Module: cirq.linalg

Types and methods related to performing linear algebra.

Focuses on methods useful for analyzing and optimizing quantum circuits. Avoids duplicating functionality present in numpy.

Modules

combinators module: Utility methods for combining matrices.

decompositions module: Utility methods for breaking matrices into useful pieces.

diagonalize module: Utility methods for diagonalizing matrices.

operator_spaces module: Utilities for manipulating linear operators as elements of vector space.

predicates module: Utility methods for checking properties of matrices.

tolerance module: Utility for testing approximate equality of matrices and scalars within

transformations module: Utility methods for transforming matrices or vectors.

Classes

class AxisAngleDecomposition: Represents a unitary operation as an axis, angle, and global phase.

class KakDecomposition: A convenient description of an arbitrary two-qubit operation.

Functions

all_near_zero(...): Checks if the tensor's elements are all near zero.

all_near_zero_mod(...): Checks if the tensor's elements are all near multiples of the period.

allclose_up_to_global_phase(...): Determines if a ~= b * exp(i t) for some t.

apply_matrix_to_slices(...): Left-multiplies an NxN matrix onto N slices of a numpy array.

axis_angle(...): Decomposes a single-qubit unitary into axis, angle, and global phase.

bidiagonalize_real_matrix_pair_with_symmetric_products(...): Finds orthogonal matrices that diagonalize both mat1 and mat2.

bidiagonalize_unitary_with_special_orthogonals(...): Finds orthogonal matrices L, R such that L @ matrix @ R is diagonal.

block_diag(...): Concatenates blocks into a block diagonal matrix.

deconstruct_single_qubit_matrix_into_angles(...): Breaks down a 2x2 unitary into more useful ZYZ angle parameters.

diagonalize_real_symmetric_and_sorted_diagonal_matrices(...): Returns an orthogonal matrix that diagonalizes both given matrices.

diagonalize_real_symmetric_matrix(...): Returns an orthogonal matrix that diagonalizes the given matrix.

dot(...): Computes the dot/matrix product of a sequence of values.

expand_matrix_in_orthogonal_basis(...): Computes coefficients of expansion of m in basis.

extract_right_diag(...): Extract a diagonal unitary from a 3-CNOT two-qubit unitary.

hilbert_schmidt_inner_product(...): Computes Hilbert-Schmidt inner product of two matrices.

is_cptp(...): Determines if a channel is completely positive trace preserving (CPTP).

is_diagonal(...): Determines if a matrix is a approximately diagonal.

is_hermitian(...): Determines if a matrix is approximately Hermitian.

is_normal(...): Determines if a matrix is approximately normal.

is_orthogonal(...): Determines if a matrix is approximately orthogonal.

is_special_orthogonal(...): Determines if a matrix is approximately special orthogonal.

is_special_unitary(...): Determines if a matrix is approximately unitary with unit determinant.

is_unitary(...): Determines if a matrix is approximately unitary.

kak_canonicalize_vector(...): Canonicalizes an XX/YY/ZZ interaction by swap/negate/shift-ing axes.

kak_decomposition(...): Decomposes a 2-qubit unitary into 1-qubit ops and XX/YY/ZZ interactions.

kak_vector(...): Compute the KAK vectors of one or more two qubit unitaries.

kron(...): Computes the kronecker product of a sequence of values.

kron_bases(...): Creates tensor product of bases.

kron_factor_4x4_to_2x2s(...): Splits a 4x4 matrix U = kron(A, B) into A, B, and a global factor.

kron_with_controls(...): Computes the kronecker product of a sequence of values and control tags.

map_eigenvalues(...): Applies a function to the eigenvalues of a matrix.

match_global_phase(...): Phases the given matrices so that they agree on the phase of one entry.

matrix_commutes(...): Determines if two matrices approximately commute.

matrix_from_basis_coefficients(...): Computes linear combination of basis vectors with given coefficients.

num_cnots_required(...): Returns the min number of CNOT/CZ gates required by a two-qubit unitary.

partial_trace(...): Takes the partial trace of a given tensor.

partial_trace_of_state_vector_as_mixture(...): Returns a mixture representing a state vector with only some qubits kept.

pow_pauli_combination(...): Computes non-negative integer power of single-qubit Pauli combination.

reflection_matrix_pow(...): Raises a matrix with two opposing eigenvalues to a power.

scatter_plot_normalized_kak_interaction_coefficients(...): Plots the interaction coefficients of many two-qubit operations.

slice_for_qubits_equal_to(...): Returns an index corresponding to a desired subset of an np.ndarray.

so4_to_magic_su2s(...): Finds 2x2 special-unitaries A, B where mat = Mag.H @ kron(A, B) @ Mag.

sub_state_vector(...): Attempts to factor a state vector into two parts and return one of them.

targeted_conjugate_about(...): Conjugates the given tensor about the target tensor.

targeted_left_multiply(...): Left-multiplies the given axes of the target tensor by the given matrix.

to_special(...): Converts a unitary matrix to a special unitary matrix.

unitary_eig(...): Gives the guaranteed unitary eigendecomposition of a normal matrix.

CONTROL_TAG Instance of numpy.ndarray

A special indicator value for cirq.kron_with_controls.

This value is a stand-in for "control operations on the other qubits based
on the value of this qubit", which otherwise doesn't have a proper matrix.

PAULI_BASIS

{
 'I': array([[1., 0.],
       [0., 1.]]),
 'X': array([[0., 1.],
       [1., 0.]]),
 'Y': array([[ 0.+0.j, -0.-1.j],
       [ 0.+1.j,  0.+0.j]]),
 'Z': array([[ 1.,  0.],
       [ 0., -1.]])
}

The four Pauli matrices (including identity) keyed by character.