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

# SupportsCommutators

*class* `SupportsCommutators(*args, **kwargs)`

Bases: [`Protocol`](https://docs.python.org/3/library/typing.html#typing.Protocol)

A Protocol indicating support for efficient commutator generation.

Implementation of this protocol requires the three methods below. See [`commutator()`](/docs/api/qiskit-fermions/operators-library-commutator "qiskit_fermions.operators.library.commutator"), [`anti_commutator()`](/docs/api/qiskit-fermions/operators-library-anti-commutator "qiskit_fermions.operators.library.anti_commutator"), and [`double_commutator()`](/docs/api/qiskit-fermions/operators-library-double-commutator "qiskit_fermions.operators.library.double_commutator") for the type-agnostic helper functions dispatching to these methods.

```pycon
>>> from qiskit_fermions.operators import FermionOperator
>>> cre_0 = FermionOperator.from_dict({((True, 0),): 1.0})
>>> ann_0 = FermionOperator.from_dict({((False, 0),): 1.0})
>>> comm = FermionOperator._commutator_(cre_0, ann_0)
>>> print(format(comm.normal_ordered().simplify()))
 -1.000000e0 +0.000000e0j * ()
  2.000000e0 +0.000000e0j * (+0 -0)
```

**Protocol Methods**

### \_anti\_commutator\_

*static* `_anti_commutator_(op_a, op_b)`

Computes the anti-commutator of two operator instances.

See [`anti_commutator()`](/docs/api/qiskit-fermions/operators-library-anti-commutator "qiskit_fermions.operators.library.anti_commutator") for more details.

**Parameters**

- **op\_a** (*T*)
- **op\_b** (*T*)

**Return type**

*T*

### \_commutator\_

*static* `_commutator_(op_a, op_b)`

Computes the commutator of two operator instances.

See [`commutator()`](/docs/api/qiskit-fermions/operators-library-commutator "qiskit_fermions.operators.library.commutator") for more details.

**Parameters**

- **op\_a** (*T*)
- **op\_b** (*T*)

**Return type**

*T*

### \_double\_commutator\_

*static* `_double_commutator_(op_a, op_b, op_c, sign)`

Computes the double-commutator of three operator instances.

See [`double_commutator()`](/docs/api/qiskit-fermions/operators-library-double-commutator "qiskit_fermions.operators.library.double_commutator") for more details.

**Parameters**

- **op\_a** (*T*)
- **op\_b** (*T*)
- **op\_c** (*T*)
- **sign** ([*bool*](https://docs.python.org/3/library/functions.html#bool))

**Return type**

*T*