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#
# Licensed under the Apache License, Version 2.0 (the "License"). You
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#
# or in the "license" file accompanying this file. This file is
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from collections.abc import Iterable
from functools import lru_cache
import numpy as np
[docs]
def verify_quantum_operator_matrix_dimensions(matrix: np.ndarray) -> None:
"""Verifies matrix is square and matrix dimensions are positive powers of 2,
raising `ValueError` otherwise.
Args:
matrix (ndarray): matrix to verify
Raises:
ValueError: If `matrix` is not a two-dimensional square matrix,
or has a dimension length that is not a positive power of 2
"""
if not is_square_matrix(matrix):
raise ValueError(f"{matrix} is not a two-dimensional square matrix")
matrix = np.array(matrix, dtype=complex)
qubit_count = int(np.log2(matrix.shape[0]))
if 2**qubit_count != matrix.shape[0] or qubit_count < 1:
raise ValueError(f"`matrix` dimension {matrix.shape[0]} is not a positive power of 2")
[docs]
def is_hermitian(matrix: np.ndarray) -> bool:
r"""Whether matrix is Hermitian
A square matrix :math:`U` is Hermitian if
.. math:: U = U^\dagger
where :math:`U^\dagger` is the conjugate transpose of :math:`U`.
Args:
matrix (ndarray): matrix to verify
Returns:
bool: If matrix is Hermitian
"""
return np.allclose(matrix, matrix.conj().T)
[docs]
def is_square_matrix(matrix: np.ndarray) -> bool:
"""Whether matrix is square, meaning it has exactly two dimensions and the dimensions are equal
Args:
matrix (np.ndarray): matrix to verify
Returns:
bool: If matrix is square
"""
return len(matrix.shape) == 2 and matrix.shape[0] == matrix.shape[1]
[docs]
def is_unitary(matrix: np.ndarray) -> bool:
r"""Whether matrix is unitary
A square matrix :math:`U` is unitary if
.. math:: UU^\dagger = I
where :math:`U^\dagger` is the conjugate transpose of :math:`U`
and :math:`I` is the identity matrix.
Args:
matrix (np.ndarray): matrix to verify
Returns:
bool: If matrix is unitary
"""
return np.allclose(np.eye(len(matrix)), matrix.dot(matrix.T.conj()))
[docs]
def is_cptp(matrices: Iterable[np.ndarray]) -> bool:
"""Whether a transformation defined by these matrices as Kraus operators is a
completely positive trace preserving (CPTP) map. This is the requirement for
a transformation to be a quantum channel.
Reference: Section 8.2.3 in Nielsen & Chuang (2010) 10th edition.
Args:
matrices (Iterable[ndarray]): List of matrices representing Kraus operators.
Returns:
bool: If the matrices define a CPTP map.
"""
E = sum(np.dot(matrix.T.conjugate(), matrix) for matrix in matrices)
return np.allclose(E, np.eye(*E.shape))
[docs]
@lru_cache
def get_pauli_eigenvalues(num_qubits: int) -> np.ndarray:
"""Get the eigenvalues of Pauli operators and their tensor products as
an immutable Numpy ndarray.
Args:
num_qubits (int): the number of qubits the operator acts on
Returns:
np.ndarray: the eigenvalues of a Pauli product operator of the given size
"""
if num_qubits == 1:
eigs = np.array([1, -1])
eigs.setflags(write=False)
return eigs
eigs = np.concatenate(
[get_pauli_eigenvalues(num_qubits - 1), -get_pauli_eigenvalues(num_qubits - 1)]
)
eigs.setflags(write=False)
return eigs