---
title: commutator (latest version)
description: API reference for qiskit_fermions.operators.library.commutator in the latest version of qiskit-fermions
source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/qiskit-fermions/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-fermions/protocols-supports-commutators "qiskit_fermions.protocols.SupportsCommutators") protocol.

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

```pycon
>>> from qiskit_fermions.operators import FermionOperator
>>> from qiskit_fermions.operators.library import commutator
>>> op1 = FermionOperator.from_dict({((True, 0), (False, 0)): 1})
>>> op2 = FermionOperator.from_dict({((False, 0), (True, 0)): 2})
>>> comm = commutator(op1, op2)
>>> comm = comm.normal_ordered()
>>> canon = comm.simplify()
>>> assert canon == FermionOperator.zero()
```

**Parameters**

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

**Returns**

The commutator $[A, B]$.

**Return type**

*T*