Алгоритм Саймона

task4/main.py

@@ -0,0 +1,91 @@
+"""Алгоритм Бернштейна–Вазирани в Cirq."""
+
+import random
+
+import cirq
+
+
+def main():
+    """Выполняет алгоритм BV."""
+    # Количество кубитов
+    qubit_count = 8
+    # Количество выборок из схемы
+    circuit_sample_count = 3
+
+    # Выберите кубиты для использования
+    input_qubits = [cirq.GridQubit(i, 0) for i in range(qubit_count)]
+    output_qubit = cirq.GridQubit(qubit_count, 0)
+
+    # Выберите коэффициенты для оракула и создайте схему для его запроса
+    secret_bias_bit = random.randint(0, 1)
+    secret_factor_bits = [random.randint(0, 1) for _ in range(qubit_count)]
+
+    oracle = make_oracle(
+        input_qubits, output_qubit, secret_factor_bits, secret_bias_bit
+    )
+
+    print(
+        "Secret function:\nf(x) = x*<{}> + {} (mod 2)".format(
+            ", ".join(str(e) for e in secret_factor_bits), secret_bias_bit
+        )
+    )
+
+    # Встраиваем оракул в специальную квантовую схему, запрашивая ее ровно один раз
+    circuit = make_bernstein_vazirani_circuit(input_qubits, output_qubit, oracle)
+    print("\nCircuit:")
+    print(circuit)
+
+    # Выберем из схемы пару раз
+    simulator = cirq.Simulator()
+    result = simulator.run(circuit, repetitions=circuit_sample_count)
+    frequencies = result.histogram(key="result", fold_func=bitstring)
+    print("\nSampled results:\n{}".format(frequencies))
+
+    # Проверить, действительно ли мы нашли секретное значение
+    most_common_bitstring = frequencies.most_common(1)[0][0]
+    print(
+        "\nMost common matches secret factors:\n{}".format(
+            most_common_bitstring == bitstring(secret_factor_bits)
+        )
+    )
+
+
+def make_oracle(input_qubits, output_qubit, secret_factor_bits, secret_bias_bit):
+    """Вентили, реализующие функцию f(a) = a*factors + bias (mod 2)."""
+    if secret_bias_bit:
+        yield cirq.X(output_qubit)
+
+    for qubit, bit in zip(input_qubits, secret_factor_bits):
+        if bit:
+            yield cirq.CNOT(qubit, output_qubit)
+
+
+def make_bernstein_vazirani_circuit(input_qubits, output_qubit, oracle):
+    """Находит множители в f (a) = a * factors + bias (mod 2) с помощью одного запроса."""
+    c = cirq.Circuit()
+
+    # Инициализировать кубиты
+    c.append(
+        [
+            cirq.X(output_qubit),
+            cirq.H(output_qubit),
+            cirq.H.on_each(*input_qubits),
+        ]
+    )
+
+    # Запрос оракула
+    c.append(oracle)
+
+    # Измерение по оси X
+    c.append([cirq.H.on_each(*input_qubits), cirq.measure(*input_qubits, key="result")])
+
+    return c
+
+
+def bitstring(bits):
+    """Создает битовую строку из итерации битов."""
+    return "".join(str(int(b)) for b in bits)
+
+
+if __name__ == "__main__":
+    main()

task5/main.py

@@ -0,0 +1,104 @@
+from __future__ import annotations
+
+from collections import Counter
+
+import cirq
+import numpy as np
+import scipy as sp
+
+
+def main(qubit_count=3):
+
+    data = []  # we'll store here the results
+
+    # define a secret string:
+    secret_string = np.random.randint(2, size=qubit_count)
+
+    print(f"Secret string = {secret_string}")
+
+    n_samples = 100
+    for _ in range(n_samples):
+        flag = False  # check if we have a linearly independent set of measures
+        while not flag:
+            # Choose qubits to use.
+            input_qubits = [cirq.GridQubit(i, 0) for i in range(qubit_count)]  # input x
+            output_qubits = [
+                cirq.GridQubit(i + qubit_count, 0) for i in range(qubit_count)
+            ]  # output f(x)
+
+            # Pick coefficients for the oracle and create a circuit to query it.
+            oracle = make_oracle(input_qubits, output_qubits, secret_string)
+
+            # Embed oracle into special quantum circuit querying it exactly once
+            circuit = make_simon_circuit(input_qubits, output_qubits, oracle)
+
+            # Sample from the circuit a n-1 times (n = qubit_count).
+            simulator = cirq.Simulator()
+            results = [
+                simulator.run(circuit).measurements["result"][0]
+                for _ in range(qubit_count - 1)
+            ]
+
+            # Classical Post-Processing:
+            flag = post_processing(data, results)
+
+    freqs = Counter(data)
+    print("Circuit:")
+    print(circuit)
+    print(f"Most common answer was : {freqs.most_common(1)[0]}")
+
+
+def make_oracle(input_qubits, output_qubits, secret_string):
+    """Gates implementing the function f(a) = f(b) iff a ⨁ b = s"""
+    # Copy contents to output qubits:
+    for control_qubit, target_qubit in zip(input_qubits, output_qubits):
+        yield cirq.CNOT(control_qubit, target_qubit)
+
+    # Create mapping:
+    if sum(secret_string):  # check if the secret string is non-zero
+        # Find significant bit of secret string (first non-zero bit)
+        significant = list(secret_string).index(1)
+
+        # Add secret string to input according to the significant bit:
+        for j in range(len(secret_string)):
+            if secret_string[j] > 0:
+                yield cirq.CNOT(input_qubits[significant], output_qubits[j])
+
+
+def make_simon_circuit(input_qubits, output_qubits, oracle):
+    """Solves for the secret period s of a 2-to-1 function such that
+    f(x) = f(y) iff x ⨁ y = s
+    """
+
+    c = cirq.Circuit()
+
+    # Initialize qubits.
+    c.append([cirq.H.on_each(*input_qubits)])
+
+    # Query oracle.
+    c.append(oracle)
+
+    # Measure in X basis.
+    c.append([cirq.H.on_each(*input_qubits), cirq.measure(*input_qubits, key="result")])
+
+    return c
+
+
+def post_processing(data, results):
+    """Solves a system of equations with modulo 2 numbers"""
+    sing_values = sp.linalg.svdvals(results)
+    tolerance = 1e-5
+    if (
+        sum(sing_values < tolerance) == 0
+    ):  # check if measurements are linearly dependent
+        flag = True
+        null_space = sp.linalg.null_space(results).T[0]
+        solution = np.around(null_space, 3)  # chop very small values
+        minval = abs(min(solution[np.nonzero(solution)], key=abs))
+        solution = (solution / minval % 2).astype(int)  # renormalize vector mod 2
+        data.append(str(solution))
+        return flag
+
+
+if __name__ == "__main__":
+    main()