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

# IQP

*class* `qiskit.circuit.library.IQP(interactions)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.2/qiskit/circuit/library/iqp.py#L24-L83)

Bases: [`QuantumCircuit`](/docs/api/qiskit/2.2/qiskit.circuit.QuantumCircuit "qiskit.circuit.quantumcircuit.QuantumCircuit")

Instantaneous quantum polynomial (IQP) circuit.

The circuit consists of a column of Hadamard gates, a column of powers of T gates, a sequence of powers of CS gates (up to $\frac{n^2-n}{2}$ of them), and a final column of Hadamard gates, as introduced in \[1].

The circuit is parameterized by an n x n interactions matrix. The powers of each T gate are given by the diagonal elements of the interactions matrix. The powers of the CS gates are given by the upper triangle of the interactions matrix.

Reference Circuit:

![Diagram illustrating the previously described circuit.](https://eu-de.quantum.cloud.ibm.com/docs/images/api/qiskit/2.2/qiskit-circuit-library-IQP-1.avif)

Expanded Circuit:

![Diagram illustrating the previously described circuit.](https://eu-de.quantum.cloud.ibm.com/docs/images/api/qiskit/2.2/qiskit-circuit-library-IQP-2.avif)

References:

\[1] M. J. Bremner et al. Average-case complexity versus approximate simulation of commuting quantum computations, Phys. Rev. Lett. 117, 080501 (2016). [arXiv:1504.07999](https://arxiv.org/abs/1504.07999)

Create IQP circuit.

> **Deprecated since version 2.1**
>
> The class `qiskit.circuit.library.iqp.IQP` is deprecated as of Qiskit 2.1. It will be removed in Qiskit 3.0. Use the qiskit.circuit.library.iqp function instead.

**Parameters**

**interactions** ([*list*](https://docs.python.org/3/library/stdtypes.html#list) *| np.ndarray*) – input n-by-n symmetric matrix.

**Raises**

[**CircuitError**](/docs/api/qiskit/2.2/circuit#qiskit.circuit.CircuitError "qiskit.circuit.CircuitError") – if the inputs is not as symmetric 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
```