BlockEncoding.from_eye

classmethod BlockEncoding.from_eye(diagonal_index: int = 0) → BlockEncoding

Constructs a BlockEncoding of a 2-D array with ones on the diagonal and zeros elsewhere.

Parameters:

diagonal_indexint

Index of the diagonal to set to one: 0 (the default) refers to the main diagonal, a positive value refers to an upper diagonal, and a negative value to a lower diagonal.

Returns:

BlockEncoding

A BlockEncoding representing an array where all elements are equal to zero, except for the \(k\)-th diagonal, whose values are equal to one.

Examples

from qrisp import *
from qrisp.block_encodings import BlockEncoding

# diagonal_index = 0: ones on the main diagonal
BE1 = BlockEncoding.from_eye(diagonal_index=0)

# diagonal_index = -2: ones on the second lower subdiagonal
# (non-cyclic) shift |x> -> |x+2>
BE2 = BlockEncoding.from_eye(diagonal_index=-2)

BE3 = BE1.kron(BE2)

def operand_prep():
    operand1 = QuantumFloat(3)
    operand2 = QuantumFloat(3)
    h(operand1)
    cx(operand1, operand2)
    return operand1, operand2

@terminal_sampling
def main():
    operand1, operand2 = BE3.apply_rus(operand_prep)()
    return operand1, operand2

main()
# {(0.0, 2.0): 0.16666666666666666,
# (1.0, 3.0): 0.16666666666666666,
# (2.0, 4.0): 0.16666666666666666,
# (3.0, 5.0): 0.16666666666666666,
# (4.0, 6.0): 0.16666666666666666,
# (5.0, 7.0): 0.16666666666666666}