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

# iqp

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

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/1.3/qiskit/circuit/library/iqp.py#L86-L147)

Bases:

Instantaneous quantum polynomial time (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 $n \times n$ 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://quantum.cloud.ibm.com/docs/images/api/qiskit/1.3/qiskit-circuit-library-iqp_function-1.avif)

**Expanded Circuit:**

> ![Diagram illustrating the previously described circuit.](https://quantum.cloud.ibm.com/docs/images/api/qiskit/1.3/qiskit-circuit-library-iqp_function-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)

**Parameters**

**interactions** ([*Sequence*](https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence)*\[*[*Sequence*](https://docs.python.org/3/library/collections.abc.html#collections.abc.Sequence)*\[*[*int*](https://docs.python.org/3/library/functions.html#int)*]]*) – The interactions as symmetric square matrix. If `None`, then the `num_qubits` argument must be set and a random IQP circuit will be generated.

**Returns**

An IQP circuit.

**Return type**

[*QuantumCircuit*](/docs/api/qiskit/1.3/qiskit.circuit.QuantumCircuit "qiskit.circuit.quantumcircuit.QuantumCircuit")