# 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.
"""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)
```