Cirq: Demonstrates the Bernstein–Vazirani algorithm.

BVA.py

"""Demonstrates the Bernstein–Vazirani algorithm.

The (non-recursive) Bernstein–Vazirani algorithm takes a black-box oracle
implementing a function f(a) = a·factors + bias (mod 2), where 'bias' is 0 or 1,
'a' and 'factors' are vectors with all elements equal to 0 or 1, and the
algorithm solves for 'factors' in a single query to the oracle.
=== EXAMPLE OUTPUT ===
Secret function:
f(a) = a·<0, 0, 1, 0, 0, 1, 1, 1> + 0 (mod 2)
Sampled results:
Counter({'00100111': 3})
Most common matches secret factors:
True
"""
import random
import cirq


def main(qubit_count=8):
    circuit_sample_count = 3

    # Choose qubits to use.
    input_qubits = [cirq.GridQubit(i, 0) for i in range(qubit_count)]
    output_qubit = cirq.GridQubit(qubit_count, 0)

    # Pick coefficients for the oracle and create a circuit to query it.
    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(a) = a·<{}> + {} (mod 2)".format(
            ", ".join(str(e) for e in secret_factor_bits), secret_bias_bit
        )
    )

    # Embed the oracle into a special quantum circuit querying it exactly once.
    circuit = make_bernstein_vazirani_circuit(input_qubits, output_qubit, oracle)

    # Sample from the circuit a couple times.
    simulator = cirq.Simulator()
    result = simulator.run(circuit, repetitions=circuit_sample_count)
    frequencies = result.histogram(key="result", fold_func=bitstring)
    print("Sampled results:\n{}".format(frequencies))

    # Check if we actually found the secret value.
    most_common_bitstring = frequencies.most_common(1)[0][0]
    print(
        "Most 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):
    """Gates implementing the function 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):
    """Solves for factors in f(a) = a·factors + bias (mod 2) with one query."""

    c = cirq.Circuit()

    # Initialize qubits.
    c.append(
        [cirq.X(output_qubit), cirq.H(output_qubit), 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 bitstring(bits):
    return "".join(str(int(b)) for b in bits)


if __name__ == "__main__":
    main()