---
title: CommutativeOptimization (v2.4)
description: API reference for qiskit.transpiler.passes.CommutativeOptimization in qiskit v2.4
source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/qiskit/2.4/qiskit.transpiler.passes.CommutativeOptimization
---

# CommutativeOptimization

*class* `qiskit.transpiler.passes.CommutativeOptimization(*args, **kwargs)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.4/qiskit/transpiler/passes/optimization/commutative_optimization.py#L24-L73)

Bases: [`TransformationPass`](/docs/api/qiskit/2.4/qiskit.transpiler.TransformationPass "qiskit.transpiler.basepasses.TransformationPass")

Cancel/merge gates exploiting commutativity relations.

Specifically, the pass:

- Cancels pairs of inverse gates, including pairs that are inverse up to a global phase (adjusting the global phase if necessary).
- Attempts to merge consecutive gates when possible, for example sequences of RZ-gates, RX-gates, Pauli rotations, and so on.

This pass unifies and extends the functionality of both [`CommutativeCancellation`](/docs/api/qiskit/2.4/qiskit.transpiler.passes.CommutativeCancellation "qiskit.transpiler.passes.CommutativeCancellation") and [`CommutativeInverseCancellation`](/docs/api/qiskit/2.4/qiskit.transpiler.passes.CommutativeInverseCancellation "qiskit.transpiler.passes.CommutativeInverseCancellation").

**Parameters**

- **approximation\_degree** – the threshold used in the average gate fidelity computation to decide whether pairs of gates can be considered as canceling or commuting.
- **matrix\_max\_num\_qubits** – Upper-bound on the number of qubits for the matrix-based commutativity and inverse checks.

## Attributes

### is\_analysis\_pass

Check if the pass is an analysis pass.

If the pass is an AnalysisPass, that means that the pass can analyze the DAG and write the results of that analysis in the property set. Modifications on the DAG are not allowed by this kind of pass.

### is\_transformation\_pass

Check if the pass is a transformation pass.

If the pass is a TransformationPass, that means that the pass can manipulate the DAG, but cannot modify the property set (but it can be read).

## Methods

### execute

`execute(passmanager_ir, state, callback=None)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.4/qiskit/transpiler/basepasses.py#L161-L180)

Execute optimization task for input Qiskit IR.

**Parameters**

- **passmanager\_ir** ([*Any*](https://docs.python.org/3/library/typing.html#typing.Any)) – Qiskit IR to optimize.
- **state** ([*PassManagerState*](/docs/api/qiskit/2.4/qiskit.passmanager.PassManagerState "qiskit.passmanager.compilation_status.PassManagerState")) – State associated with workflow execution by the pass manager itself.
- **callback** ([*Callable*](https://docs.python.org/3/library/collections.abc.html#collections.abc.Callable) *| None*) – A callback function which is called per execution of optimization task.

**Returns**

Optimized Qiskit IR and state of the workflow.

**Return type**

[tuple](https://docs.python.org/3/library/stdtypes.html#tuple)\[[*Any*](https://docs.python.org/3/library/typing.html#typing.Any), [*PassManagerState*](/docs/api/qiskit/2.4/qiskit.passmanager.PassManagerState "qiskit.passmanager.compilation_status.PassManagerState")]

### name

`name()`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.4/qiskit/passmanager/base_tasks.py#L67-L69)

Name of the pass.

**Return type**

[str](https://docs.python.org/3/library/stdtypes.html#str)

### run

`run(dag)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.4/qiskit/transpiler/passes/optimization/commutative_optimization.py#L55-L73)

Run the CommutativeOptimization pass on dag.

**Parameters**

**dag** ([*DAGCircuit*](/docs/api/qiskit/2.4/qiskit.dagcircuit.DAGCircuit "qiskit.dagcircuit.DAGCircuit")) – the DAG to be optimized.

**Returns**

the optimized DAG.

**Return type**

[DAGCircuit](/docs/api/qiskit/2.4/qiskit.dagcircuit.DAGCircuit "qiskit.dagcircuit.DAGCircuit")

### update\_status

`update_status(state, run_state)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.4/qiskit/transpiler/basepasses.py#L182-L190)

Update workflow status.

**Parameters**

- **state** ([*PassManagerState*](/docs/api/qiskit/2.4/qiskit.passmanager.PassManagerState "qiskit.passmanager.compilation_status.PassManagerState")) – Pass manager state to update.
- **run\_state** (*RunState*) – Completion status of current task.

**Returns**

Updated pass manager state.

**Return type**

[*PassManagerState*](/docs/api/qiskit/2.4/qiskit.passmanager.PassManagerState "qiskit.passmanager.compilation_status.PassManagerState")