# This code is part of Qiskit.
#
# (C) Copyright IBM 2017, 2020.
#
# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
#
# 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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"""Graph State circuit."""
from __future__ import annotations
import numpy as np
from qiskit.circuit.quantumcircuit import QuantumCircuit
from qiskit.circuit.exceptions import CircuitError
[ドキュメント]class GraphState(QuantumCircuit):
r"""Circuit to prepare a graph state.
Given a graph G = (V, E), with the set of vertices V and the set of edges E,
the corresponding graph state is defined as
.. math::
|G\rangle = \prod_{(a,b) \in E} CZ_{(a,b)} {|+\rangle}^{\otimes V}
Such a state can be prepared by first preparing all qubits in the :math:`+`
state, then applying a :math:`CZ` gate for each corresponding graph edge.
Graph state preparation circuits are Clifford circuits, and thus
easy to simulate classically. However, by adding a layer of measurements
in a product basis at the end, there is evidence that the circuit becomes
hard to simulate [2].
**Reference Circuit:**
.. plot::
from qiskit.circuit.library import GraphState
from qiskit.tools.jupyter.library import _generate_circuit_library_visualization
import rustworkx as rx
G = rx.generators.cycle_graph(5)
circuit = GraphState(rx.adjacency_matrix(G))
_generate_circuit_library_visualization(circuit)
**References:**
[1] M. Hein, J. Eisert, H.J. Briegel, Multi-party Entanglement in Graph States,
`arXiv:0307130 <https://arxiv.org/pdf/quant-ph/0307130.pdf>`_
[2] D. Koh, Further Extensions of Clifford Circuits & their Classical Simulation Complexities.
`arXiv:1512.07892 <https://arxiv.org/pdf/1512.07892.pdf>`_
"""
def __init__(self, adjacency_matrix: list | np.ndarray) -> None:
"""Create graph state preparation circuit.
Args:
adjacency_matrix: input graph as n-by-n list of 0-1 lists
Raises:
CircuitError: If adjacency_matrix is not symmetric.
The circuit prepares a graph state with the given adjacency
matrix.
"""
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="graph: %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] == 1:
circuit.cz(i, j)
super().__init__(*circuit.qregs, name=circuit.name)
self.compose(circuit.to_gate(), qubits=self.qubits, inplace=True)