pauliarray.binary package

Submodules

pauliarray.binary.bit_operations module

pauliarray.binary.bit_operations.add(bit_matrix_1: np.ndarray[np.bool], bit_matrix_2: np.ndarray[np.bool]) → np.ndarray[np.bool]

Performs element-wise XOR operation between two binary matrices.

Parameters:

• bit_matrix_1 ("np.ndarray[np.bool]") – First binary matrix.

• bit_matrix_2 ("np.ndarray[np.bool]") – Second binary matrix.

Returns:

Element-wise XOR result of the two input matrices.

Return type:

“np.ndarray[np.bool]”

pauliarray.binary.bit_operations.bit_sum(bit_strings: np.ndarray[np.bool]) → int

Calculates the sum of booleans along the last axis of the input array.

Parameters:

bit_strings ("np.ndarray[np.bool]") – Array of booleans.

Returns:

Sum of bits along the last axis.

Return type:

int

pauliarray.binary.bit_operations.dot(bit_strings_1: np.ndarray[np.bool], bit_strings_2: np.ndarray[np.bool]) → np.ndarray[np.int]

Computes the dot product between two arrays of boolean values.

Parameters:

• bit_strings_1 ("np.ndarray[np.bool]") – First array of boolean values.

• bit_strings_2 ("np.ndarray[np.bool]") – Second array of boolean values.

Returns:

Dot product of the two input arrays.

Return type:

“np.ndarray[np.int]”

pauliarray.binary.bit_operations.intersection(bit_strings_1: np.ndarray[np.bool], bit_strings_2: np.ndarray[np.bool]) → np.ndarray[np.bool]

Computes the intersection of two sets of bit strings.

Args

bit_strings_1 (“np.ndarray[np.bool]”): First array of boolean values. bit_strings_2 (“np.ndarray[np.bool]”): Second array of boolean values.

Returns

“np.ndarray[np.bool]”: Intersection of the input bit strings.

pauliarray.binary.bit_operations.intersection_row_space(bit_matrix_1: np.ndarray[np.bool], bit_matrix_2: np.ndarray[np.bool]) → np.ndarray[np.bool]

Given two matrices which rows are spanning two subspace, this fonction returns rows spanning the intersection subspace.

Parameters:

• bit_matrix_1 ("np.ndarray[np.bool]") – First binary matrix.

• bit_matrix_2 ("np.ndarray[np.bool]") – Second binary matrix.

Returns:

Rows spanning the intersection subspace.

Return type:

“np.ndarray[np.bool]”

pauliarray.binary.bit_operations.inv(bit_matrix: np.ndarray[np.bool]) → np.ndarray[np.bool]

Computes the inverse of a binary matrix.

Parameters:

bit_matrix ("np.ndarray[np.bool]") – Input binary matrix.

Returns:

Inverse of the input binary matrix.

Return type:

“np.ndarray[np.bool]”

pauliarray.binary.bit_operations.is_orthogonal(bit_strings_1: np.ndarray[np.bool], bit_strings_2: np.ndarray[np.bool]) → np.ndarray[np.bool]

Checks if two sets of bit strings are orthogonal.

Parameters:

• bit_strings_1 ("np.ndarray[np.bool]") – First array of boolean values.

• bit_strings_2 ("np.ndarray[np.bool]") – Second array of boolean values.

Returns

“np.ndarray[np.bool]”: True if the input bit strings are orthogonal, False otherwise.

pauliarray.binary.bit_operations.kernel(bit_matrix: np.ndarray[np.bool]) → np.ndarray[np.bool]

Computes the Kernel of a two dimensions “np.ndarray[np.bool]”. The Kernel of a matrix A is a matrix which the columns are formed by the vectors x such that

\[A x = 0.\]

Parameters:

bit_matrix ("np.ndarray[np.bool]") – Input binary matrix.

Returns:

Kernel of the input binary matrix.

Return type:

“np.ndarray[np.bool]”

pauliarray.binary.bit_operations.matmul(bit_matrix_1: np.ndarray[np.bool], bit_matrix_2: np.ndarray[np.bool]) → np.ndarray[np.bool]

Performs matrix multiplication over binary matrices.

Parameters:

• bit_matrix_1 ("np.ndarray[np.bool]") – First binary matrix.

• bit_matrix_2 ("np.ndarray[np.bool]") – Second binary matrix.

Returns:

Resultant binary matrix after multiplication.

Return type:

“np.ndarray[np.bool]”

pauliarray.binary.bit_operations.orthogonal_basis(bit_strings: np.ndarray[np.bool]) → np.ndarray[np.bool]

Computes the orthogonal basis of the given set of bit strings.

Parameters:

bit_strings ("np.ndarray[np.bool]") – Input array of bit strings.

Returns

“np.ndarray[np.bool]”: Orthogonal basis of the input bit strings.

pauliarray.binary.bit_operations.orthogonal_complement(bit_strings: np.ndarray[np.bool]) → np.ndarray[np.bool]

Computes the orthogonal complement of the given set of bit strings.

Parameters:

bit_strings ("np.ndarray[np.bool]") – Input array of bit strings.

Returns

“np.ndarray[np.bool]”: Orthogonal basis of the input bit strings.

pauliarray.binary.bit_operations.rank(bit_matrix: np.ndarray[np.bool]) → int

Computes the rank of a binary matrix.

Parameters:

bit_matrix ("np.ndarray[np.bool]") – Input binary matrix.

Returns:

Rank of the binary matrix.

Return type:

int

pauliarray.binary.bit_operations.row_echelon(bit_matrix: np.ndarray[np.bool]) → np.ndarray[np.bool]

Applies Gauss-Jordan elimination on a binary matrix to produce row echelon form.

Parameters:

bit_matrix ("np.ndarray[np.bool]") – Input binary matrix.

Returns:

Row echelon form of the provided matrix.

Return type:

“np.ndarray[np.bool]”

pauliarray.binary.bit_operations.row_space(bits: np.ndarray[np.bool]) → np.ndarray[np.bool]

Computes the row space of a binary matrix using Gauss-Jordan elimination and removing the zero lines.

Parameters:

bits ("np.ndarray[np.bool]") – Input binary matrix.

Returns

“np.ndarray[np.bool]”: Row space of the current matrix

pauliarray.binary.bit_operations.strings_to_ints(bit_strings: np.ndarray[np.bool]) → np.ndarray[np.int]

Converts binary strings to integers.

Parameters:

bit_strings ("np.ndarray[np.bool]") – Input array of binary strings.

Returns:

Integers obtained from input binary strings

Return type:

“np.ndarray[np.int]”

pauliarray.binary.symplectic module

pauliarray.binary.symplectic.coisotropic_subspace(orthogonal_zx_strings: np.ndarray[np.bool]) → np.ndarray[np.bool]

Given a list of zx_strings which are mutually orthogonal in the smplectic sense, returns a list of zx_strings which are orthogonal to the provided zx_strings. For zx_strings of length 2*n, the number of returned zx_strings is 2*n - rank(zx_strings). The returned zx_strings might not be mutually orthogonal in the symplectic sense.

Parameters:

• orthogonal_zx_strings ("np.ndarray[np.bool]") – A list of zx_strings (2d-array of bools) which are mutually

• strings. (orthogonal. Last dimension is along the length of the)

Returns:

A list of zx_strings defining the coisotropic subspace.

Return type:

“np.ndarray[np.bool]”

pauliarray.binary.symplectic.conjugate_subspace(isotropic_zx_strings: np.ndarray[np.bool]) → np.ndarray[np.bool]

Conctruct a conjugate subspace to the provided isotropic subspace. Each zx_string the conjugate subspace is orthogonal ins the symplectic sense to all provided zx_strings of the isotropic subspace, except for one : its conjugate.

Parameters:

isotropic_zx_strings ("np.ndarray[np.bool]") – Isotropic subspace.

Returns:

Conjugate subspace to the input isotropic subspace.

Return type:

“np.ndarray[np.bool]”

pauliarray.binary.symplectic.dot(zx_strings_1: np.ndarray[np.bool], zx_strings_2: np.ndarray[np.bool]) → np.ndarray[np.int]

Computes the binary dot product between two zx boolean strings.

Parameters:

• zx_strings_1 ("np.ndarray[np.bool]") – First input zx string to compute the dot product with.

• zx_strings_2 ("np.ndarray[np.bool]") – Second input zx string to compute the dot product with.

Returns:

Dot product of the two input arrays.

Return type:

“np.ndarray[np.int]”

pauliarray.binary.symplectic.flip_zx(zx_strings: np.ndarray[np.bool]) → np.ndarray[np.bool]

Flips an input zx string into an xz string.

Parameters:

zx_strings ("np.ndarray[np.bool]") – Input zx string to flip

Returns:

Flipped zx string (xz string)

Return type:

“np.ndarray[np.bool]”

pauliarray.binary.symplectic.gram_schmidt_orthogonalization(zx_strings: np.ndarray[np.bool]) → np.ndarray[np.bool]

Performs a Gram Schmidt orthogonalization procedure in the symplectic space.

Parameters:

zx_strings ("np.ndarray[np.bool]") – Input space.

Returns:

Bit strings which are mutually symplectic orthogonal spawning the same space as the input.

Return type:

“np.ndarray[np.bool]”

pauliarray.binary.symplectic.is_coisotropic(zx_strings: np.ndarray[np.bool]) → bool

Checks if a given list of zx_strings defines an coisotropic subspace.

Parameters:

• zx_strings ("np.ndarray[np.bool]") – A list of zx_strings (2d-array of bools) defining a subspace.

• strings. (Last dimension is along the length of the)

Returns:

Wether or not input is coisotropic

Return type:

bool

pauliarray.binary.symplectic.is_isotropic(zx_strings: np.ndarray[np.bool]) → bool

Checks if a given list of zx_strings defines an isotropic subspace.

Parameters:

• zx_strings ("np.ndarray[np.bool]") – A list of zx_strings (2d-array of bools) defining a subspace.

• strings. (Last dimension is along the length of the)

Returns:

Wether or not input is isotropic

Return type:

bool

pauliarray.binary.symplectic.is_lagrangian(zx_strings: np.ndarray[np.bool]) → bool

Checks if a given list of zx_strings defines a Lagrangian subspace.

Parameters:

• zx_strings ("np.ndarray[np.bool]") – A list of zx_strings (2d-array of bools) defining a subspace.

• strings. (Last dimension is along the length of the)

Returns:

Wether or not input is lagrangian

Return type:

bool

pauliarray.binary.symplectic.is_orthogonal(zx_strings_1: np.ndarray[np.bool], zx_strings_2: np.ndarray[np.bool]) → np.ndarray[np.bool]

Check if the zx_strings of one string array are orthogonal to the zx_strings of an other string array element wise and using the simplectic dot product. Two zx_strings are orthogonal if the symplectic dot product is 0.

Parameters:

• zx_strings_1 ("np.ndarray[np.bool]") – A list of zx_strings defining a subspace.

• strings. (Last dimension is along the length of the)

• zx_strings_2 ("np.ndarray[np.bool]") – A list of zx_strings defining a subspace.

• strings.

Returns:

Wether or not the two input string are orthogonal to each other.

Return type:

“np.ndarray[np.bool]”

pauliarray.binary.symplectic.isotropic_subspace(orthogonal_zx_strings: np.ndarray[np.bool]) → np.ndarray[np.bool]

Given a list of zx_strings which are mutually orthogonal in the smplectic sense, returns a list of zx_strings which are mutually orthogonal and linearly independent.

Parameters:

• orthogonal_zx_strings ("np.ndarray[np.bool]") – A list of zx_strings (2d-array of bools) which are mutually

• strings. (orthogonal. Last dimension is along the length of the)

Returns:

A list of zx_strings defining the isotropic subspace.

Return type:

“np.ndarray[np.bool]”

pauliarray.binary.symplectic.lagrangian_subspace(orthogonal_zx_strings: np.ndarray[np.bool]) → np.ndarray[np.bool]

Given a list of zx_strings of length 2*n which are mutually orthogonal in the smplectic sense, returns a list of n zx_strings which are mutually orthogonal and orthogonal to the provided zx_strings.

Parameters:

• orthogonal_zx_strings ("np.ndarray[np.bool]") – A list of zx_strings (2d-array of bools) which are mutually

• strings. (orthogonal. Last dimension is along the length of the)

Returns:

A list of zx_strings defining the Lagrangian subspace.

Return type:

“np.ndarray[np.bool]”

pauliarray.binary.symplectic.merge_zx_strings(z_strings: np.ndarray[np.bool], x_strings: np.ndarray[np.bool]) → np.ndarray[np.bool]

Merges z and x strings to create one zx string.

Parameters:

• z_strings ("np.ndarray[np.bool]") – First string to concatenate (z)

• x_strings ("np.ndarray[np.bool]") – Second string to concatenate (x)

Returns:

Concatenated zx string.

Return type:

“np.ndarray[np.bool]”

pauliarray.binary.symplectic.orthogonal_complement(zx_strings: np.ndarray[np.bool]) → np.ndarray[np.bool]

Finds a list of zx_strings which or orthogonal in the symplectic sense to the provided zx_strings. For zx_strings of length 2*n, the number of returned zx_strings is 2*n - rank(zx_strings). The returned zx_strings might not be mutually orthogonal in the symplectic sense.

Parameters:

• zx_strings ("np.ndarray[np.bool]") – A list of zx_strings (2d-array of bools) defining a subspace.

• strings. (Last dimension is along the length of the)

Returns:

A list of zx_strings defining the orthogonal completement.

Return type:

“np.ndarray[np.bool]”

pauliarray.binary.symplectic.split_zx_strings(zx_strings: np.ndarray[np.bool]) → tuple[np.ndarray[np.bool], np.ndarray[np.bool]]

Split one concatenated zx string into a z string and an x string.

Parameters:

zx_strings ("np.ndarray[np.bool]") – Concatenated zx string

Returns:

Split z string and x string.

Return type:

tuple[“np.ndarray[np.bool]”, “np.ndarray[np.bool]”]

Module contents

Binary module. Implements operations on binary data structures.