---
title: GraphState (v2.0)
description: API reference for qiskit.circuit.library.GraphState in qiskit v2.0
source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/qiskit/2.0/qiskit.circuit.library.GraphState
---

# GraphState

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

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.0/qiskit/circuit/library/graph_state.py#L23-L86)

Bases: [`QuantumCircuit`](/docs/api/qiskit/2.0/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/2.0/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 1.3\_pending**
>
> The class `qiskit.circuit.library.graph_state.GraphState` is pending deprecation as of Qiskit 1.3. It will be marked deprecated in a future release, and then removed no earlier than 3 months after the release date. 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/2.0/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

### ancillas

A list of `AncillaQubit`s in the order that they were added. You should not mutate this.

### clbits

A list of `Clbit`s in the order that they were added. You should not mutate this.

**Example**

```python
from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit

qr1 = QuantumRegister(2)
qr2 = QuantumRegister(1)
cr1 = ClassicalRegister(2)
cr2 = ClassicalRegister(1)
qc = QuantumCircuit(qr1, qr2, cr1, cr2)

print("List the qubits in this circuit:", qc.qubits)
print("List the classical bits in this circuit:", qc.clbits)
```

```text
List the qubits in this circuit: [Qubit(QuantumRegister(2, 'q0'), 0),
Qubit(QuantumRegister(2, 'q0'), 1), Qubit(QuantumRegister(1, 'q1'), 0)]
List the classical bits in this circuit: [Clbit(ClassicalRegister(2, 'c0'), 0),
Clbit(ClassicalRegister(2, 'c0'), 1), Clbit(ClassicalRegister(1, 'c1'), 0)]
```

### cregs

A list of `Clbit`s in the order that they were added. You should not mutate this.

### data

The circuit data (instructions and context).

**Example**

```python
from qiskit import QuantumCircuit

qc = QuantumCircuit(2, 2)
qc.measure([0], [1])
print(qc.data)
```

```text
[CircuitInstruction(operation=Instruction(name='measure', num_qubits=1,
num_clbits=1, params=[]), qubits=(Qubit(QuantumRegister(2, 'q'), 0),),
clbits=(Clbit(ClassicalRegister(2, 'c'), 1),))]
```

**Returns**

A list-like object containing the [`CircuitInstruction`](/docs/api/qiskit/2.0/qiskit.circuit.CircuitInstruction "qiskit.circuit.CircuitInstruction") instances in the circuit.

### duration

The total duration of the circuit, set by a scheduling transpiler pass. Its unit is specified by [`unit`](#qiskit.circuit.library.GraphState.unit "qiskit.circuit.library.GraphState.unit").

> **Deprecated since version 1.3.0**
>
> The property `qiskit.circuit.quantumcircuit.QuantumCircuit.duration` is deprecated as of Qiskit 1.3.0. It will be removed in Qiskit 3.0.0.

### global\_phase

The global phase of the current circuit scope in radians.

**Example**

```python
from qiskit import QuantumCircuit

circuit = QuantumCircuit(2)
circuit.h(0)
circuit.cx(0, 1)
print(circuit.global_phase)
```

```text
0.0
```

```python
from numpy import pi

circuit.global_phase = pi/4
print(circuit.global_phase)
```

```text
0.7853981633974483
```

### instances

Default value: `357`

### layout

Return any associated layout information about the circuit.

This attribute contains an optional [`TranspileLayout`](/docs/api/qiskit/2.0/qiskit.transpiler.TranspileLayout "qiskit.transpiler.TranspileLayout") object. This is typically set on the output from [`transpile()`](/docs/api/qiskit/2.0/compiler#qiskit.compiler.transpile "qiskit.compiler.transpile") or [`PassManager.run()`](/docs/api/qiskit/2.0/qiskit.transpiler.PassManager#run "qiskit.transpiler.PassManager.run") to retain information about the permutations caused on the input circuit by transpilation.

There are two types of permutations caused by the [`transpile()`](/docs/api/qiskit/2.0/compiler#qiskit.compiler.transpile "qiskit.compiler.transpile") function: an initial layout that permutes the qubits based on the selected physical qubits on the [`Target`](/docs/api/qiskit/2.0/qiskit.transpiler.Target "qiskit.transpiler.Target"), and a final layout, which is an output permutation caused by [`SwapGate`](/docs/api/qiskit/2.0/qiskit.circuit.library.SwapGate "qiskit.circuit.library.SwapGate")s inserted during routing.

**Example**

```python
from qiskit import QuantumCircuit
from qiskit.providers.fake_provider import GenericBackendV2
from qiskit.transpiler import generate_preset_pass_manager

# Create circuit to test transpiler on
qc = QuantumCircuit(3, 3)
qc.h(0)
qc.cx(0, 1)
qc.swap(1, 2)
qc.cx(0, 1)

# Add measurements to the circuit
qc.measure([0, 1, 2], [0, 1, 2])

# Specify the QPU to target
backend = GenericBackendV2(3)

# Transpile the circuit
pass_manager = generate_preset_pass_manager(
optimization_level=1, backend=backend
)
transpiled = pass_manager.run(qc)

# Print the layout after transpilation
print(transpiled.layout.routing_permutation())
```

```text
[0, 1, 2]
```

### metadata

Arbitrary user-defined dictionary of metadata for the circuit.

Qiskit will not examine the content of this mapping, but it will pass it through the transpiler and reattach it to the output, so you can track your own metadata.

**Example**

```python
from qiskit import QuantumCircuit

qc = QuantumCircuit(2, 2, metadata={'experiment_type': 'Bell state experiment'})

print(qc.metadata)
```

```text
{'experiment_type': 'Bell state experiment'}
```

### num\_ancillas

Return the number of ancilla qubits.

**Example**

```python
from qiskit import QuantumCircuit, QuantumRegister, AncillaRegister

# Create a 2-qubit quantum circuit
reg = QuantumRegister(2)
qc = QuantumCircuit(reg)

# Create an ancilla register with 1 qubit
anc = AncillaRegister(1)
qc.add_register(anc)  # Add the ancilla register to the circuit

print("Number of ancilla qubits:", qc.num_ancillas)
```

```text
Number of ancilla qubits: 1
```

### num\_captured\_stretches

The number of stretches in the circuit marked as captured from an enclosing scope.

This is the length of the `iter_captured_stretches()` iterable. If this is non-zero, [`num_input_vars`](#qiskit.circuit.library.GraphState.num_input_vars "qiskit.circuit.library.GraphState.num_input_vars") must be zero.

### num\_captured\_vars

The number of real-time classical variables in the circuit marked as captured from an enclosing scope.

This is the length of the `iter_captured_vars()` iterable. If this is non-zero, [`num_input_vars`](#qiskit.circuit.library.GraphState.num_input_vars "qiskit.circuit.library.GraphState.num_input_vars") must be zero.

### num\_clbits

Return number of classical bits.

**Example**

```python
from qiskit import QuantumCircuit

# Create a new circuit with two qubits and one classical bit
qc = QuantumCircuit(2, 1)
print("Number of classical bits:", qc.num_clbits)
```

```text
Number of classical bits: 1
```

### num\_declared\_stretches

The number of stretches in the circuit that are declared by this circuit scope, excluding captures.

This is the length of the `iter_declared_stretches()` iterable.

### num\_declared\_vars

The number of real-time classical variables in the circuit that are declared by this circuit scope, excluding inputs or captures.

This is the length of the `iter_declared_vars()` iterable.

### num\_identifiers

The number of real-time classical variables and stretches in the circuit.

This is equal to [`num_vars()`](#qiskit.circuit.library.GraphState.num_vars "qiskit.circuit.library.GraphState.num_vars") + [`num_stretches()`](#qiskit.circuit.library.GraphState.num_stretches "qiskit.circuit.library.GraphState.num_stretches").

### num\_input\_vars

The number of real-time classical variables in the circuit marked as circuit inputs.

This is the length of the `iter_input_vars()` iterable. If this is non-zero, [`num_captured_vars`](#qiskit.circuit.library.GraphState.num_captured_vars "qiskit.circuit.library.GraphState.num_captured_vars") must be zero.

### num\_parameters

The number of parameter objects in the circuit.

### num\_qubits

Return number of qubits.

### num\_stretches

The number of stretches in the circuit.

This is the length of the `iter_stretches()` iterable.

### num\_vars

The number of real-time classical variables in the circuit.

This is the length of the `iter_vars()` iterable.

### op\_start\_times

Return a list of operation start times.

> **Note**
>
> This attribute computes the estimate starting time of the operations in the scheduled circuit and only works for simple circuits that have no control flow or other classical feed-forward operations.

This attribute is enabled once one of scheduling analysis passes runs on the quantum circuit.

**Example**

```python
from qiskit import QuantumCircuit
from qiskit.providers.fake_provider import GenericBackendV2
from qiskit.transpiler import generate_preset_pass_manager

qc = QuantumCircuit(2)
qc.h(0)
qc.cx(0, 1)
qc.measure_all()

# Print the original circuit
print("Original circuit:")
print(qc)

# Transpile the circuit with a specific basis gates list and print the resulting circuit
backend = GenericBackendV2(2, basis_gates=['u1', 'u2', 'u3', 'cx'])
pm = generate_preset_pass_manager(
    optimization_level=1, backend=backend, scheduling_method="alap"
)
transpiled_qc = pm.run(qc)
print("Transpiled circuit with basis gates ['u1', 'u2', 'u3', 'cx']:")
print(transpiled_qc)

# Print the start times of each instruction in the transpiled circuit
print("Start times of instructions in the transpiled circuit:")
for instruction, start_time in zip(transpiled_qc.data, transpiled_qc.op_start_times):
    print(f"{instruction.operation.name}: {start_time}")
```

```text
Original circuit:
        ┌───┐      ░ ┌─┐
q_0: ┤ H ├──■───░─┤M├───
        └───┘┌─┴─┐ ░ └╥┘┌─┐
q_1: ─────┤ X ├─░──╫─┤M├
            └───┘ ░  ║ └╥┘
meas: 2/══════════════╩══╩═
                    0  1

Transpiled circuit with basis gates ['u1', 'u2', 'u3', 'cx']:
            ┌─────────┐          ░ ┌─────────────────┐┌─┐
q_0 -> 0 ───┤ U2(0,π) ├──────■───░─┤ Delay(1255[dt]) ├┤M├
        ┌──┴─────────┴───┐┌─┴─┐ ░ └───────┬─┬───────┘└╥┘
q_1 -> 1 ┤ Delay(196[dt]) ├┤ X ├─░─────────┤M├─────────╫─
        └────────────────┘└───┘ ░         └╥┘         ║
meas: 2/═══════════════════════════════════╩══════════╩═
                                            1          0

Start times of instructions in the transpiled circuit:
u2: 0
delay: 0
cx: 196
barrier: 2098
delay: 2098
measure: 3353
measure: 2098
```

**Returns**

List of integers representing instruction estimated start times. The index corresponds to the index of instruction in `QuantumCircuit.data`.

**Raises**

[**AttributeError**](https://docs.python.org/3/library/exceptions.html#AttributeError) – When circuit is not scheduled.

### parameters

The parameters defined in the circuit.

This attribute returns the [`Parameter`](/docs/api/qiskit/2.0/qiskit.circuit.Parameter "qiskit.circuit.Parameter") objects in the circuit sorted alphabetically. Note that parameters instantiated with a [`ParameterVector`](/docs/api/qiskit/2.0/qiskit.circuit.ParameterVector "qiskit.circuit.ParameterVector") are still sorted numerically.

**Examples**

The snippet below shows that insertion order of parameters does not matter.

```python
>>> from qiskit.circuit import QuantumCircuit, Parameter
>>> a, b, elephant = Parameter("a"), Parameter("b"), Parameter("elephant")
>>> circuit = QuantumCircuit(1)
>>> circuit.rx(b, 0)
>>> circuit.rz(elephant, 0)
>>> circuit.ry(a, 0)
>>> circuit.parameters  # sorted alphabetically!
ParameterView([Parameter(a), Parameter(b), Parameter(elephant)])
```

Bear in mind that alphabetical sorting might be unintuitive when it comes to numbers. The literal “10” comes before “2” in strict alphabetical sorting.

```python
>>> from qiskit.circuit import QuantumCircuit, Parameter
>>> angles = [Parameter("angle_1"), Parameter("angle_2"), Parameter("angle_10")]
>>> circuit = QuantumCircuit(1)
>>> circuit.u(*angles, 0)
>>> circuit.draw()
   ┌─────────────────────────────┐
q: ┤ U(angle_1,angle_2,angle_10) ├
   └─────────────────────────────┘
>>> circuit.parameters
ParameterView([Parameter(angle_1), Parameter(angle_10), Parameter(angle_2)])
```

To respect numerical sorting, a [`ParameterVector`](/docs/api/qiskit/2.0/qiskit.circuit.ParameterVector "qiskit.circuit.ParameterVector") can be used.

```python
>>> from qiskit.circuit import QuantumCircuit, Parameter, ParameterVector
>>> x = ParameterVector("x", 12)
>>> circuit = QuantumCircuit(1)
>>> for x_i in x:
...     circuit.rx(x_i, 0)
>>> circuit.parameters
ParameterView([
    ParameterVectorElement(x[0]), ParameterVectorElement(x[1]),
    ParameterVectorElement(x[2]), ParameterVectorElement(x[3]),
    ..., ParameterVectorElement(x[11])
])
```

**Returns**

The sorted [`Parameter`](/docs/api/qiskit/2.0/qiskit.circuit.Parameter "qiskit.circuit.Parameter") objects in the circuit.

### prefix

Default value: `'circuit'`

### qregs

A list of `Qubit`s in the order that they were added. You should not mutate this.

### qubits

A list of `Qubit`s in the order that they were added. You should not mutate this.

### unit

The unit that [`duration`](#qiskit.circuit.library.GraphState.duration "qiskit.circuit.library.GraphState.duration") is specified in.

> **Deprecated since version 1.3.0**
>
> The property `qiskit.circuit.quantumcircuit.QuantumCircuit.unit` is deprecated as of Qiskit 1.3.0. It will be removed in Qiskit 3.0.0.

### 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
```