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

# Operator Representations

This module provides the data structures for representing bosonic operators.

|                                                                                                                                                                       |                                                                    |
| --------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ------------------------------------------------------------------ |
| [`OperatorTrait`](/docs/api/qiskit-bosons/operators-operator-trait#qiskit_bosons.operators.OperatorTrait "qiskit_bosons.operators.OperatorTrait")(\*args, \*\*kwargs) | A protocol indicating all methods implemented by operator classes. |

## Boson Operator

This operator represents bosonic operators in terms of the second-quantization creation and annihilation operators, which obey the canonical commutation relations

$$
\left[b_i, b^\dagger_j\right] = \delta_{ij}, \qquad
\left[b_i, b_j\right] = \left[b^\dagger_i, b^\dagger_j\right] = 0 \, .
$$

|                                                                                                                                                                                  |                                            |
| -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ------------------------------------------ |
| [`BosonAction`](/docs/api/qiskit-bosons/operators-boson-action-boson-action#qiskit_bosons.operators.boson_action.BosonAction "qiskit_bosons.operators.boson_action.BosonAction") | A bosonic creation or annihilation action. |

|                                                                                                                                                                                       |                                                                  |
| ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ---------------------------------------------------------------- |
| [`BosonOperator`](/docs/api/qiskit-bosons/operators-boson-operator#qiskit_bosons.operators.BosonOperator "qiskit_bosons.operators.BosonOperator")(coeffs, actions, modes, boundaries) | A bosonic operator.                                              |
| [`cre`](/docs/api/qiskit-bosons/operators-cre#qiskit_bosons.operators.cre "qiskit_bosons.operators.cre")(mode)                                                                        | Constructs a creation action on the bosonic mode at `mode`.      |
| [`ann`](/docs/api/qiskit-bosons/operators-ann#qiskit_bosons.operators.ann "qiskit_bosons.operators.ann")(mode)                                                                        | Constructs an annihilation action on the bosonic mode at `mode`. |

> **Note**
>
> A bosonic mode has an **infinite-dimensional** Fock space. [`BosonOperator`](/docs/api/qiskit-bosons/operators-boson-operator#qiskit_bosons.operators.BosonOperator "qiskit_bosons.operators.BosonOperator") is exact and carries no occupation cutoff; a truncation is introduced only when mapping to qubits (see [`qiskit_bosons.mappers`](/docs/api/qiskit-bosons/mappers#module-qiskit_bosons.mappers "qiskit_bosons.mappers")). Two consequences are visible directly in this API: a mode index may repeat within a single term, and [`max_occupation()`](/docs/api/qiskit-bosons/operators-boson-operator#qiskit_bosons.operators.BosonOperator.max_occupation "qiskit_bosons.operators.BosonOperator.max_occupation") and [`mode_occupations()`](/docs/api/qiskit-bosons/operators-boson-operator#qiskit_bosons.operators.BosonOperator.mode_occupations "qiskit_bosons.operators.BosonOperator.mode_occupations") report the cutoff such a term demands.

## Operator Library

A library of the model Hamiltonians that recur in bosonic simulation is provided in [`qiskit_bosons.operators.library`](/docs/api/qiskit-bosons/operators-library#module-qiskit_bosons.operators.library "qiskit_bosons.operators.library").