grover's

Author: mrtkp9993

06_Grovers_Algorithm.py

@@ -0,0 +1,54 @@
+'''
+    Grover's algorithm
+
+    For given an oracle function f : {0, 1}^n -> {0, 1}^n, ∃! ω : f(ω) = a, 
+    find ω.
+
+    Although the purpose of Grover's algorithm is usually described as "searching a database", 
+    it may be more accurate to describe it as "inverting a function". Roughly speaking, if we 
+    have a function y=f(x) that can be evaluated on a quantum computer, Grover's algorithm 
+    allows us to calculate x when given y. Inverting a function is related to the searching of 
+    a database because we could come up with a function that produces a particular value of y 
+    if x matches a desired entry in a database, and another value of y for other values of x.
+
+    Source: https://www.quantiki.org/wiki/grovers-search-algorithm
+
+'''
+from qiskit import IBMQ, BasicAer
+from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister, execute
+
+qr = QuantumRegister(3)  # Initialize qubits
+cr = ClassicalRegister(3)  # Initialize bits for record measurements
+circuit = QuantumCircuit(qr, cr)
+
+# We want to search two marked states
+# |101> and |110>
+
+# Apply Hadamard to all qubits
+circuit.h(qr)
+circuit.barrier()
+
+# Phase oracle (Marks states |101> and |110> as results)
+circuit.cz(qr[2], qr[0])
+circuit.cz(qr[2], qr[1])
+
+# Inversion around the average
+circuit.h(qr)
+circuit.x(qr)
+circuit.barrier()
+circuit.h(qr[2])
+circuit.ccx(qr[0], qr[1], qr[2])
+circuit.h(qr[2])
+circuit.barrier()
+circuit.x(qr)
+circuit.h(qr)
+
+# Measure
+circuit.measure(qr, cr)
+
+# Run our circuit with local simulator
+backend = BasicAer.get_backend('qasm_simulator')
+shots = 1024
+results = execute(circuit, backend=backend, shots=shots).result()
+answer = results.get_counts()
+print(answer)

README.md

@@ -58,6 +58,14 @@ Scheme for `n=3`:
 
 ![Quantum Phase Estimation](./circuit_diagrams/e3_quantum_phase_estimation.png)
 
+### Grover's Algorithm
+
+> Problem. For given an oracle function f : {0, 1}^n -> {0, 1}^n, ∃! ω : f(ω) = a, find ω.
+
+Scheme for `n=3`:
+
+![Grover's Algorithm](./circuit_diagrams/06_grovers_algorithm.png)
+
 ## References
 
 * [Jonahtan Hui, Quantum Computing Series, Medium](https://medium.com/@jonathan_hui/qc-quantum-computing-series-10ddd7977abd)