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

# Evolution

*class* `Evolution(num_modes, operator, time=1.0, *, synthesis=None, atomic=False)`

Bases: [`BosonicGate`](/docs/api/qiskit-bosons/circuit-bosonic-gate "qiskit_bosons.circuit.bosonic_gate.BosonicGate")

Implements the time evolution of a bosonic operator.

Given a bosonic `operator` $H$ and an evolution `time` $t$, this gate implements the unitary

$$
U = e^{-i t H}.
$$

For $U$ to be unitary, $H$ must be Hermitian. This is the caller’s responsibility and is not verified; [`is_hermitian()`](/docs/api/qiskit-bosons/operators-boson-operator#is_hermitian "qiskit_bosons.operators.BosonOperator.is_hermitian") can check it.

> **Note**
>
> Breaking this gate down in bosonic space (into a circuit of smaller [`Evolution`](#qiskit_bosons.circuit.library.Evolution "qiskit_bosons.circuit.library.Evolution") gates) is **optional**, and it is what the [`synthesis`](/docs/api/qiskit-bosons/circuit-bosonic-gate#synthesis "qiskit_bosons.circuit.BosonicGate.synthesis") attribute governs. The gate can equally be handed straight to the boson-to-qubit stage, which maps and synthesizes it whole, however many terms its `operator` holds. See [`synthesis`](/docs/api/qiskit-bosons/circuit-library-synthesis#module-qiskit_bosons.circuit.library.synthesis "qiskit_bosons.circuit.library.synthesis").
>
> When it is decomposed (by [`decompose()`](/docs/api/qiskit-bosons/circuit-bosonic-circuit#decompose "qiskit_bosons.circuit.BosonicCircuit.decompose"), for instance) [`synthesis`](/docs/api/qiskit-bosons/circuit-bosonic-gate#synthesis "qiskit_bosons.circuit.BosonicGate.synthesis") decides how. It defaults to [`BosonicLieTrotter`](/docs/api/qiskit-bosons/circuit-library-synthesis-bosonic-lie-trotter "qiskit_bosons.circuit.library.synthesis.BosonicLieTrotter"), which splits the evolution group-by-group when the `operator` has [`groups`](/docs/api/qiskit-bosons/operators-boson-operator#groups "qiskit_bosons.operators.BosonOperator.groups") assigned (see [Group operator terms: use the operator structure](/docs/addons/qiskit-bosons/guides/grouping#grouping-explanation)), and term-by-term otherwise (exact only when the individual factors mutually commute). Another method can be chosen, for a whole circuit, with the [`B2BSynthesis`](/docs/api/qiskit-bosons/transpiler-passes-b-2-b-synthesis "qiskit_bosons.transpiler.passes.B2BSynthesis") transpiler pass; [`BosonicQDrift`](/docs/api/qiskit-bosons/circuit-library-synthesis-bosonic-q-drift "qiskit_bosons.circuit.library.synthesis.BosonicQDrift"), for example, replaces the evolution with a randomized sample of its terms. The gates it emits are [`atomic`](/docs/api/qiskit-bosons/circuit-bosonic-gate#atomic "qiskit_bosons.circuit.BosonicGate.atomic"), so [`synthesis`](/docs/api/qiskit-bosons/circuit-bosonic-gate#synthesis "qiskit_bosons.circuit.BosonicGate.synthesis") no longer applies to them.

> **Note**
>
> This gate carries **no occupation cutoff**. It is defined purely in terms of the bosonic operator, whose Fock space is infinite-dimensional. The truncation is introduced later, by the boson-to-qubit encoding chosen during transpilation – which is precisely what lets one ansatz be evaluated at several truncation levels without rebuilding it. See [`occupation_encoding()`](/docs/api/qiskit-bosons/mappers-library-occupation-encoding "qiskit_bosons.mappers.library.occupation_encoding").

Initializing an instance of this gate can be done with the arguments listed below.

**Parameters**

- **num\_modes** ([*int*](https://docs.python.org/3/builtins/functions.html#int)) – the number of bosonic modes on which this gate acts.
- **operator** ([*OperatorTrait*](/docs/api/qiskit-bosons/operators-operator-trait "qiskit_bosons.operators.OperatorTrait")) – the Hermitian operator $H$ under which to time evolve the acted-upon bosonic modes.
- **time** ([*float*](https://docs.python.org/3/builtins/functions.html#float)) – the evolution time $t$ entering the exponent of $e^{-i t H}$. A negative value evolves backwards in time.
- **synthesis** ([*B2BSynthesisPlugin*](/docs/api/qiskit-bosons/circuit-library-synthesis-b-2-b-synthesis-plugin "qiskit_bosons.circuit.library.synthesis.B2BSynthesisPlugin") *| None*) – the boson-to-boson synthesis method with which to decompose this gate, when it gets decomposed at all. If `None` (the default), a [`BosonicLieTrotter`](/docs/api/qiskit-bosons/circuit-library-synthesis-bosonic-lie-trotter "qiskit_bosons.circuit.library.synthesis.BosonicLieTrotter") instance is used.
- **atomic** ([*bool*](https://docs.python.org/3/builtins/functions.html#bool)) – whether this gate is a fully decomposed factor which must not be broken down any further in bosonic space. See [`BosonicGate.atomic`](/docs/api/qiskit-bosons/circuit-bosonic-gate#atomic "qiskit_bosons.circuit.BosonicGate.atomic").

## Attributes

### operator

The operator under which to time evolve the acted-upon bosonic modes.

## Methods

### inverse

`inverse(annotated=False)`

Returns the inverse of this gate, $e^{+i t H}$.

**Parameters**

**annotated** ([*bool*](https://docs.python.org/3/builtins/functions.html#bool)) – ignored. The inverse of this gate is another [`Evolution`](#qiskit_bosons.circuit.library.Evolution "qiskit_bosons.circuit.library.Evolution"), so it never needs to be an [`AnnotatedOperation`](/docs/api/qiskit/qiskit.circuit.AnnotatedOperation).

**Returns**

An [`Evolution`](#qiskit_bosons.circuit.library.Evolution "qiskit_bosons.circuit.library.Evolution") gate evolving the same operator for the negated time.

**Return type**

[*Evolution*](#qiskit_bosons.circuit.library.Evolution "qiskit_bosons.circuit.library.evolution.Evolution")