---
title: pauli_two_design (v2.2)
description: API reference for qiskit.circuit.library.pauli_two_design in qiskit v2.2
source: https://quantum.cloud.ibm.com/docs/en/api/qiskit/2.2/qiskit.circuit.library.pauli_two_design
---

# qiskit.circuit.library.pauli\_two\_design

`qiskit.circuit.library.pauli_two_design(num_qubits, reps=3, seed=None, insert_barriers=False, parameter_prefix='θ', name='PauliTwoDesign')`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.2/qiskit/circuit/library/n_local/pauli_two_design.py#L25-L112)

Construct a Pauli 2-design ansatz.

This class implements a particular form of a 2-design circuit \[1], which is frequently studied in quantum machine learning literature, such as, e.g., the investigation of Barren plateaus in variational algorithms \[2].

The circuit consists of alternating rotation and entanglement layers with an initial layer of $\sqrt{H} = RY(\pi/4)$ gates. The rotation layers contain single qubit Pauli rotations, where the axis is chosen uniformly at random to be X, Y or Z. The entanglement layers is compromised of pairwise CZ gates with a total depth of 2.

For instance, the circuit could look like this:

```python
     ┌─────────┐┌──────────┐       ░ ┌──────────┐       ░  ┌──────────┐
q_0: ┤ RY(π/4) ├┤ RZ(θ[0]) ├─■─────░─┤ RY(θ[4]) ├─■─────░──┤ RZ(θ[8]) ├
     ├─────────┤├──────────┤ │     ░ ├──────────┤ │     ░  ├──────────┤
q_1: ┤ RY(π/4) ├┤ RZ(θ[1]) ├─■──■──░─┤ RY(θ[5]) ├─■──■──░──┤ RX(θ[9]) ├
     ├─────────┤├──────────┤    │  ░ ├──────────┤    │  ░ ┌┴──────────┤
q_2: ┤ RY(π/4) ├┤ RX(θ[2]) ├─■──■──░─┤ RY(θ[6]) ├─■──■──░─┤ RX(θ[10]) ├
     ├─────────┤├──────────┤ │     ░ ├──────────┤ │     ░ ├───────────┤
q_3: ┤ RY(π/4) ├┤ RZ(θ[3]) ├─■─────░─┤ RX(θ[7]) ├─■─────░─┤ RY(θ[11]) ├
     └─────────┘└──────────┘       ░ └──────────┘       ░ └───────────┘
```

Examples:

```python
from qiskit.circuit.library import pauli_two_design
circuit = pauli_two_design(4, reps=2, seed=5, insert_barriers=True)
circuit.draw("mpl")
```

![Circuit diagram output by the previous code.](https://quantum.cloud.ibm.com/docs/images/api/qiskit/2.2/qiskit-circuit-library-pauli_two_design-1.avif)

**Parameters**

- **num\_qubits** ([*int*](https://docs.python.org/3/library/functions.html#int)) – The number of qubits of the Pauli Two-Design circuit.
- **reps** ([*int*](https://docs.python.org/3/library/functions.html#int)) – Specifies how often a block consisting of a rotation layer and entanglement layer is repeated.
- **seed** ([*int*](https://docs.python.org/3/library/functions.html#int) *| None*) – The seed for randomly choosing the axes of the Pauli rotations.
- **parameter\_prefix** ([*str*](https://docs.python.org/3/library/stdtypes.html#str)) – The prefix used for the rotation parameters.
- **insert\_barriers** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) – If `True`, barriers are inserted in between each layer. If `False`, no barriers are inserted. Defaults to `False`.
- **name** ([*str*](https://docs.python.org/3/library/stdtypes.html#str)) – The circuit name.

**Returns**

A Pauli 2-design circuit.

**Return type**

[QuantumCircuit](/docs/api/qiskit/2.2/qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit")

References:

\[1] Nakata et al., Unitary 2-designs from random X- and Z-diagonal unitaries. [arXiv:1502.07514](https://arxiv.org/pdf/1502.07514.pdf)

\[2] McClean et al., Barren plateaus in quantum neural network training landscapes. [arXiv:1803.11173](https://arxiv.org/pdf/1803.11173.pdf)