---
title: GraphState (v2.3)
description: API reference for qiskit.circuit.library.GraphState in qiskit v2.3
source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/qiskit/2.3/qiskit.circuit.library.GraphState
---

# GraphState

*class* `qiskit.circuit.library.GraphState(adjacency_matrix)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.3/qiskit/circuit/library/graph_state.py#L23-L86)

Bases: [`QuantumCircuit`](/docs/api/qiskit/2.3/qiskit.circuit.QuantumCircuit "qiskit.circuit.quantumcircuit.QuantumCircuit")

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

$$
|G\rangle = \prod_{(a,b) \in E} CZ_{(a,b)} {|+\rangle}^{\otimes V}
$$

Such a state can be prepared by first preparing all qubits in the $+$ state, then applying a $CZ$ 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:

![Diagram illustrating the previously described circuit.](https://eu-de.quantum.cloud.ibm.com/docs/images/api/qiskit/2.3/qiskit-circuit-library-GraphState-1.avif)

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)

Create graph state preparation circuit.

> **Deprecated since version 2.1**
>
> The class `qiskit.circuit.library.graph_state.GraphState` is deprecated as of Qiskit 2.1. It will be removed in Qiskit 3.0. Use qiskit.circuit.library.GraphStateGate instead.

**Parameters**

**adjacency\_matrix** ([*list*](https://docs.python.org/3/library/stdtypes.html#list) *| np.ndarray*) – input graph as n-by-n list of 0-1 lists

**Raises**

[**CircuitError**](/docs/api/qiskit/2.3/circuit#qiskit.circuit.CircuitError "qiskit.circuit.CircuitError") – If adjacency\_matrix is not symmetric.

The circuit prepares a graph state with the given adjacency matrix.

## Attributes

### name

Type: `str`

A human-readable name for the circuit.

**Example**

```python
from qiskit import QuantumCircuit

qc = QuantumCircuit(2, 2, name="my_circuit")
print(qc.name)
```

```text
my_circuit
```