---
title: GraphStateGate (v1.3)
description: API reference for qiskit.circuit.library.GraphStateGate in qiskit v1.3
source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/qiskit/1.3/qiskit.circuit.library.GraphStateGate
---

# GraphStateGate

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

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/1.3/qiskit/circuit/library/graph_state.py#L88-L171)

Bases: [`Gate`](/docs/api/qiskit/1.3/qiskit.circuit.Gate "qiskit.circuit.gate.Gate")

A gate representing 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:**

```python
from qiskit.circuit import QuantumCircuit
from qiskit.circuit.library import GraphStateGate
import rustworkx as rx

G = rx.generators.cycle_graph(5)
circuit = QuantumCircuit(5)
circuit.append(GraphStateGate(rx.adjacency_matrix(G)), [0, 1, 2, 3, 4])
circuit.decompose().draw('mpl')
```

![Circuit diagram output by the previous code.](https://eu-de.quantum.cloud.ibm.com/docs/images/api/qiskit/1.3/qiskit-circuit-library-GraphStateGate-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)

**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/1.3/circuit#qiskit.circuit.CircuitError "qiskit.circuit.CircuitError") – If adjacency\_matrix is not symmetric.

The gate represents a graph state with the given adjacency matrix.

## Attributes

### adjacency\_matrix

Returns the adjacency matrix.

### base\_class

Get the base class of this instruction. This is guaranteed to be in the inheritance tree of `self`.

The “base class” of an instruction is the lowest class in its inheritance tree that the object should be considered entirely compatible with for \_all\_ circuit applications. This typically means that the subclass is defined purely to offer some sort of programmer convenience over the base class, and the base class is the “true” class for a behavioral perspective. In particular, you should *not* override [`base_class`](#qiskit.circuit.library.GraphStateGate.base_class "qiskit.circuit.library.GraphStateGate.base_class") if you are defining a custom version of an instruction that will be implemented differently by hardware, such as an alternative measurement strategy, or a version of a parametrized gate with a particular set of parameters for the purposes of distinguishing it in a [`Target`](/docs/api/qiskit/1.3/qiskit.transpiler.Target "qiskit.transpiler.Target") from the full parametrized gate.

This is often exactly equivalent to `type(obj)`, except in the case of singleton instances of standard-library instructions. These singleton instances are special subclasses of their base class, and this property will return that base. For example:

```python
>>> isinstance(XGate(), XGate)
True
>>> type(XGate()) is XGate
False
>>> XGate().base_class is XGate
True
```

In general, you should not rely on the precise class of an instruction; within a given circuit, it is expected that `Instruction.name` should be a more suitable discriminator in most situations.

### condition

The classical condition on the instruction.

> **Deprecated since version 1.3.0**
>
> The property `qiskit.circuit.instruction.Instruction.condition` is deprecated as of qiskit 1.3.0. It will be removed in 2.0.0.

### condition\_bits

Get Clbits in condition.

> **Deprecated since version 1.3.0**
>
> The property `qiskit.circuit.instruction.Instruction.condition_bits` is deprecated as of qiskit 1.3.0. It will be removed in 2.0.0.

### decompositions

Get the decompositions of the instruction from the SessionEquivalenceLibrary.

### definition

Return definition in terms of other basic gates.

### duration

Get the duration.

> **Deprecated since version 1.3.0**
>
> The property `qiskit.circuit.instruction.Instruction.duration` is deprecated as of qiskit 1.3.0. It will be removed in Qiskit 2.0.0.

### label

Return instruction label

### mutable

Is this instance is a mutable unique instance or not.

If this attribute is `False` the gate instance is a shared singleton and is not mutable.

### name

Return the name.

### num\_clbits

Return the number of clbits.

### num\_qubits

Return the number of qubits.

### params

The parameters of this `Instruction`. Ideally these will be gate angles.

### unit

Get the time unit of duration.

> **Deprecated since version 1.3.0**
>
> The property `qiskit.circuit.instruction.Instruction.unit` is deprecated as of qiskit 1.3.0. It will be removed in Qiskit 2.0.0.

## Methods

### validate\_parameter

`validate_parameter(parameter)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/1.3/qiskit/circuit/library/graph_state.py#L157-L159)

Parameter validation