Quellcode für qiskit.circuit.library.hidden_linear_function

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# (C) Copyright IBM 2017, 2020.
# This code is licensed under the Apache License, Version 2.0. You may
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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

[Doku]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: Consider the quadratic form .. 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:** .. plot:: from qiskit.circuit.library import HiddenLinearFunction from qiskit.tools.jupyter.library import _generate_circuit_library_visualization A = [[1, 1, 0], [1, 0, 1], [0, 1, 1]] circuit = HiddenLinearFunction(A) _generate_circuit_library_visualization(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. """ adjacency_matrix = np.asarray(adjacency_matrix) if not np.allclose(adjacency_matrix, adjacency_matrix.transpose()): raise CircuitError("The adjacency matrix must be symmetric.") num_qubits = len(adjacency_matrix) 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): if adjacency_matrix[i][j]: circuit.cz(i, j) for i in range(num_qubits): if adjacency_matrix[i][i]: circuit.s(i) circuit.h(range(num_qubits)) super().__init__(*circuit.qregs, name=circuit.name) self.compose(circuit.to_gate(), qubits=self.qubits, inplace=True)