VQE_Tutorial_Part5.ipynb

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    "# Tutorial on Variational Quantum Eigensolver (Part V)\n",
    "## Inside the *Qiskit* implementation of VQE\n",
    "\n",
    "---\n",
    "This part of the tutorial is based on the [Max-Cut and Traveling Salesman Problem](https://qiskit.org/documentation/tutorials/optimization/6_examples_max_cut_and_tsp.html) which is part of the IBM Qiskit documentation.\n",
    "\n",
    "During this Tutorial we will use the [VQE implementation of Qiskit](https://qiskit.org/documentation/stubs/qiskit.aqua.algorithms.VQE.html) and investigate what is going on inside. We will use a simple Hamiltonian and problem to explore the VQE. We will use the 'Max-Cut' Problem and the same adjacency matrix we used in previous Notebooks.\n",
    "\n",
    "We attempted to call Real Cloud Devices with the VQE implementation of Qiskit but we enter in a queue of an average 40 min. wait time for each iteration, which makes it impractical. Instead, we keep using the local statevector simulator.\n",
    "\n",
    "When we enable the loggin of the VQE implementation we will see that the actual procedure is very similar to what we saw in the Part II of this Tutorial. The only difference is that you can define the number of levels of Y Rotation gates to generate the Ansatz with variable angles (The function generating it is `TwoLocal`), and that there is a dedicated clasical optimization algorithm [**SPSA**](https://en.wikipedia.org/wiki/Simultaneous_perturbation_stochastic_approximation).\n",
    "\n",
    "\n",
    "## Import libraries \n",
    "\n",
    "We import all necessary functions from IBM qiskit and python **libraries**, that we will later use on this Notebook.\n"
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     "text": [
      "Libraries loaded successfully.\n"
     ]
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    "# Packages to define and plot node network.\n",
    "import numpy as np\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Import Qiskit libraries\n",
    "from qiskit import Aer\n",
    "from qiskit.optimization.applications.ising import max_cut\n",
    "from qiskit.aqua.algorithms import VQE, NumPyMinimumEigensolver\n",
    "from qiskit.aqua.components.optimizers import SPSA\n",
    "from qiskit.aqua import aqua_globals, QuantumInstance\n",
    "from qiskit.circuit.library import TwoLocal\n",
    "from qiskit.optimization.applications.ising.common import sample_most_likely\n",
    "\n",
    "print(\"Libraries loaded successfully.\")\n",
    "\n",
    "# Setup aqua logging\n",
    "import logging\n",
    "from qiskit.aqua import set_qiskit_aqua_logging\n",
    "#set_qiskit_aqua_logging(logging.DEBUG)  # choose INFO, DEBUG to see the log\n",
    "set_qiskit_aqua_logging(logging.INFO)\n",
    "\n",
    "# Call to Real Cloud devices. We will keep commented as this is not efficient for VQE due to long wait times.\n",
    "#from qiskit.providers.ibmq import least_busy\n",
    "#from qiskit.tools.monitor import job_monitor\n",
    "#from qiskit import IBMQ\n",
    "#IBMQ.save_account('b34d54b460e56752c548f81ff431174ddb290d1572bd92a6e92e5a1a5afd830c2cccc4c806a4312f34f429eb372244dd2bea3e5360608e65584d1a9307938914')\n",
    "#IBMQ.load_account()"
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    "## Definition of Graph and Adjacency Matrix\n",
    "\n",
    "We will be coloring the nodes in Red and Blue to separate the $x_i=0$ from the $x_i=1$. \n",
    "\n",
    "We use the same Nodes structure we explored in previous Notebooks (Same Adjacency Matrix)\n"
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     "metadata": {},
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   ],
   "source": [
    "# Generating a graph of 5 nodes\n",
    "\n",
    "n=5 # Number of nodes in graph\n",
    "G=nx.Graph()\n",
    "G.add_nodes_from(np.arange(0,n,1))\n",
    "elist=[(0,1,3.0),(0,2,1.0),(0,3,3.0),(1,4,2.0),(3,4,2.0),(2,3,3.0)]\n",
    "# tuple is (i,j,weight) where (i,j) is the edge\n",
    "\n",
    "G.add_weighted_edges_from(elist)\n",
    "\n",
    "colors = ['r' for node in G.nodes()]\n",
    "pos = nx.spring_layout(G)\n",
    "\n",
    "def draw_graph(G, colors, pos):\n",
    "    default_axes = plt.axes(frameon=True)\n",
    "    nx.draw_networkx(G, node_color=colors, node_size=600, alpha=.8, ax=default_axes, pos=pos)\n",
    "    edge_labels = nx.get_edge_attributes(G, 'weight')\n",
    "    nx.draw_networkx_edge_labels(G, pos=pos, edge_labels=edge_labels)\n",
    "    \n",
    "draw_graph(G, colors, pos)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ajacency Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Adjacency Matrix:\n",
      "\n",
      "[[0. 3. 1. 3. 0.]\n",
      " [3. 0. 0. 0. 2.]\n",
      " [1. 0. 0. 3. 0.]\n",
      " [3. 0. 3. 0. 2.]\n",
      " [0. 2. 0. 2. 0.]]\n"
     ]
    }
   ],
   "source": [
    "# Computing the weight matrix from the random graph\n",
    "w = np.zeros([n,n])\n",
    "for i in range(n):\n",
    "    for j in range(n):\n",
    "        temp = G.get_edge_data(i,j,default=0)\n",
    "        if temp != 0:\n",
    "            w[i,j] = temp['weight']\n",
    "print (\"Adjacency Matrix:\\n\")\n",
    "print(w)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create Max-Cut HAMILTONIAN (OPERATOR)\n",
    "\n",
    "Based on Adjacency Matrix it generates the operator `qubitOp`\n",
    "\n",
    "See the Part II of this tutorial to check what is under the hood."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Offset: -7.0\n",
      "Ising Hamiltonian:\n",
      "IIIZZ\t(1.5+0j)\n",
      "IIZIZ\t(0.5+0j)\n",
      "IZIIZ\t(1.5+0j)\n",
      "IZZII\t(1.5+0j)\n",
      "ZIIZI\t(1+0j)\n",
      "ZZIII\t(1+0j)\n",
      "\n",
      "Each of the rows is a Hamiltonian Sum Term. Total 6 terms with 5 qubits each.\n"
     ]
    }
   ],
   "source": [
    "# Create MaxCut Hamiltonian Operator with Qiskit\n",
    "qubitOp, offset = max_cut.get_operator(w)\n",
    "print('Offset:', offset)\n",
    "print('Ising Hamiltonian:')\n",
    "print(qubitOp.print_details())\n",
    "print('Each of the rows is a Hamiltonian Sum Term. Total 6 terms with 5 qubits each.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Quantum Simulation with VQE\n",
    "\n",
    "Making use of Hamiltonian Operator `qubitOp` as input for the `VQE` qiskit function. \n",
    "\n",
    "Note that we comment out the code that would enable VQE with a Cloud real device. As in previous Notebooks, this procedure shows to be **impractical** as we will enter in around 40m queue wait time for each iteration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2021-02-15 18:02:46,522:qiskit.aqua.quantum_instance:INFO: statevector backend only works with shot=1, changing shots from 1024 to 1.\n",
      "2021-02-15 18:02:46,522:qiskit.aqua.quantum_instance:INFO: \n",
      "Qiskit Terra version: 0.16.1\n",
      "Backend: 'statevector_simulator (AerProvider)', with following setting:\n",
      "{'basis_gates': ['u1', 'u2', 'u3', 'u', 'p', 'r', 'rx', 'ry', 'rz', 'id', 'x', 'y', 'z', 'h', 's', 'sdg', 'sx', 't', 'tdg', 'swap', 'cx', 'cy', 'cz', 'csx', 'cp', 'cu1', 'cu2', 'cu3', 'rxx', 'ryy', 'rzz', 'rzx', 'ccx', 'cswap', 'mcx', 'mcy', 'mcz', 'mcsx', 'mcp', 'mcu1', 'mcu2', 'mcu3', 'mcrx', 'mcry', 'mcrz', 'mcr', 'mcswap', 'unitary', 'diagonal', 'multiplexer', 'initialize', 'kraus', 'roerror', 'delay'], 'coupling_map': None}\n",
      "{'initial_layout': None, 'seed_transpiler': 10598, 'optimization_level': None}\n",
      "RunConfig(max_credits=10, seed_simulator=10598, shots=1)\n",
      "{'timeout': None}\n",
      "{}\n",
      "{}\n",
      "Measurement mitigation: None\n",
      "2021-02-15 18:02:46,552:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: \n",
      "==================== Setting of VQE ============================\n",
      "Algorithm: VQE\n",
      "-- max_evals_grouped: 1\n",
      "-- circuit_sampler: <qiskit.aqua.operators.converters.circuit_sampler.CircuitSampler object at 0x000001CA1BBDA100>\n",
      "-- expectation: <qiskit.aqua.operators.expectations.matrix_expectation.MatrixExpectation object at 0x000001CA1BBDA310>\n",
      "-- user_valid_expectation: False\n",
      "-- include_custom: False\n",
      "-- expect_op: None\n",
      "-- operator: SummedOp([\n",
      "  1.5 * IIIZZ,\n",
      "  0.5 * IIZIZ,\n",
      "  1.5 * IZIIZ,\n",
      "  1.5 * IZZII,\n",
      "  ZIIZI,\n",
      "  ZZIII\n",
      "])\n",
      "-- quantum_instance: \n",
      "Qiskit Terra version: 0.16.1\n",
      "Backend: 'statevector_simulator (AerProvider)', with following setting:\n",
      "{'basis_gates': ['u1', 'u2', 'u3', 'u', 'p', 'r', 'rx', 'ry', 'rz', 'id', 'x', 'y', 'z', 'h', 's', 'sdg', 'sx', 't', 'tdg', 'swap', 'cx', 'cy', 'cz', 'csx', 'cp', 'cu1', 'cu2', 'cu3', 'rxx', 'ryy', 'rzz', 'rzx', 'ccx', 'cswap', 'mcx', 'mcy', 'mcz', 'mcsx', 'mcp', 'mcu1', 'mcu2', 'mcu3', 'mcrx', 'mcry', 'mcrz', 'mcr', 'mcswap', 'unitary', 'diagonal', 'multiplexer', 'initialize', 'kraus', 'roerror', 'delay'], 'coupling_map': None}\n",
      "{'initial_layout': None, 'seed_transpiler': 10598, 'optimization_level': None}\n",
      "RunConfig(max_credits=10, seed_simulator=10598, shots=1)\n",
      "{'timeout': None}\n",
      "{}\n",
      "{}\n",
      "Measurement mitigation: None\n",
      "-- optimizer: <qiskit.aqua.components.optimizers.spsa.SPSA object at 0x000001CA1B444670>\n",
      "-- gradient: None\n",
      "-- cost_fn: <bound method VQE._energy_evaluation of <qiskit.aqua.algorithms.minimum_eigen_solvers.vqe.VQE object at 0x000001CA1BAF4130>>\n",
      "-- initial_point: Random seed\n",
      "-- var_form:      ┌──────────┐   ┌──────────┐                        ┌───────────┐»\n",
      "q_0: ┤ RY(θ[0]) ├─■─┤ RY(θ[5]) ├─────────────────■──────┤ RY(θ[10]) ├»\n",
      "     ├──────────┤ │ └──────────┘┌──────────┐     │      └───────────┘»\n",
      "q_1: ┤ RY(θ[1]) ├─■──────■──────┤ RY(θ[6]) ├─────■────────────■──────»\n",
      "     ├──────────┤        │      └──────────┘┌──────────┐      │      »\n",
      "q_2: ┤ RY(θ[2]) ├────────■───────────■──────┤ RY(θ[7]) ├──────■──────»\n",
      "     ├──────────┤                    │      └──────────┘ ┌──────────┐»\n",
      "q_3: ┤ RY(θ[3]) ├────────────────────■───────────■───────┤ RY(θ[8]) ├»\n",
      "     ├──────────┤                                │       ├──────────┤»\n",
      "q_4: ┤ RY(θ[4]) ├────────────────────────────────■───────┤ RY(θ[9]) ├»\n",
      "     └──────────┘                                        └──────────┘»\n",
      "«                               ┌───────────┐                          »\n",
      "«q_0: ───────────────────■──────┤ RY(θ[15]) ├───────────────────■──────»\n",
      "«     ┌───────────┐      │      └───────────┘┌───────────┐      │      »\n",
      "«q_1: ┤ RY(θ[11]) ├──────■────────────■──────┤ RY(θ[16]) ├──────■──────»\n",
      "«     └───────────┘┌───────────┐      │      └───────────┘┌───────────┐»\n",
      "«q_2: ──────■──────┤ RY(θ[12]) ├──────■────────────■──────┤ RY(θ[17]) ├»\n",
      "«           │      └───────────┘┌───────────┐      │      └───────────┘»\n",
      "«q_3: ──────■────────────■──────┤ RY(θ[13]) ├──────■────────────■──────»\n",
      "«                        │      ├───────────┤                   │      »\n",
      "«q_4: ───────────────────■──────┤ RY(θ[14]) ├───────────────────■──────»\n",
      "«                               └───────────┘                          »\n",
      "«     ┌───────────┐                                       \n",
      "«q_0: ┤ RY(θ[20]) ├───────────────────────────────────────\n",
      "«     └───────────┘┌───────────┐                          \n",
      "«q_1: ──────■──────┤ RY(θ[21]) ├──────────────────────────\n",
      "«           │      └───────────┘┌───────────┐             \n",
      "«q_2: ──────■────────────■──────┤ RY(θ[22]) ├─────────────\n",
      "«     ┌───────────┐      │      └───────────┘┌───────────┐\n",
      "«q_3: ┤ RY(θ[18]) ├──────■────────────■──────┤ RY(θ[23]) ├\n",
      "«     ├───────────┤                   │      ├───────────┤\n",
      "«q_4: ┤ RY(θ[19]) ├───────────────────■──────┤ RY(θ[24]) ├\n",
      "«     └───────────┘                          └───────────┘\n",
      "-- var_form_params: [Parameter(θ[0]), Parameter(θ[10]), Parameter(θ[11]), Parameter(θ[12]), Parameter(θ[13]), Parameter(θ[14]), Parameter(θ[15]), Parameter(θ[16]), Parameter(θ[17]), Parameter(θ[18]), Parameter(θ[19]), Parameter(θ[1]), Parameter(θ[20]), Parameter(θ[21]), Parameter(θ[22]), Parameter(θ[23]), Parameter(θ[24]), Parameter(θ[2]), Parameter(θ[3]), Parameter(θ[4]), Parameter(θ[5]), Parameter(θ[6]), Parameter(θ[7]), Parameter(θ[8]), Parameter(θ[9])]\n",
      "-- parameterized_circuits: None\n",
      "-- ret: None\n",
      "-- eval_time: None\n",
      "-- callback: None\n",
      "-- aux_op_nones: []\n",
      "-- aux_operators: []\n",
      "-- eval_count: 0\n",
      "===============================================================\n",
      "NLocal: TwoLocal\n",
      "-- data: [(<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBD8670>, [Qubit(QuantumRegister(5, 'q'), 0)], []), (<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBD86A0>, [Qubit(QuantumRegister(5, 'q'), 1)], []), (<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBD8760>, [Qubit(QuantumRegister(5, 'q'), 2)], []), (<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBD87C0>, [Qubit(QuantumRegister(5, 'q'), 3)], []), (<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBD8820>, [Qubit(QuantumRegister(5, 'q'), 4)], []), (<qiskit.circuit.library.standard_gates.z.CZGate object at 0x000001CA1BBD8850>, [Qubit(QuantumRegister(5, 'q'), 0), Qubit(QuantumRegister(5, 'q'), 1)], []), (<qiskit.circuit.library.standard_gates.z.CZGate object at 0x000001CA1BBD8520>, [Qubit(QuantumRegister(5, 'q'), 1), Qubit(QuantumRegister(5, 'q'), 2)], []), (<qiskit.circuit.library.standard_gates.z.CZGate object at 0x000001CA1BBD8490>, [Qubit(QuantumRegister(5, 'q'), 2), Qubit(QuantumRegister(5, 'q'), 3)], []), (<qiskit.circuit.library.standard_gates.z.CZGate object at 0x000001CA1BBD84F0>, [Qubit(QuantumRegister(5, 'q'), 3), Qubit(QuantumRegister(5, 'q'), 4)], []), (<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBD8AC0>, [Qubit(QuantumRegister(5, 'q'), 0)], []), (<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBD8B20>, [Qubit(QuantumRegister(5, 'q'), 1)], []), (<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBD8B80>, [Qubit(QuantumRegister(5, 'q'), 2)], []), (<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBD8BE0>, [Qubit(QuantumRegister(5, 'q'), 3)], []), (<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBD8970>, [Qubit(QuantumRegister(5, 'q'), 4)], []), (<qiskit.circuit.library.standard_gates.z.CZGate object at 0x000001CA1BBD8C40>, [Qubit(QuantumRegister(5, 'q'), 0), Qubit(QuantumRegister(5, 'q'), 1)], []), (<qiskit.circuit.library.standard_gates.z.CZGate object at 0x000001CA1BBD8190>, [Qubit(QuantumRegister(5, 'q'), 1), Qubit(QuantumRegister(5, 'q'), 2)], []), (<qiskit.circuit.library.standard_gates.z.CZGate object at 0x000001CA1BBD8430>, [Qubit(QuantumRegister(5, 'q'), 2), Qubit(QuantumRegister(5, 'q'), 3)], []), (<qiskit.circuit.library.standard_gates.z.CZGate object at 0x000001CA1BBD89A0>, [Qubit(QuantumRegister(5, 'q'), 3), Qubit(QuantumRegister(5, 'q'), 4)], []), (<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBD8F70>, [Qubit(QuantumRegister(5, 'q'), 0)], []), (<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBD8040>, [Qubit(QuantumRegister(5, 'q'), 1)], []), (<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBD8D60>, [Qubit(QuantumRegister(5, 'q'), 2)], []), (<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBD8130>, [Qubit(QuantumRegister(5, 'q'), 3)], []), (<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBD8F40>, [Qubit(QuantumRegister(5, 'q'), 4)], []), (<qiskit.circuit.library.standard_gates.z.CZGate object at 0x000001CA1BBD8910>, [Qubit(QuantumRegister(5, 'q'), 0), Qubit(QuantumRegister(5, 'q'), 1)], []), (<qiskit.circuit.library.standard_gates.z.CZGate object at 0x000001CA1BBD80A0>, [Qubit(QuantumRegister(5, 'q'), 1), Qubit(QuantumRegister(5, 'q'), 2)], []), (<qiskit.circuit.library.standard_gates.z.CZGate object at 0x000001CA1BBDD070>, [Qubit(QuantumRegister(5, 'q'), 2), Qubit(QuantumRegister(5, 'q'), 3)], []), (<qiskit.circuit.library.standard_gates.z.CZGate object at 0x000001CA1BBDD100>, [Qubit(QuantumRegister(5, 'q'), 3), Qubit(QuantumRegister(5, 'q'), 4)], []), (<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBDD280>, [Qubit(QuantumRegister(5, 'q'), 0)], []), (<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBDD2E0>, [Qubit(QuantumRegister(5, 'q'), 1)], []), (<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BABF0D0>, [Qubit(QuantumRegister(5, 'q'), 2)], []), (<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001C9C2613EE0>, [Qubit(QuantumRegister(5, 'q'), 3)], []), (<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBDD220>, [Qubit(QuantumRegister(5, 'q'), 4)], []), (<qiskit.circuit.library.standard_gates.z.CZGate object at 0x000001CA1BBDD310>, [Qubit(QuantumRegister(5, 'q'), 0), Qubit(QuantumRegister(5, 'q'), 1)], []), (<qiskit.circuit.library.standard_gates.z.CZGate object at 0x000001CA1BBD85E0>, [Qubit(QuantumRegister(5, 'q'), 1), Qubit(QuantumRegister(5, 'q'), 2)], []), (<qiskit.circuit.library.standard_gates.z.CZGate object at 0x000001CA1BBDD370>, [Qubit(QuantumRegister(5, 'q'), 2), Qubit(QuantumRegister(5, 'q'), 3)], []), (<qiskit.circuit.library.standard_gates.z.CZGate object at 0x000001CA1BBDD400>, [Qubit(QuantumRegister(5, 'q'), 3), Qubit(QuantumRegister(5, 'q'), 4)], []), (<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBDD580>, [Qubit(QuantumRegister(5, 'q'), 0)], []), (<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBDD5E0>, [Qubit(QuantumRegister(5, 'q'), 1)], []), (<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBDD640>, [Qubit(QuantumRegister(5, 'q'), 2)], []), (<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBDD6A0>, [Qubit(QuantumRegister(5, 'q'), 3)], []), (<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBDD700>, [Qubit(QuantumRegister(5, 'q'), 4)], [])]\n",
      "-- qregs: [QuantumRegister(5, 'q')]\n",
      "-- qubits: [Qubit(QuantumRegister(5, 'q'), 0), Qubit(QuantumRegister(5, 'q'), 1), Qubit(QuantumRegister(5, 'q'), 2), Qubit(QuantumRegister(5, 'q'), 3), Qubit(QuantumRegister(5, 'q'), 4)]\n",
      "-- parameter_table: ParameterTable({Parameter(θ[0]): [(<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBD8670>, 0)], Parameter(θ[1]): [(<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBD86A0>, 0)], Parameter(θ[2]): [(<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBD8760>, 0)], Parameter(θ[3]): [(<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBD87C0>, 0)], Parameter(θ[4]): [(<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBD8820>, 0)], Parameter(θ[5]): [(<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBD8AC0>, 0)], Parameter(θ[6]): [(<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBD8B20>, 0)], Parameter(θ[7]): [(<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBD8B80>, 0)], Parameter(θ[8]): [(<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBD8BE0>, 0)], Parameter(θ[9]): [(<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBD8970>, 0)], Parameter(θ[10]): [(<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBD8F70>, 0)], Parameter(θ[11]): [(<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBD8040>, 0)], Parameter(θ[12]): [(<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBD8D60>, 0)], Parameter(θ[13]): [(<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBD8130>, 0)], Parameter(θ[14]): [(<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBD8F40>, 0)], Parameter(θ[15]): [(<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBDD280>, 0)], Parameter(θ[16]): [(<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBDD2E0>, 0)], Parameter(θ[17]): [(<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BABF0D0>, 0)], Parameter(θ[18]): [(<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001C9C2613EE0>, 0)], Parameter(θ[19]): [(<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBDD220>, 0)], Parameter(θ[20]): [(<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBDD580>, 0)], Parameter(θ[21]): [(<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBDD5E0>, 0)], Parameter(θ[22]): [(<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBDD640>, 0)], Parameter(θ[23]): [(<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBDD6A0>, 0)], Parameter(θ[24]): [(<qiskit.circuit.library.standard_gates.ry.RYGate object at 0x000001CA1BBDD700>, 0)]})\n",
      "-- clbits: []\n",
      "-- ancillas: []\n",
      "-- calibrations: defaultdict(<class 'dict'>, {})\n",
      "-- layout: None\n",
      "-- global_phase: 0\n",
      "-- cregs: []\n",
      "-- num_qubits: 5\n",
      "-- insert_barriers: False\n",
      "-- reps: 4\n",
      "-- entanglement_blocks: [<qiskit.circuit.quantumcircuit.QuantumCircuit object at 0x000001CA1BBDAA30>]\n",
      "-- rotation_blocks: [<qiskit.circuit.quantumcircuit.QuantumCircuit object at 0x000001CA1BBDAC40>]\n",
      "-- prepended_blocks: []\n",
      "-- prepended_entanglement: []\n",
      "-- appended_blocks: []\n",
      "-- appended_entanglement: []\n",
      "-- entanglement: linear\n",
      "-- entangler_maps: None\n",
      "-- ordered_parameters: θ, ['θ[0]', 'θ[1]', 'θ[2]', 'θ[3]', 'θ[4]', 'θ[5]', 'θ[6]', 'θ[7]', 'θ[8]', 'θ[9]', 'θ[10]', 'θ[11]', 'θ[12]', 'θ[13]', 'θ[14]', 'θ[15]', 'θ[16]', 'θ[17]', 'θ[18]', 'θ[19]', 'θ[20]', 'θ[21]', 'θ[22]', 'θ[23]', 'θ[24]']\n",
      "-- overwrite_block_parameters: True\n",
      "-- skip_final_rotation_layer: False\n",
      "-- skip_unentangled_qubits: False\n",
      "-- initial_state: None\n",
      "-- initial_state_circuit: None\n",
      "-- bounds: None\n",
      "===============================================================\n",
      "Optimizer: SPSA\n",
      "-- gradient_support_level: 1\n",
      "-- bounds_support_level: 1\n",
      "-- initial_point_support_level: 3\n",
      "-- options: {'save_steps': 1, 'last_avg': 1}\n",
      "-- max_evals_grouped: 1\n",
      "-- maxiter: 64\n",
      "-- parameters: [0.62831853 0.1        0.602      0.101      0.        ]\n",
      "-- skip_calibration: False\n",
      "===============================================================\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2021-02-15 18:02:46,553:qiskit.aqua.algorithms.vq_algorithm:INFO: Starting optimizer.\n",
      "bounds=[(None, None), (None, None), (None, None), (None, None), (None, None), (None, None), (None, None), (None, None), (None, None), (None, None), (None, None), (None, None), (None, None), (None, None), (None, None), (None, None), (None, None), (None, None), (None, None), (None, None), (None, None), (None, None), (None, None), (None, None), (None, None)]\n",
      "initial point=[ 2.2915011  -5.60685044 -3.51406148 -3.9663008  -4.07268656  3.92189524\n",
      "  5.31991014 -2.80764892  4.01815433  4.89953608  0.16299155 -3.20486934\n",
      "  4.07454007 -3.59696069  3.03436447  1.63287677  5.37095801 -3.36894106\n",
      "  3.75891723  0.22826859 -3.37337151 -4.19837424 -0.02778464  1.03954849\n",
      " -3.96672584]\n",
      "2021-02-15 18:02:46,574:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [0.46875856] - 11.98983 (ms), eval count: 1\n",
      "2021-02-15 18:02:46,579:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-0.54378374] - 3.99828 (ms), eval count: 2\n",
      "2021-02-15 18:02:46,584:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [0.13970821] - 3.99899 (ms), eval count: 3\n",
      "2021-02-15 18:02:46,590:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-0.18135665] - 4.99916 (ms), eval count: 4\n",
      "2021-02-15 18:02:46,596:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-0.19282777] - 5.00393 (ms), eval count: 5\n",
      "2021-02-15 18:02:46,603:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [0.02112877] - 5.99957 (ms), eval count: 6\n",
      "2021-02-15 18:02:46,611:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-0.12358775] - 6.99925 (ms), eval count: 7\n",
      "2021-02-15 18:02:46,616:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-0.10547508] - 3.99947 (ms), eval count: 8\n",
      "2021-02-15 18:02:46,622:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [0.29447576] - 5.00035 (ms), eval count: 9\n",
      "2021-02-15 18:02:46,630:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-0.36717903] - 6.00100 (ms), eval count: 10\n",
      "2021-02-15 18:02:46,637:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-0.10268337] - 5.99933 (ms), eval count: 11\n",
      "2021-02-15 18:02:46,646:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [0.02567637] - 6.99449 (ms), eval count: 12\n",
      "2021-02-15 18:02:46,652:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [0.20521067] - 3.99923 (ms), eval count: 13\n",
      "2021-02-15 18:02:46,659:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-0.59606011] - 6.00362 (ms), eval count: 14\n",
      "2021-02-15 18:02:46,665:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [0.90603951] - 5.00298 (ms), eval count: 15\n",
      "2021-02-15 18:02:46,670:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-0.9563071] - 3.99566 (ms), eval count: 16\n",
      "2021-02-15 18:02:46,679:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [0.95804869] - 8.00276 (ms), eval count: 17\n",
      "2021-02-15 18:02:46,683:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-0.93946893] - 4.03070 (ms), eval count: 18\n",
      "2021-02-15 18:02:46,689:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [0.37896031] - 4.96435 (ms), eval count: 19\n",
      "2021-02-15 18:02:46,697:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-0.8172849] - 5.99861 (ms), eval count: 20\n",
      "2021-02-15 18:02:46,703:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [0.06676256] - 4.99773 (ms), eval count: 21\n",
      "2021-02-15 18:02:46,711:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-0.34072129] - 6.96826 (ms), eval count: 22\n",
      "2021-02-15 18:02:46,718:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-0.7902425] - 5.00107 (ms), eval count: 23\n",
      "2021-02-15 18:02:46,725:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [0.83573262] - 5.99742 (ms), eval count: 24\n",
      "2021-02-15 18:02:46,732:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [0.35218829] - 6.03700 (ms), eval count: 25\n",
      "2021-02-15 18:02:46,737:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-0.47324308] - 4.00066 (ms), eval count: 26\n",
      "2021-02-15 18:02:46,745:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-0.14175306] - 7.00045 (ms), eval count: 27\n",
      "2021-02-15 18:02:46,750:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-0.31113825] - 4.02832 (ms), eval count: 28\n",
      "2021-02-15 18:02:46,758:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-0.58817975] - 6.00052 (ms), eval count: 29\n",
      "2021-02-15 18:02:46,764:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [0.02288634] - 4.96650 (ms), eval count: 30\n",
      "2021-02-15 18:02:46,769:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-1.05135803] - 4.02951 (ms), eval count: 31\n",
      "2021-02-15 18:02:46,776:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-0.66540644] - 6.03127 (ms), eval count: 32\n",
      "2021-02-15 18:02:46,782:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-0.91553331] - 4.99892 (ms), eval count: 33\n",
      "2021-02-15 18:02:46,789:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-1.37859586] - 6.00290 (ms), eval count: 34\n",
      "2021-02-15 18:02:46,800:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-1.21001576] - 9.03893 (ms), eval count: 35\n",
      "2021-02-15 18:02:46,806:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-1.85653848] - 4.99845 (ms), eval count: 36\n",
      "2021-02-15 18:02:46,812:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-2.21834402] - 3.99828 (ms), eval count: 37\n",
      "2021-02-15 18:02:46,818:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-2.0189316] - 4.99892 (ms), eval count: 38\n",
      "2021-02-15 18:02:46,825:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-2.01912534] - 6.00338 (ms), eval count: 39\n",
      "2021-02-15 18:02:46,833:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-2.29667971] - 5.99885 (ms), eval count: 40\n",
      "2021-02-15 18:02:46,842:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-2.1465122] - 7.00402 (ms), eval count: 41\n",
      "2021-02-15 18:02:46,851:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-2.31156419] - 6.99878 (ms), eval count: 42\n",
      "2021-02-15 18:02:46,857:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-2.39436059] - 4.99868 (ms), eval count: 43\n",
      "2021-02-15 18:02:46,864:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-2.21292955] - 5.00107 (ms), eval count: 44\n",
      "2021-02-15 18:02:46,871:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-2.4512306] - 4.99964 (ms), eval count: 45\n",
      "2021-02-15 18:02:46,879:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-2.20638296] - 6.00028 (ms), eval count: 46\n",
      "2021-02-15 18:02:46,885:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-2.26456851] - 4.99320 (ms), eval count: 47\n",
      "2021-02-15 18:02:46,891:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-2.41359442] - 5.00059 (ms), eval count: 48\n",
      "2021-02-15 18:02:46,899:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-2.6093985] - 5.99861 (ms), eval count: 49\n",
      "2021-02-15 18:02:46,904:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-2.17331313] - 3.99852 (ms), eval count: 50\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2021-02-15 18:02:46,914:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-2.69387095] - 6.99782 (ms), eval count: 51\n",
      "2021-02-15 18:02:46,921:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-2.37979039] - 5.99813 (ms), eval count: 52\n",
      "2021-02-15 18:02:46,931:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-2.00396105] - 7.00212 (ms), eval count: 53\n",
      "2021-02-15 18:02:46,938:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-3.26204899] - 5.00035 (ms), eval count: 54\n",
      "2021-02-15 18:02:46,945:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-4.2545141] - 4.98509 (ms), eval count: 55\n",
      "2021-02-15 18:02:46,951:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-3.45788779] - 5.00035 (ms), eval count: 56\n",
      "2021-02-15 18:02:46,959:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-4.11204391] - 7.00092 (ms), eval count: 57\n",
      "2021-02-15 18:02:46,967:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-4.44989648] - 6.99759 (ms), eval count: 58\n",
      "2021-02-15 18:02:46,974:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-4.32892128] - 6.00028 (ms), eval count: 59\n",
      "2021-02-15 18:02:46,981:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-4.40388117] - 5.00536 (ms), eval count: 60\n",
      "2021-02-15 18:02:46,988:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-3.90335974] - 4.99940 (ms), eval count: 61\n",
      "2021-02-15 18:02:46,996:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-4.70932095] - 6.00028 (ms), eval count: 62\n",
      "2021-02-15 18:02:47,002:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-4.03533854] - 3.99899 (ms), eval count: 63\n",
      "2021-02-15 18:02:47,009:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-4.78308378] - 5.99980 (ms), eval count: 64\n",
      "2021-02-15 18:02:47,015:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.04742369] - 4.99916 (ms), eval count: 65\n",
      "2021-02-15 18:02:47,021:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-4.19014673] - 3.99709 (ms), eval count: 66\n",
      "2021-02-15 18:02:47,029:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-4.90081622] - 7.49850 (ms), eval count: 67\n",
      "2021-02-15 18:02:47,035:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.22314126] - 3.99923 (ms), eval count: 68\n",
      "2021-02-15 18:02:47,040:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.0520062] - 4.00209 (ms), eval count: 69\n",
      "2021-02-15 18:02:47,046:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.05565698] - 3.99876 (ms), eval count: 70\n",
      "2021-02-15 18:02:47,052:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.27467276] - 5.00107 (ms), eval count: 71\n",
      "2021-02-15 18:02:47,057:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.12063902] - 3.99709 (ms), eval count: 72\n",
      "2021-02-15 18:02:47,063:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-4.95474754] - 4.99797 (ms), eval count: 73\n",
      "2021-02-15 18:02:47,070:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.36648762] - 5.02586 (ms), eval count: 74\n",
      "2021-02-15 18:02:47,076:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.51856246] - 5.99980 (ms), eval count: 75\n",
      "2021-02-15 18:02:47,081:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.02763663] - 4.03523 (ms), eval count: 76\n",
      "2021-02-15 18:02:47,089:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.2659848] - 6.99854 (ms), eval count: 77\n",
      "2021-02-15 18:02:47,099:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.5204849] - 8.99935 (ms), eval count: 78\n",
      "2021-02-15 18:02:47,110:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.35050275] - 9.00006 (ms), eval count: 79\n",
      "2021-02-15 18:02:47,124:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.25934838] - 10.99920 (ms), eval count: 80\n",
      "2021-02-15 18:02:47,132:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.31360273] - 6.99759 (ms), eval count: 81\n",
      "2021-02-15 18:02:47,141:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.23813994] - 8.00133 (ms), eval count: 82\n",
      "2021-02-15 18:02:47,148:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.31612208] - 4.99701 (ms), eval count: 83\n",
      "2021-02-15 18:02:47,154:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.57459839] - 3.99995 (ms), eval count: 84\n",
      "2021-02-15 18:02:47,161:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.31095881] - 5.99957 (ms), eval count: 85\n",
      "2021-02-15 18:02:47,171:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.57608788] - 6.99949 (ms), eval count: 86\n",
      "2021-02-15 18:02:47,177:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.66331446] - 4.99940 (ms), eval count: 87\n",
      "2021-02-15 18:02:47,183:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.32649423] - 5.00035 (ms), eval count: 88\n",
      "2021-02-15 18:02:47,192:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.57953967] - 6.99997 (ms), eval count: 89\n",
      "2021-02-15 18:02:47,199:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.43957525] - 5.02968 (ms), eval count: 90\n",
      "2021-02-15 18:02:47,206:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.57523292] - 5.97286 (ms), eval count: 91\n",
      "2021-02-15 18:02:47,212:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.50437107] - 5.00083 (ms), eval count: 92\n",
      "2021-02-15 18:02:47,218:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.30830549] - 4.99964 (ms), eval count: 93\n",
      "2021-02-15 18:02:47,225:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.6567933] - 5.99957 (ms), eval count: 94\n",
      "2021-02-15 18:02:47,230:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.49196773] - 3.99828 (ms), eval count: 95\n",
      "2021-02-15 18:02:47,237:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.5573201] - 4.99821 (ms), eval count: 96\n",
      "2021-02-15 18:02:47,246:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.62934854] - 8.00538 (ms), eval count: 97\n",
      "2021-02-15 18:02:47,252:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.62668926] - 5.00011 (ms), eval count: 98\n",
      "2021-02-15 18:02:47,258:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.2908638] - 4.99964 (ms), eval count: 99\n",
      "2021-02-15 18:02:47,265:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.52675823] - 4.99606 (ms), eval count: 100\n",
      "2021-02-15 18:02:47,270:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.73738641] - 3.99995 (ms), eval count: 101\n",
      "2021-02-15 18:02:47,277:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.51771034] - 4.99821 (ms), eval count: 102\n",
      "2021-02-15 18:02:47,283:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.45033844] - 3.99542 (ms), eval count: 103\n",
      "2021-02-15 18:02:47,290:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.45666547] - 5.99885 (ms), eval count: 104\n",
      "2021-02-15 18:02:47,298:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.66772271] - 7.00164 (ms), eval count: 105\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2021-02-15 18:02:47,303:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.48487554] - 3.99923 (ms), eval count: 106\n",
      "2021-02-15 18:02:47,312:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.72072047] - 6.99544 (ms), eval count: 107\n",
      "2021-02-15 18:02:47,318:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.67067774] - 4.99678 (ms), eval count: 108\n",
      "2021-02-15 18:02:47,327:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.62404974] - 6.99735 (ms), eval count: 109\n",
      "2021-02-15 18:02:47,334:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.75533053] - 4.99892 (ms), eval count: 110\n",
      "2021-02-15 18:02:47,340:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.56742519] - 5.00131 (ms), eval count: 111\n",
      "2021-02-15 18:02:47,347:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.5833857] - 6.07109 (ms), eval count: 112\n",
      "2021-02-15 18:02:47,347:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.18057787] - 0.00000 (ms), eval count: 113\n",
      "2021-02-15 18:02:47,360:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.76431002] - 4.99868 (ms), eval count: 114\n",
      "2021-02-15 18:02:47,367:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.67942628] - 4.99749 (ms), eval count: 115\n",
      "2021-02-15 18:02:47,373:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.7177497] - 5.01299 (ms), eval count: 116\n",
      "2021-02-15 18:02:47,380:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.6085959] - 4.99964 (ms), eval count: 117\n",
      "2021-02-15 18:02:47,386:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.57598215] - 5.00059 (ms), eval count: 118\n",
      "2021-02-15 18:02:47,392:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.61505521] - 4.99988 (ms), eval count: 119\n",
      "2021-02-15 18:02:47,398:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.67925] - 3.99804 (ms), eval count: 120\n",
      "2021-02-15 18:02:47,403:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.5558349] - 3.99995 (ms), eval count: 121\n",
      "2021-02-15 18:02:47,411:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.47266701] - 5.00131 (ms), eval count: 122\n",
      "2021-02-15 18:02:47,416:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.64398446] - 3.99923 (ms), eval count: 123\n",
      "2021-02-15 18:02:47,422:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.55573521] - 5.00464 (ms), eval count: 124\n",
      "2021-02-15 18:02:47,429:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.80970743] - 3.99804 (ms), eval count: 125\n",
      "2021-02-15 18:02:47,435:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.62468239] - 5.00083 (ms), eval count: 126\n",
      "2021-02-15 18:02:47,442:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.77375542] - 6.00314 (ms), eval count: 127\n",
      "2021-02-15 18:02:47,448:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.58520099] - 3.99899 (ms), eval count: 128\n",
      "2021-02-15 18:02:47,454:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.81138542] - 4.00019 (ms), eval count: 129\n",
      "2021-02-15 18:02:47,462:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.71841985] - 6.99544 (ms), eval count: 130\n",
      "2021-02-15 18:02:47,467:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.82000516] - 4.00281 (ms), eval count: 131\n",
      "2021-02-15 18:02:47,474:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.55008804] - 4.99916 (ms), eval count: 132\n",
      "2021-02-15 18:02:47,480:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.62979927] - 4.99845 (ms), eval count: 133\n",
      "2021-02-15 18:02:47,487:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.71565626] - 4.99630 (ms), eval count: 134\n",
      "2021-02-15 18:02:47,494:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.8112172] - 6.00386 (ms), eval count: 135\n",
      "2021-02-15 18:02:47,500:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.60176716] - 4.99773 (ms), eval count: 136\n",
      "2021-02-15 18:02:47,507:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.6579717] - 5.00250 (ms), eval count: 137\n",
      "2021-02-15 18:02:47,512:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.71686662] - 3.99685 (ms), eval count: 138\n",
      "2021-02-15 18:02:47,518:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.75862242] - 3.99733 (ms), eval count: 139\n",
      "2021-02-15 18:02:47,525:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.79492531] - 5.99980 (ms), eval count: 140\n",
      "2021-02-15 18:02:47,532:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.75131574] - 4.99797 (ms), eval count: 141\n",
      "2021-02-15 18:02:47,538:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.75883019] - 4.99940 (ms), eval count: 142\n",
      "2021-02-15 18:02:47,545:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.66622888] - 4.98772 (ms), eval count: 143\n",
      "2021-02-15 18:02:47,553:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.60689965] - 6.99925 (ms), eval count: 144\n",
      "2021-02-15 18:02:47,563:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.74193242] - 6.99568 (ms), eval count: 145\n",
      "2021-02-15 18:02:47,569:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.67825278] - 3.99923 (ms), eval count: 146\n",
      "2021-02-15 18:02:47,576:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.82010314] - 5.00011 (ms), eval count: 147\n",
      "2021-02-15 18:02:47,582:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.67816962] - 5.00083 (ms), eval count: 148\n",
      "2021-02-15 18:02:47,587:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.81450559] - 3.99995 (ms), eval count: 149\n",
      "2021-02-15 18:02:47,593:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.82715066] - 3.99923 (ms), eval count: 150\n",
      "2021-02-15 18:02:47,599:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.80220657] - 4.00019 (ms), eval count: 151\n",
      "2021-02-15 18:02:47,605:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.71969488] - 3.99947 (ms), eval count: 152\n",
      "2021-02-15 18:02:47,612:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Energy evaluation returned [-5.89671358] - 6.00004 (ms), eval count: 153\n",
      "2021-02-15 18:02:47,614:qiskit.aqua.algorithms.minimum_eigen_solvers.vqe:INFO: Optimization complete in 1.06065034866333 seconds.\n",
      "Found opt_params [ 0.57775842 -5.13963895 -3.83959682 -3.44528868 -4.55866536  2.93548706\n",
      "  5.66338964 -3.02909245  3.15538246  3.80897734 -0.02693097 -4.87792711\n",
      "  4.35119509 -3.42941675  3.29018818  1.70527492  4.30343296 -3.00508584\n",
      "  2.13966661  0.17826555 -3.65612291 -4.58054034  0.14555112  1.53203046\n",
      " -4.79959291] in 153 evals\n"
     ]
    }
   ],
   "source": [
    "# USING Real Cloud Device : Note that this is not efficient as it will enter in a queue for each iteration.\n",
    "# ************************************************\n",
    "# provider = IBMQ.get_provider(hub='ibm-q')\n",
    "# backend = least_busy(provider.backends(filters=lambda x: x.configuration().n_qubits >= n and not x.configuration().simulator and x.status().operational==True))\n",
    "# print(\"least busy backend: \", backend)\n",
    "# job = execute(circuit, backend, shots=n_experiments, optimization_level=3)\n",
    "# job_monitor(job)\n",
    "# result = job.result()\n",
    "# ************************************************\n",
    "\n",
    "# USING The Statevector simulator and VQE\n",
    "aqua_globals.random_seed = np.random.default_rng(123)\n",
    "seed = 10598\n",
    "backend = Aer.get_backend('statevector_simulator')\n",
    "quantum_instance = QuantumInstance(backend, seed_simulator=seed, seed_transpiler=seed)\n",
    "\n",
    "# construct VQE\n",
    "spsa = SPSA(maxiter=64)\n",
    "ry = TwoLocal(qubitOp.num_qubits, 'ry', 'cz', reps=4, entanglement='linear')\n",
    "vqe = VQE(qubitOp, ry, spsa, quantum_instance=quantum_instance)\n",
    "\n",
    "# run VQE\n",
    "result = vqe.run(quantum_instance)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Display Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "energy: -5.896713575626536\n",
      "time: 1.06065034866333\n",
      "max-cut objective: -12.896713575626535\n",
      "solution: [1. 0. 1. 0. 1.]\n",
      "solution objective: 13.0\n"
     ]
    },
    {
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       "     <!-- θ[12] -->\r\n",
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       "      <use xlink:href=\"#DejaVuSans-952\"/>\r\n",
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       "      <use transform=\"translate(70.439453 -16.3125)scale(0.7)\" xlink:href=\"#DejaVuSans-89\"/>\r\n",
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       "      <use transform=\"translate(70.439453 -16.3125)scale(0.7)\" xlink:href=\"#DejaVuSans-89\"/>\r\n",
       "     </g>\r\n",
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       "   </g>\r\n",
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       "     <!-- θ[14] -->\r\n",
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       "      <use xlink:href=\"#DejaVuSans-952\"/>\r\n",
       "      <use x=\"61.181641\" xlink:href=\"#DejaVuSans-91\"/>\r\n",
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       "     </g>\r\n",
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       "   </g>\r\n",
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       "     <!-- θ[15] -->\r\n",
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       "      <use xlink:href=\"#DejaVuSans-952\"/>\r\n",
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       "      <use transform=\"translate(70.439453 -16.3125)scale(0.7)\" xlink:href=\"#DejaVuSans-89\"/>\r\n",
       "     </g>\r\n",
       "    </g>\r\n",
       "   </g>\r\n",
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       "     <!-- θ[16] -->\r\n",
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       "      <use xlink:href=\"#DejaVuSans-952\"/>\r\n",
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       "     </g>\r\n",
       "    </g>\r\n",
       "   </g>\r\n",
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       "     <!-- $\\mathrm{R}_\\mathrm{Y}$ -->\r\n",
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       "      <use transform=\"translate(70.439453 -16.3125)scale(0.7)\" xlink:href=\"#DejaVuSans-89\"/>\r\n",
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       "     <!-- θ[18] -->\r\n",
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       "      <use xlink:href=\"#DejaVuSans-952\"/>\r\n",
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       "     </g>\r\n",
       "    </g>\r\n",
       "   </g>\r\n",
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       "    <g clip-path=\"url(#p0b9fb24076)\">\r\n",
       "     <!-- $\\mathrm{R}_\\mathrm{Y}$ -->\r\n",
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       "      <use transform=\"translate(70.439453 -16.3125)scale(0.7)\" xlink:href=\"#DejaVuSans-89\"/>\r\n",
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       "      <use xlink:href=\"#DejaVuSans-952\"/>\r\n",
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   "source": [
    "# print results\n",
    "x = sample_most_likely(result.eigenstate)\n",
    "print('energy:', result.eigenvalue.real)\n",
    "print('time:', result.optimizer_time)\n",
    "print('max-cut objective:', result.eigenvalue.real + offset)\n",
    "print('solution:', max_cut.get_graph_solution(x))\n",
    "print('solution objective:', max_cut.max_cut_value(x, w))\n",
    "display(ry.draw(output='mpl',scale=0.9,justify=\"left\"))\n",
    "\n",
    "# plot results\n",
    "colors = ['r' if max_cut.get_graph_solution(x)[i] == 0 else 'c' for i in range(n)]\n",
    "draw_graph(G, colors, pos)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Final Ansatz State Histogram after VQE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Note:\n",
      "10 in binary is : 01010\n",
      "21 in binary is : 10101\n"
     ]
    },
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     "metadata": {
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     "output_type": "display_data"
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   ],
   "source": [
    "print(\"Note:\")\n",
    "print(\"10 in binary is :\",format(10, '05b'))\n",
    "print(\"21 in binary is :\",format(21, '05b'))\n",
    "plt.bar(list(range(32)),abs(result.eigenstate.real))\n",
    "plt.show()"
   ]
  },
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   "metadata": {},
   "source": [
    "---\n",
    "This part of the tutorial is based on the [Max-Cut and Traveling Salesman Problem](https://qiskit.org/documentation/tutorials/optimization/6_examples_max_cut_and_tsp.html) which is part of the IBM Qiskit documentation.\n",
    "\n",
    "---"
   ]
  }
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