Simon's algorithm added

Author: mrtkp9993

04-Simon's Algorithm.py

@@ -0,0 +1,79 @@
+'''
+    Bernstein-Vazirani Algorithm
+
+    We know that an oracle function f which has period a:
+
+    f : {0, 1}^n -> {0, 1}^n
+
+    ∃!a != 0: ∀x f(x) = f(y) => y = x ⊕ a
+
+    Task: Find a.
+
+'''
+from qiskit import IBMQ, BasicAer
+from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister, execute
+
+qr = QuantumRegister(4)  # Initialize qubits
+cr = ClassicalRegister(4)  # Initialize bits for record measurements
+circuit = QuantumCircuit(qr, cr)
+
+# First two qubits form a register to store x, last two qubits from a register to store f(x)
+# Apply Hadamard to first two
+circuit.h(qr[0])
+circuit.h(qr[1])
+
+circuit.barrier()
+
+# Oracle function, a = 11
+circuit.cx(qr[0], qr[2])
+circuit.cx(qr[1], qr[2])
+circuit.cx(qr[0], qr[3])
+circuit.cx(qr[1], qr[3])
+
+circuit.barrier()
+
+# Measure last two qubits
+circuit.measure(qr[2], cr[2])
+circuit.measure(qr[3], cr[3])
+
+circuit.barrier()
+
+# Apply Hadamard to first two qubits
+circuit.h(qr[0])
+circuit.h(qr[1])
+
+circuit.barrier()
+
+circuit.measure(qr[0], cr[0])
+circuit.measure(qr[1], cr[1])
+
+# 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()
+
+# Categorize measurements by input register values
+answer_plot = {}
+for measresult in answer.keys():
+    measresult_input = measresult[2:]
+    if measresult_input in answer_plot:
+        answer_plot[measresult_input] += answer[measresult]
+    else:
+        answer_plot[measresult_input] = answer[measresult]
+
+print(answer_plot)
+
+
+def sdotz(a, b):  # Calculate the dot product of the results
+    accum = 0
+    for i in range(len(a)):
+        accum += int(a[i]) * int(b[i])
+    return (accum % 2)
+
+
+print('s, z, s.z (mod 2)')
+for z_rev in answer_plot:
+    z = z_rev[::-1]
+    print(f'{11}, {z}, {11}.{z}={sdotz("11",z)}')
+# We can recover the value of a = 11.

README.md

@@ -23,4 +23,6 @@ Quantum computing examples with Qiskit.
 
 **Simon's Algorithm**
 
-> Problem. For given an oracle function f : {0, 1}^n -> {0, 1}^n which has period `a` like following: ∃!a != 0: ∀x f(x) = f(y) => y = x ⊕ a. Determine a.
+> Problem. For given an oracle function f : {0, 1}^n -> {0, 1}^n which has period `a`: ∃!a != 0: ∀x f(x) = f(y) => y = x ⊕ a. Determine a.
+
+![Simon's Algorithm](./circuit_diagrams/04_simon.png)