hqs_quantum_solver.util

hqs_quantum_solver.util#

Miscellaneous utility functions.

Functions

commutator(A, B)

Computes the commutator of two matrices.

split_diagonal(a)

Splits a 2d array into diagonal and off-diagonal elements.

unit_vector(dim, i[, dtype])

Creates a cannonical unit vector.

unit_vector_index(v, *[, decimal])

Given a canonical unit vector, returns the index of the one in the vector.
commutator(A: ndarray, B: ndarray) → ndarray#

Computes the commutator of two matrices.

split_diagonal(a: ndarray) → tuple[ndarray, ndarray]#

Splits a 2d array into diagonal and off-diagonal elements.

Parameters:

a (ndarray) – The input array. Must be a 2d array.

Returns:

Returns (diag, offdiag), the diagonal and off-diagonal

elements, respectively.

Return type:

tuple[ndarray,ndarray]

Raises:

ValueError – When the array is of invalid shape.

unit_vector(dim: int, i: int, dtype: DTypeLike = None) → np.ndarray#

Creates a cannonical unit vector.

The i-th cannonical unit vector \(\mathbf{e}_i\) is defined by

\[\begin{split}\big(\mathbf{e}_i\big)_j = \begin{cases} 1 & \text{if $i = j$,} \\ 0 & \text{otherwise.} \end{cases}\end{split}\]
Parameters:

  • dim (int) – The length of the vector.

  • i (int) – The position of the non-zero element.

  • dtype (DTypeLike) – The dtype of the vector to be constructed.

unit_vector_index(v: ArrayLike, *, decimal: int = 7) → int#

Given a canonical unit vector, returns the index of the one in the vector.

Parameters:

  • v (ArrayLike) – The unit vector.

  • decimal (int) – The number of decimal places to which to compare the given vector.

Returns:

The index.

Return type:

int

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