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algos

This module contains Qiskit implementations of example algorithms to analyse the effects of isotropic errors.

isotropic.algos

grover

Grover's algorithm implementation and utilities for isotropic error analysis.

get_grover_answer(result)

Extract the measurement counts from the result of a Grover circuit execution.

Parameters:

Name Type Description Default
result PrimitiveResult

The result object returned by executing the Grover circuit.

 required

Returns:

Type Description
tuple[dict, str]

A tuple containing the counts dictionary and the most probable search item.
Source code in src/isotropic/algos/grover.py 
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def get_grover_answer(result: PrimitiveResult) -> tuple[dict, str]:
    """
    Extract the measurement counts from the result of a Grover circuit execution.

    Parameters
    ----------
    result : PrimitiveResult
        The result object returned by executing the Grover circuit.

    Returns
    -------
    tuple[dict, str]
        A tuple containing the counts dictionary and the most probable search item.
    """
    if not isinstance(result, PrimitiveResult):
        raise TypeError("The result must be an instance of PrimitiveResult.")

    counts = result[0].data.c0.get_counts()
    grover_answer = max(counts, key=counts.get)

    return counts, grover_answer

get_grover_circuit(num_qubits, U_w, iterations)

Create a Grover circuit with the given number of qubits, oracle, and iterations.

Parameters:

Name Type Description Default
num_qubits int

The number of qubits used to encode the states.

 required
U_w Operator

The oracle that marks the solution states.

 required
iterations int

The number of Grover iterations to perform.

 required

Returns:

Type Description
QuantumCircuit

The constructed Grover quantum circuit.
Source code in src/isotropic/algos/grover.py 
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def get_grover_circuit(
    num_qubits: int, U_w: Operator, iterations: int
) -> QuantumCircuit:
    """
    Create a Grover circuit with the given number of qubits, oracle, and iterations.

    Parameters
    ----------
    num_qubits : int
        The number of qubits used to encode the states.
    U_w : Operator
        The oracle that marks the solution states.
    iterations : int
        The number of Grover iterations to perform.

    Returns
    -------
    QuantumCircuit
        The constructed Grover quantum circuit.
    """

    if U_w.num_qubits != num_qubits:
        raise ValueError(
            "Oracle U_w must have the same number of qubits as num_qubits."
        )

    qr = QuantumRegister(num_qubits)
    cr = ClassicalRegister(num_qubits)
    qcirc = QuantumCircuit(qr, cr)

    # Initializing the circuit
    for i in range(num_qubits):
        qcirc.h(i)

    for i in range(iterations):
        qcirc.barrier()

        # Oracle to introduce negative phase (circuit of above matrix)
        qcirc.append(U_w, qr)

        qcirc.barrier()

        # Diffusion operator
        for qubit in range(num_qubits):
            qcirc.h(qubit)
        for qubit in range(num_qubits):
            qcirc.x(qubit)
        qcirc.h(num_qubits - 1)
        qcirc.mcx(list(range(num_qubits - 1)), num_qubits - 1)
        qcirc.h(num_qubits - 1)
        for qubit in range(num_qubits):
            qcirc.x(qubit)
        for qubit in range(num_qubits):
            qcirc.h(qubit)

    return qcirc

optimal_num_iterations(num_solutions, num_qubits)

Return the optimal number of iterations, if the number of solutions is known.

Parameters:

Name Type Description Default
num_solutions int

The number of solutions.

 required
num_qubits int

The number of qubits used to encode the states.

 required

Returns:

Type Description
int

The optimal number of iterations for Grover's algorithm to succeed.
Source code in src/isotropic/algos/grover.py 
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def optimal_num_iterations(num_solutions: int, num_qubits: int) -> int:
    """
    Return the optimal number of iterations, if the number of solutions is known.

    Parameters
    ----------
    num_solutions : int
        The number of solutions.
    num_qubits : int
        The number of qubits used to encode the states.

    Returns
    -------
    int
        The optimal number of iterations for Grover's algorithm to succeed.
    """
    amplitude = jnp.sqrt(num_solutions / 2**num_qubits)
    return round(jnp.arccos(amplitude) / (2 * jnp.arcsin(amplitude)))