English
Languages
English
Japanese
German
Korean
Shortcuts

Source code for qiskit.circuit.library.graph_state

# 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
# that they have been altered from the originals.

# pylint: disable=no-member

"""Graph State circuit."""

from typing import Union, List

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


[docs]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:** .. jupyter-execute:: :hide-code: from qiskit.circuit.library import GraphState import qiskit.tools.jupyter import networkx as nx G = nx.Graph() G.add_edges_from([(1, 2), (2, 3), (3, 4), (4, 5), (5, 1)]) adjmat = nx.adjacency_matrix(G) circuit = GraphState(adjmat.toarray()) %circuit_library_info 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>`_ """
[docs] def __init__(self, adjacency_matrix: Union[List, np.array]) -> 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) super().__init__(num_qubits, name="graph: %s" % (adjacency_matrix)) self.h(range(num_qubits)) for i in range(num_qubits): for j in range(i+1, num_qubits): if adjacency_matrix[i][j] == 1: self.cz(i, j)

© Copyright 2020, Qiskit Development Team. Last updated on 2021/02/27.

Built with Sphinx using a theme provided by Read the Docs.