qiskit.circuit.library.hidden_linear_function のソースコード

# This code is part of Qiskit.
#
# (C) Copyright IBM 2017, 2020.
#
# obtain a copy of this license in the LICENSE.txt file in the root directory
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
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"""Hidden Linear Function circuit."""

from typing import Union, List

import numpy as np
from qiskit.circuit.quantumcircuit import QuantumCircuit
from qiskit.circuit.exceptions import CircuitError

[ドキュメント]class HiddenLinearFunction(QuantumCircuit):
r"""Circuit to solve the hidden linear function problem.

The 2D Hidden Linear Function problem is determined by a 2D adjacency
matrix A, where only elements that are nearest-neighbor on a grid have
non-zero entries. Each row/column corresponds to one binary variable
:math:x_i.

The hidden linear function problem is as follows:

.. math::

q(x) = \sum_{i,j=1}^{n}{x_i x_j} ~(\mathrm{mod}~ 4)

and restrict :math:q(x) onto the nullspace of A. This results in a linear
function.

.. math::

2 \sum_{i=1}^{n}{z_i x_i} ~(\mathrm{mod}~ 4)  \forall  x \in \mathrm{Ker}(A)

and the goal is to recover this linear function (equivalently a vector
:math:[z_0, ..., z_{n-1}]). There can be multiple solutions.

In [1] it is shown that the present circuit solves this problem
on a quantum computer in constant depth, whereas any corresponding
solution on a classical computer would require circuits that grow
logarithmically with :math:n. Thus this circuit is an example
of quantum advantage with shallow circuits.

**Reference Circuit:**

.. jupyter-execute::
:hide-code:

from qiskit.circuit.library import HiddenLinearFunction
import qiskit.tools.jupyter
A = [[1, 1, 0], [1, 0, 1], [0, 1, 1]]
circuit = HiddenLinearFunction(A)
%circuit_library_info circuit

**Reference:**

[1] S. Bravyi, D. Gosset, R. Koenig, Quantum Advantage with Shallow Circuits, 2017.
arXiv:1704.00690 <https://arxiv.org/abs/1704.00690>_
"""

def __init__(self, adjacency_matrix: Union[List[List[int]], np.ndarray]) -> None:
"""Create new HLF circuit.

Args:
adjacency_matrix: a symmetric n-by-n list of 0-1 lists.
n will be the number of qubits.

Raises:
CircuitError: If A is not symmetric.
"""
raise CircuitError("The adjacency matrix must be symmetric.")

circuit = QuantumCircuit(num_qubits, name="hlf: %s" % adjacency_matrix)

circuit.h(range(num_qubits))
for i in range(num_qubits):
for j in range(i + 1, num_qubits):