BlockEncoding.__mul__

BlockEncoding.__mul__(other: ArrayLike) → BlockEncoding

Returns a BlockEncoding of the scaled operator.

This method implements the scalar multiplication \(c \cdot A\), where \(A\) is the operator encoded by this instance and \(c\) is the provided scalar.

Parameters:

otherArrayLike

The scalar scaling factor (coefficient) to apply. Can be a Python float, a JAX/NumPy scalar, or a 0-dimensional array.

Returns:

BlockEncoding

A new BlockEncoding instance representing the scaled operator.

Notes

• Multiplying by a scalar \(c\) results in a new BlockEncoding of \(cA\) by updating \(\alpha \rightarrow c\alpha\).

Examples

Define two block-encodings and implement their scaled sum as a new block encoding.

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 = 2*H1 + H2

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

BE_mul = 2*BE1 + BE2
BE_mul_r = BE1*2 + 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)
res_be_mul_r = main(BE_mul_r)

print("Result from BE of 2 * H1 + H2: ", res_be3)
print("Result from 2 * BE1 + BE2: ", res_be_mul)
print("Result from BE1 * 2 + BE2: ", res_be_mul_r)
# Result from BE of 2 * H1 + H2:  {3.0: 0.5614033770142979, 0.0: 0.21929831149285103, 4.0: 0.21929831149285103}
# Result from 2 * BE1 + BE2:  {3.0: 0.5614033770142979, 0.0: 0.21929831149285103, 4.0: 0.21929831149285103}
# Result from BE1 * 2 + BE2:  {3.0: 0.5614033770142979, 0.0: 0.21929831149285103, 4.0: 0.21929831149285103}