9369634159388589, theta_2: 1.6724786370702835, phi_0: 0.23452034324522408, lam_2: 1.2844375620293884, lam_3: 0.0, lam_1: 2.2394242408406675, lam_0: 2.4283622182861277, theta_0: 2.0508230875941647, phi_3: 1.6638595378398793, theta_3: 2.8108724224129618, phi_1: 0.3289124675729238}  samples= None\n",
-      "E=+0.85149431  angles= {theta_1: 0.2023642802237453, phi_2: 0.9369636874231029, theta_2: 1.6724786704097288, phi_0: 0.23452034324522408, lam_2: 1.2844372717859731, lam_3: 0.0, lam_1: 2.2394241923699836, lam_0: 2.4283624897703713, theta_0: 2.050823147531501, phi_3: 1.6638598242833953, theta_3: 2.8108721796234564, phi_1: 0.3289124675729238}  samples= None\n",
-      "E=+0.81863091  angles= {theta_1: 0.770960170998253, phi_2: 2.138384505960894, theta_2: 1.82001836892913, phi_0: 0.23452034324522408, lam_2: 0.0, lam_3: 0.0, lam_1: 2.0249230194821095, lam_0: 3.6297833083081628, theta_0: 2.3160686088759577, phi_3: 2.931481100380665, theta_3: 1.736436469372996, phi_1: 0.32891246757292425}  samples= None\n",
-      "E=+0.16575584  angles= {theta_1: 0.48666216136838614, phi_2: 1.5376739609498764, theta_2: 1.7462485029997068, phi_0: 0.23452034324522408, lam_2: 0.642218781014694, lam_3: 0.0, lam_1: 2.1321736301613887, lam_0: 3.0290727632971453, theta_0: 2.183445848235061, phi_3: 2.297670319110272, theta_3: 2.273654445892979, phi_1: 0.32891246757292425}  samples= None\n",
-      "E=+0.16575572  angles= {theta_1: 0.48666227262304407, phi_2: 1.5376739611263435, theta_2: 1.7462486073305992, phi_0: 0.23452034324522408, lam_2: 0.6422185127771218, lam_3: 0.0, lam_1: 2.132173524155168, lam_0: 3.029072763473612, theta_0: 2.1834456081792064, phi_3: 2.2976704050408365, theta_3: 2.273654352135036, phi_1: 0.32891246757292425}  samples= None\n",
-      "E=+0.16575582  angles= {theta_1: 0.4866621494975738, phi_2: 1.5376739299684588, theta_2: 1.7462484283132789, phi_0: 0.23452034324522453, lam_2: 0.6422187020957812, lam_3: 0.0, lam_1: 2.132173575551841, lam_0: 3.0290727323157274, theta_0: 2.1834458264374574, phi_3: 2.29767031979944, theta_3: 2.2736544354244668, phi_1: 0.32891246757292425}  samples= None\n",
-      "E=+0.16575574  angles= {theta_1: 0.48666227988751487, phi_2: 1.5376737685485447, theta_2: 1.7462481752768262, phi_0: 0.23452034324522408, lam_2: 0.6422185089202155, lam_3: 0.0, lam_1: 2.1321733759939048, lam_0: 3.0290725708958157, theta_0: 2.1834457798304143, phi_3: 2.2976701916997615, theta_3: 2.273654181670317, phi_1: 0.32891246757292425}  samples= None\n",
-      "E=+0.08113876  angles= {theta_1: 0.5427053432896312, phi_2: 1.3917605441194907, theta_2: 1.499116903717589, phi_0: 0.2345203442100483, lam_2: 0.0, lam_3: 0.0, lam_1: 1.767930638584934, lam_0: 2.8831593468762438, theta_0: 1.8389547309123337, phi_3: 2.387441218774743, theta_3: 2.129888432702298, phi_1: 0.3289124675729247}  samples= None\n",
-      "E=+0.08726450  angles= {theta_1: 0.5146837523290086, phi_2: 1.4647172525346837, theta_2: 1.622682703358648, phi_0: 0.23452034372763642, lam_2: 0.32110939050734677, lam_3: 0.0, lam_1: 1.9500521343731614, lam_0: 2.9561160550866945, theta_0: 2.011200289573697, phi_3: 2.342555768942508, theta_3: 2.2017714392976386, phi_1: 0.3289124675729247}  samples= None\n",
-      "E=+0.07436449  angles= {theta_1: 0.5286945478093199, phi_2: 1.4282388983270873, theta_2: 1.5608998035381185, phi_0: 0.23452034396884214, lam_2: 0.1605546952536736, lam_3: 0.0, lam_1: 1.8589913864790477, lam_0: 2.919637700981469, theta_0: 1.9250775102430155, phi_3: 2.3649984938586255, theta_3: 2.165829935999968, phi_1: 0.3289124675729247}  samples= None\n",
-      "E=+0.07436447  angles= {theta_1: 0.5286945539738492, phi_2: 1.4282388811537676, theta_2: 1.5608997893806995, phi_0: 0.23452034396884214, lam_2: 0.16055465306835526, lam_3: 1.3108153540386525e-07, lam_1: 1.8589913525322808, lam_0: 2.91963768380815, theta_0: 1.9250774762797043, phi_3: 2.3649984869514364, theta_3: 2.165829920201008, phi_1: 0.3289124675729247}  samples= None\n",
-      "E=+0.07436448  angles= {theta_1: 0.5286945569985897, phi_2: 1.4282388919853437, theta_2: 1.5608998117277175, phi_0: 0.2345203439688408, lam_2: 0.1605546850756836, lam_3: 0.0, lam_1: 1.8589913740684647, lam_0: 2.9196376946397256, theta_0: 1.9250774978573206, phi_3: 2.364998484604847, theta_3: 2.1658299247020203, phi_1: 0.3289124675729247}  samples= None\n",
-      "E=+0.07436449  angles= {theta_1: 0.5286945452911498, phi_2: 1.428238899428805, theta_2: 1.5608998006492636, phi_0: 0.23452034396883725, lam_2: 0.16055469563179736, lam_3: 0.0, lam_1: 1.858991377976206, lam_0: 2.9196377020831874, theta_0: 1.9250775002608946, phi_3: 2.36499848958337, theta_3: 2.165829937176665, phi_1: 0.3289124675729247}  samples= None\n",
-      "E=+0.07436449  angles= {theta_1: 0.5286945451915859, phi_2: 1.428238905615189, theta_2: 1.5608998115570107, phi_0: 0.23452034396881904, lam_2: 0.16055470981843056, lam_3: 0.0, lam_1: 1.8589913754294178, lam_0: 2.9196377082695713, theta_0: 1.9250775033341594, phi_3: 2.3649984844601795, theta_3: 2.1658299404436274, phi_1: 0.3289124675729247}  samples= None\n",
-      "E=+0.00709803  angles= {theta_1: 0.5606696392198067, phi_2: 1.3640003738170998, theta_2: 1.529935097807913, phi_0: 0.23452026377458557, lam_2: 0.0, lam_3: 0.2190515959374082, lam_1: 1.5777560538300686, lam_0: 2.855399178375335, theta_0: 1.6224789494137757, phi_3: 2.2321879608371633, theta_3: 2.0777091495701763, phi_1: 0.3289124675729256}  samples= None\n",
-      "E=+0.00709803  angles= {theta_1: 0.5606696392039807, phi_2: 1.364000371409756, theta_2: 1.5299350986021882, phi_0: 0.23452026377458557, lam_2: 0.0, lam_3: 0.2190516011976067, lam_1: 1.577756054985087, lam_0: 2.855399175967991, theta_0: 1.6224789474072632, phi_3: 2.232187956728475, theta_3: 2.077709148018407, phi_1: 0.3289124675729256}  samples= None\n",
-      "E=+0.00709803  angles= {theta_1: 0.5606696404457652, phi_2: 1.3640003758712678, theta_2: 1.5299351003827062, phi_0: 0.23452026377458557, lam_2: 0.0, lam_3: 0.21905159868476298, lam_1: 1.5777560471059562, lam_0: 2.855399180429503, theta_0: 1.6224789469409322, phi_3: 2.232187960753988, theta_3: 2.077709146686549, phi_1: 0.3289124675729256}  samples= None\n",
-      "E=+0.00004723  angles= {theta_1: 0.5682047456782451, phi_2: 1.3432743639677562, theta_2: 1.557352684944983, phi_0: 0.23452026381421165, lam_2: 0.0, lam_3: 0.310121390877224, lam_1: 1.5513916250917585, lam_0: 2.8346731681628277, theta_0: 1.5787249237101468, phi_3: 2.1741055936153617, theta_3: 2.037726258960663, phi_1: 0.3289124675729256}  samples= None\n",
-      "E=+0.00004723  angles= {theta_1: 0.5682047032403403, phi_2: 1.3432744140182464, theta_2: 1.5573526406157854, phi_0: 0.23452026381421165, lam_2: 0.0, lam_3: 0.3101213945509178, lam_1: 1.5513917157632686, lam_0: 2.834673218213318, theta_0: 1.5787247953018517, phi_3: 2.1741056465643167, theta_3: 2.037726285914776, phi_1: 0.3289124675729256}  samples= None\n",
-      "E=+0.00004723  angles= {theta_1: 0.5682047586305501, phi_2: 1.3432743399327565, theta_2: 1.5573527054670637, phi_0: 0.23452026381421165, lam_2: 0.0, lam_3: 0.31012139399891403, lam_1: 1.551391739330553, lam_0: 2.834673144127828, theta_0: 1.5787248270916314, phi_3: 2.174105566104301, theta_3: 2.037726246757807, phi_1: 0.3289124675729256}  samples= None\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "E=+0.00004723  angles= {theta_1: 0.5682047495405631, phi_2: 1.3432743674824092, theta_2: 1.5573526873581178, phi_0: 0.2345202638142112, lam_2: 0.0, lam_3: 0.3101213860430594, lam_1: 1.551391698079409, lam_0: 2.8346731716774802, theta_0: 1.5787249436490394, phi_3: 2.174105598157262, theta_3: 2.0377262555491673, phi_1: 0.3289124675729256}  samples= None\n",
-      "E=+0.00004723  angles= {theta_1: 0.5682047276855315, phi_2: 1.3432743522593686, theta_2: 1.5573526673001021, phi_0: 0.23452026381420987, lam_2: 0.0, lam_3: 0.31012140049050085, lam_1: 1.5513916613688044, lam_0: 2.834673156454439, theta_0: 1.5787249381088497, phi_3: 2.1741055840078936, theta_3: 2.0377262793832838, phi_1: 0.3289124675729256}  samples= None\n",
-      "E=+0.00000001  angles= {theta_1: 0.5670536193843128, phi_2: 1.344372507559821, theta_2: 1.5563466101327212, phi_0: 0.23452026373299661, lam_2: 0.0, lam_3: 0.3100936072527172, lam_1: 1.57078726889731, lam_0: 2.8357713116589265, theta_0: 1.5707849336977442, phi_3: 2.1753215680989224, theta_3: 2.038346318435992, phi_1: 0.3289124675729256}  samples= None\n",
-      "E=+0.00000001  angles= {theta_1: 0.5670536068271934, phi_2: 1.3443725425168338, theta_2: 1.5563466667480204, phi_0: 0.23452026373299661, lam_2: 1.2136837801435263e-07, lam_3: 0.3100937286210952, lam_1: 1.5707872705321904, lam_0: 2.8357713466159393, theta_0: 1.5707849408264822, phi_3: 2.175321526205309, theta_3: 2.038346254387977, phi_1: 0.3289124675729256}  samples= None\n",
-      "E=+0.00000001  angles= {theta_1: 0.5670536225433711, phi_2: 1.3443725161628017, theta_2: 1.5563466125885126, phi_0: 0.23452026373299617, lam_2: 0.0, lam_3: 0.3100936053340444, lam_1: 1.570787270325883, lam_0: 2.8357713202619075, theta_0: 1.5707849375850738, phi_3: 2.175321575631915, theta_3: 2.038346313459311, phi_1: 0.3289124675729256}  samples= None\n",
-      "E=+0.00000000  angles= {theta_1: 0.5670461281848205, phi_2: 1.3444030838073346, theta_2: 1.5563897167244758, phi_0: 0.23452026373288248, lam_2: 8.839510847957754e-05, lam_3: 0.3101820023612252, lam_1: 1.5707892723719388, lam_0: 2.835801887906597, theta_0: 1.5707923609973422, phi_3: 2.175294895597056, theta_3: 2.0382963240591634, phi_1: 0.3289124675729256}  samples= None\n",
-      "E=+0.00000000  angles= {theta_1: 0.5670461281848205, phi_2: 1.3444030838073346, theta_2: 1.5563897167244758, phi_0: 0.23452026373288248, lam_2: 8.839510847957754e-05, lam_3: 0.3101820023612252, lam_1: 1.5707892723719388, lam_0: 2.835801887906597, theta_0: 1.5707923609973422, phi_3: 2.175294895597056, theta_3: 2.0382963240591634, phi_1: 0.3289124675729256}  samples= None\n",
-      "Infidelity =  7.946199254149633e-12\n",
-      "Fidelity =  0.9999999999920538\n",
-      "Execution time:  7.999989986419678  sec\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "None\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "None\n"
-     ]
-    }
-   ],
-   "source": [
-    "rho_bell = tq.paulis.Projector(wfn=wfn_bell) # density operator\n",
-    "\n",
-    "# we take as initial values ther random values generated above\n",
-    "initial_values = all_values\n",
-    "# Infidelity = 1 - Fidelity\n",
-    "inf =  1.0 - tq.Objective.ExpectationValue(U=pqc, H=rho_bell)\n",
-    "\n",
-    "# we can define the bounds on the parameters\n",
-    "# Caution! Not all minimizers accept bounds! In this example, we use 'TNC' minimizer.\n",
-    "# bounds should be defined in a dictionary form, as initial_values\n",
-    "max_angles = 2*np.pi\n",
-    "min_angles = 0\n",
-    "bnds_list = [[min_angles,max_angles]]\n",
-    "for i in range(0, len(all_values)):\n",
-    "    bnds_list.append([min_angles,max_angles])\n",
-    "bnds = dict(zip([str(th[i]) for i in range(0,n_th)],bnds_list))\n",
-    "bnds = {**bnds, **dict(zip([str(phi[i]) for i in range(0,n_phi)],bnds_list))}\n",
-    "bnds = {**bnds, **dict(zip([str(lam[i]) for i in range(0,n_lam)],bnds_list))}\n",
-    "\n",
-    "# set \"silent = True\" to avoid printing all the minimization process\n",
-    "t0 = time.time()\n",
-    "infid = tq.optimizer_scipy.minimize(objective=inf, initial_values=initial_values, method = 'TNC', method_bounds = bnds, silent=True)\n",
-    "t1 = time.time()\n",
-    "\n",
-    "print(\"Infidelity = \", infid.energy)\n",
-    "print(\"Fidelity = \", 1.0-infid.energy)\n",
-    "print(\"Execution time: \", t1-t0, \" sec\" )\n",
-    "\n",
-    "print(infid.history.plot('energies', label='fidelity'))\n",
-    "print(infid.history.plot('angles', label=\"\"))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "# some example on how to use the convenience plotter\n",
-    "infid.history.plot([\"angles\", \"gradients\"], key=[\"lam_1\", \"lam_2\"], labels=[\"\", \"grad\"], title=\"Some Data\", ylim=(-1.0, 3.0), xlim=(-3, 5), loc=\"upper left\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# in case you want to extract the history data\n",
-    "history_phi_0 = infid.history.extract_angles(\"phi_0\")\n",
-    "history_energies = infid.history.extract_energies()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We can check that the final state solution is the Bell state up to a global phase:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "final state solution: \n",
-      "+0.7071e^(+0.6603πi)|00> +0.0000i|10> -0.0000|01> +0.7071e^(+0.6603πi)|11> \n"
-     ]
-    }
-   ],
-   "source": [
-    "wfn_sol = tq.simulate(pqc, variables=infid.angles)\n",
-    "print('final state solution: ')\n",
-    "print(wfn_sol)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "To obtain the angles of the PQC:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "theta_1 : 0.5670461281848205\n",
-       "phi_2 : 1.3444030838073346\n",
-       "theta_2 : 1.5563897167244758\n",
-       "phi_0 : 0.23452026373288248\n",
-       "lam_2 : 8.839510847957754e-05\n",
-       "lam_3 : 0.3101820023612252\n",
-       "lam_1 : 1.5707892723719388\n",
-       "lam_0 : 2.835801887906597\n",
-       "theta_0 : 1.5707923609973422\n",
-       "phi_3 : 2.175294895597056\n",
-       "theta_3 : 2.0382963240591634\n",
-       "phi_1 : 0.3289124675729256"
-      ]
-     },
-     "execution_count": 21,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "infid.angles"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "tqenv",
-   "language": "python",
-   "name": "tqenv"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.7.4"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}
diff --git a/tutorials/data/benzene.xyz b/tutorials/data/benzene.xyz
deleted file mode 100644
index ad8e474b..00000000
--- a/tutorials/data/benzene.xyz
+++ /dev/null
@@ -1,14 +0,0 @@
-12
-benzene CISD/3-21G equilibrium
-C 0.0000  1.4080  0.0000
-C 1.2193  0.7040  0.0000
-C 1.2193  -0.7040 0.0000
-C 0.0000  -1.4080 0.0000
-C -1.2193 -0.7040 0.0000
-C -1.2193 0.7040  0.0000
-H 0.0000  2.4980  0.0000
-H 2.1633  1.2490  0.0000
-H 2.1633  -1.2490 0.0000
-H 0.0000  -2.4980 0.0000
-H -2.1633 -1.2490 0.0000
-H -2.1633 1.2490  0.0000
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diff --git a/tutorials/psi4_pes_scan.py b/tutorials/psi4_pes_scan.py
deleted file mode 100644
index acacad0c..00000000
--- a/tutorials/psi4_pes_scan.py
+++ /dev/null
@@ -1,89 +0,0 @@
-"""
-Non Formatted Psi4 Tutorial
-Get a consistent dissociation curve
-The geometries are in data/h2o_*.xyz
-Psi4 Outputs will also be in data/
-"""
-import psi4
-import tequila as tq
-import matplotlib.pyplot as plt
-import tequila.simulators.simulator_api
-
-import numpy
-
-def generate_h2o_xyz_files(start=0.75, inc=0.05, steps=30):
-    water_geometry = """
-     0 1
-     O
-     H 1 {0}
-     H 1 {0} 2 107.6
-    """
-
-    files = []
-    Rvals = [start + inc * i for i in range(steps)]
-    for i, R in enumerate(Rvals):
-        mol = psi4.geometry(water_geometry.format(R))
-        mol.set_name("R = {}".format(R))
-        name = "data/h2o_{}.xyz".format(i)
-        files.append(name)
-        with open(name, "w") as f:
-            f.write(mol.save_string_xyz_file())
-
-    return files
-
-if __name__ == "__main__":
-
-    # generate files/get list of all generated files
-    files = generate_h2o_xyz_files()
-
-    # define parameters
-    threads = 4 # psi4 threads
-    optimizer_method = "cobyla"
-    active = {"A1": [2, 3], "B1": [0], "B2": [0, 1]} # active space for VQE
-    basis_set = "sto-3g" # basis set
-    transformation = "jordan-wigner" # qubit transformation
-    guess_wfn = None # guess_wfn to ensure convergence along the dissociation curve
-    options = {
-        'reference': 'rhf',
-        'df_scf_guess': 'False',
-        'scf_type': 'direct',
-        'e_convergence': '6',
-        'guess': 'read',
-        "frozen_docc": [2, 0, 0, 0]
-    } # psi4 options
-
-    ref_methods = ["hf", "mp2", "mp3", "ccsd", "fci"] # compute reference values with psi4
-
-    ref_energies = {m: [] for m in ref_methods}
-    energies = []
-
-    # compute stuff
-    for i, file in enumerate(files):
-        if i < 10: break
-        print("computing point {}".format(i))
-        mol = tq.chemistry.Molecule(geometry=file, basis_set=basis_set, transformation=transformation, threads=threads,
-                                    guess_wfn=guess_wfn, options=options, active_orbitals=active)
-        guess_wfn = mol.ref_wfn
-
-        for m in ref_methods:
-            print("computing ", m)
-            try:
-                ref_energies[m] += [mol.compute_energy(method=m, guess_wfn=mol.ref_wfn)]
-            except:
-                ref_energies[m] += [None]
-
-        H = mol.make_hamiltonian()
-        Uhf = mol.prepare_reference()
-
-        # stupid excuse for an vqe, but it tests consistency
-        # just evaluates the hartree fock energy
-        U = Uhf
-        hf = tq.simulate(tq.ExpectationValue(U=U, H=H))
-        energies += [hf]
-
-    plt.plot(energies, label="QHF", marker="o", linestyle="--")
-    for m in ref_methods:
-        values = ref_energies[m]
-        plt.plot(values, label=str(m))
-    plt.legend()
-    plt.show()