BlockEncoding.from_projector

classmethod BlockEncoding.from_projector(left: int | Tuple[int, ...] | Callable, right: int | Tuple[int, ...] | Callable | None = None, kernel: bool = False, num_ops: int = 1) → BlockEncoding

Constructs a BlockEncoding of a projector.

Parameters:

leftint | tuple of int | Callable

An integer or a tuple of integers representing a computational basis state \(\ket{\phi}\), or a function left(*operands) preparing a state \(\ket{\phi}\) from \(\ket{0}\).

rightint | tuple of int | Callable

An integer or a tuple of integers representing a computational basis state \(\ket{\psi}\), or a function right(*operands) preparing a state \(\ket{\psi}\) from \(\ket{0}\). Defaults to left.

kernelbool

If True, the kernel projector \(\mathbb I - \ket{\phi}\bra{\phi}\) is block-encoded. If False, the projector \(\ket{\phi}\bra{\psi}\) is block-encoded. Defaults to False.

num_opsint

The number of operand quantum variables. Automatically inferred when left or right is an integer or tuple of integers. Defaults to 1.

Returns:

BlockEncoding

A BlockEncoding representing either the projector \(\ket{\phi}\bra{\psi}\) or the kernel projector \(\mathbb I - \ket{\phi}\bra{\phi}\), depending on the value of kernel.

Examples

Example 1: Computational basis states

Define a block-encoding for the projector \(P=\ket{1}\bra{3}\).

from qrisp import *
from qrisp.block_encodings import BlockEncoding

P = BlockEncoding.from_projector(1, 3)

# Prepare operand in superposition state
def operand_prep():
    operand = QuantumFloat(2)
    h(operand)
    return operand

@terminal_sampling
def main():
    operand = P.apply_rus(operand_prep)()
    return operand

res_dict = main()
print(res_dict)
# {1.0: 1.0}

Example 2: Custom states

Define a block-encoding for the projector \(P=\ket{\psi}\bra{\psi}\) where \(\ket{\psi}\propto\ket{0}+\ket{1}+\ket{2}+\ket{3}\).

from qrisp import *
from qrisp.block_encodings import BlockEncoding

def prep_psi(qv):
    h(qv)

P = BlockEncoding.from_projector(prep_psi)

# Prepare operand in |0> state
def operand_prep():
    operand = QuantumFloat(2)
    return operand

@terminal_sampling
def main():
    operand = P.apply_rus(operand_prep)()
    return operand

res_dict = main()
print(res_dict)
# {0.0: 0.25, 1.0: 0.25, 2.0: 0.25, 3.0: 0.25}