---
title: commutator (latest version)
description: API reference for qiskit_bosons.operators.library.commutator in the latest version of qiskit-bosons
source: https://quantum.cloud.ibm.com/docs/en/api/qiskit-bosons/operators-library-commutator
---

# commutator

`commutator(op_a, op_b)`

Computes the commutator of two operators.

The commutator is defined as:

$$
[A, B] = AB - BA
$$

Operators which support this method must implement the [`SupportsCommutators`](/docs/api/qiskit-bosons/protocols-supports-commutators "qiskit_bosons.protocols.SupportsCommutators") protocol.

> **Note**
>
> Both inputs must be of the same operator type. This will also determine the output type.

```pycon
>>> from qiskit_bosons.operators import BosonOperator, ann, cre
>>> from qiskit_bosons.operators.library import commutator
>>> b = BosonOperator.from_dict({(ann(0),): 1.0})
>>> b_dag = BosonOperator.from_dict({(cre(0),): 1.0})
>>> commutator(b, b_dag).equiv(BosonOperator.one())
True
>>> n = BosonOperator.from_dict({(cre(0), ann(0)): 1.0})
>>> commutator(n, b_dag).equiv(b_dag)
True
>>> b1_dag = BosonOperator.from_dict({(cre(1),): 1.0})
>>> commutator(b_dag, b1_dag).equiv(BosonOperator.zero())
True
```

**Parameters**

- **op\_a** (*T*) – the operator $A$ above.
- **op\_b** (*T*) – the operator $B$ above.

**Returns**

The commutator $[A, B]$.

**Return type**

*T*