BlockEncoding.__matmul__

BlockEncoding.__matmul__(other: 'ArrayLike' | BlockEncoding) → BlockEncoding

Returns a BlockEncoding of the product of two operators.

This method implements the operator product \(A \cdot B\) by composing two BlockEncodings, where \(A\) and \(B\) are the operators encoded by the respective instances.

Parameters:

otherBlockEncoding

The BlockEncoding instance to be multiplied.

Returns:

BlockEncoding

A new BlockEncoding representing the operator product.

Notes

• Can only be used when both BlockEncodings have the same operand structure.

• The @ operator should be used sparingly, primarily to combine a few block encodings. For larger-scale polynomial transformations, Quantum Signal Processing (QSP) is the superior method.

• The product of two Hermitian operators A and B is Hermitian if and only if they commute, i.e., AB = BA.

Examples

Define two block-encodings and multiply them.

from qrisp import *
from qrisp.block_encodings import BlockEncoding
from qrisp.operators import X, Y, Z

# Commuting operators H1 and H2
H1 = X(0)*X(1) + 0.2*Y(0)*Y(1)
H2 = Z(0)*Z(1) + X(2)
H3 = H1 * H2

BE1 = BlockEncoding.from_operator(H1)
BE2 = BlockEncoding.from_operator(H2)
BE3 = BlockEncoding.from_operator(H3)

BE_mul = BE1 @ BE2

def operand_prep():
    qv = QuantumFloat(3)
    return qv

@terminal_sampling
def main(BE):
    qv = BE.apply_rus(operand_prep)()
    return qv

res_be3 = main(BE3)
res_be_mul = main(BE_mul)
print("Result from BE of H1 * H2: ", res_be3)
print("Result from BE1 @ BE2: ", res_be_mul)
# Result from BE of H1 * H2:  {3.0: 0.5, 7.0: 0.5}
# Result from BE1 @ BE2:  {3.0: 0.5, 7.0: 0.5}