---
title: MCXSynthesisNoAuxSP22 (dev version)
description: API reference for qiskit.transpiler.passes.synthesis.hls_plugins.MCXSynthesisNoAuxSP22 in the dev version of qiskit
source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/qiskit/dev/qiskit.transpiler.passes.synthesis.hls_plugins.MCXSynthesisNoAuxSP22
---

# MCXSynthesisNoAuxSP22

*class* `qiskit.transpiler.passes.synthesis.hls_plugins.MCXSynthesisNoAuxSP22`

[GitHub](https://github.com/Qiskit/qiskit/tree/main/qiskit/transpiler/passes/synthesis/hls_plugins.py#L1466-L1503)

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

Synthesis plugin for a multi-controlled [`XGate`](/docs/api/qiskit/dev/qiskit.circuit.library.XGate "qiskit.circuit.library.XGate") based on the implementation for [`MCPhaseGate`](/docs/api/qiskit/dev/qiskit.circuit.library.MCPhaseGate "qiskit.circuit.library.MCPhaseGate"), which is in turn based on the paper by da Silva et al. \[1] and the implementation in qclib \[2].

See \[1, 2] for details.

This plugin name is `mcx.noaux_sp22` which can be used as the key on an [`HLSConfig`](/docs/api/qiskit/dev/qiskit.transpiler.passes.HLSConfig "qiskit.transpiler.passes.HLSConfig") object to use this method with [`HighLevelSynthesis`](/docs/api/qiskit/dev/qiskit.transpiler.passes.HighLevelSynthesis "qiskit.transpiler.passes.HighLevelSynthesis").

For a multi-controlled [`XGate`](/docs/api/qiskit/dev/qiskit.circuit.library.XGate "qiskit.circuit.library.XGate") with $k$ control qubits this synthesis method requires no additional clean auxiliary qubits. The synthesized circuit consists of $k + 1$ qubits. The number of CX-gates is quadratic in $k$.

References:

\[1] A. J. da Silva and D. K. Park, Linear-depth quantum circuits for multiqubit controlled gates, [Phys. Rev. A 106, 042602](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.106.042602).

\[2] [https://github.com/qclib/qclib/blob/master/qclib/gates/ldmcu.py](https://github.com/qclib/qclib/blob/master/qclib/gates/ldmcu.py)

## Methods

### run

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

[GitHub](https://github.com/Qiskit/qiskit/tree/main/qiskit/transpiler/passes/synthesis/hls_plugins.py#L1491-L1503)

Run synthesis for the given MCX gate.