BlockEncoding.from_array#

classmethod BlockEncoding.from_array(A: ndarray[tuple[Any, ...], dtype[Any]] | csr_array | csr_matrix) → BlockEncoding[source]#

Constructs a BlockEncoding from a 2-D array.

Parameters:

Andarray | csr_array | csr_matrix: 2-D array of shape (N,N,) for a power of two N.

Returns:

BlockEncoding: A BlockEncoding representing the Hermitian part \((A+A^{\dagger})/2\).

Raises:

ValueError: If A is not a 2-D square matrix.
ValueError: If the dimension of A is not a power of two.

Notes

Block encoding based on Pauli decomposition \(O=\sum_i\alpha_i P_i\) where \(\alpha_i\) are real positive coefficients and \(P_i\) are Pauli strings (including the respective sign).
Normalization: The block-encoding normalization factor is \(\alpha = \sum_i \alpha_i\).

Examples

>>> import numpy as np
>>> from qrisp.block_encodings import BlockEncoding
>>> A = np.array([[0,1,0,1],[1,0,0,0],[0,0,1,0],[1,0,0,0]])
>>> B = BlockEncoding.from_array(A)