---
title: PMHSynthesisLinearFunction (v1.1)
description: API reference for qiskit.transpiler.passes.synthesis.high_level_synthesis.PMHSynthesisLinearFunction in qiskit v1.1
source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/qiskit/1.1/qiskit.transpiler.passes.synthesis.high_level_synthesis.PMHSynthesisLinearFunction
---

# PMHSynthesisLinearFunction

*class* `qiskit.transpiler.passes.synthesis.high_level_synthesis.PMHSynthesisLinearFunction`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/1.1/qiskit/transpiler/passes/synthesis/high_level_synthesis.py#L799-L848)

Bases: [`HighLevelSynthesisPlugin`](/docs/api/qiskit/1.1/qiskit.transpiler.passes.synthesis.plugin.HighLevelSynthesisPlugin "qiskit.transpiler.passes.synthesis.plugin.HighLevelSynthesisPlugin")

Linear function synthesis plugin based on the Patel-Markov-Hayes method.

This plugin name is :`linear_function.pmh` which can be used as the key on an [`HLSConfig`](/docs/api/qiskit/1.1/qiskit.transpiler.passes.HLSConfig "qiskit.transpiler.passes.synthesis.high_level_synthesis.HLSConfig") object to use this method with [`HighLevelSynthesis`](/docs/api/qiskit/1.1/qiskit.transpiler.passes.HighLevelSynthesis "qiskit.transpiler.passes.synthesis.high_level_synthesis.HighLevelSynthesis").

The plugin supports the following plugin-specific options:

- section size: The size of each section used in the Patel–Markov–Hayes algorithm \[1].

- **use\_inverted: Indicates whether to run the algorithm on the inverse matrix**

  and to invert the synthesized circuit. In certain cases this provides a better decomposition than the direct approach.

- **use\_transposed: Indicates whether to run the algorithm on the transposed matrix**

  and to invert the order of CX gates in the synthesized circuit. In certain cases this provides a better decomposition than the direct approach.

**References**

1. Patel, Ketan N., Igor L. Markov, and John P. Hayes, *Optimal synthesis of linear reversible circuits*, Quantum Information & Computation 8.3 (2008): 282-294. [arXiv:quant-ph/0302002 \[quant-ph\]](https://arxiv.org/abs/quant-ph/0302002)

## Methods

### run

`run(high_level_object, coupling_map=None, target=None, qubits=None, **options)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/1.1/qiskit/transpiler/passes/synthesis/high_level_synthesis.py#L822-L848)

Run synthesis for the given LinearFunction.