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---
title: MatrixExponential (latest version)
description: API reference for qiskit.synthesis.MatrixExponential in the latest version of qiskit
in_page_toc_min_heading_level: 1
python_api_type: class
python_api_name: qiskit.synthesis.MatrixExponential
---
# MatrixExponential
<Class id="qiskit.synthesis.MatrixExponential" isDedicatedPage={true} github="https://github.com/Qiskit/qiskit/tree/stable/1.2/qiskit/synthesis/evolution/matrix_synthesis.py#L20-L47" signature="qiskit.synthesis.MatrixExponential" modifiers="class">
Bases: [`EvolutionSynthesis`](qiskit.synthesis.EvolutionSynthesis "qiskit.synthesis.evolution.evolution_synthesis.EvolutionSynthesis")
Exact operator evolution via matrix exponentiation and unitary synthesis.
This class synthesis the exponential of operators by calculating their exponentially-sized matrix representation and using exact matrix exponentiation followed by unitary synthesis to obtain a circuit. This process is not scalable and serves as comparison or benchmark for small systems.
## Attributes
### settings
<Attribute id="qiskit.synthesis.MatrixExponential.settings">
Return the settings in a dictionary, which can be used to reconstruct the object.
**Returns**
A dictionary containing the settings of this product formula.
**Raises**
[**NotImplementedError**](https://docs.python.org/3/library/exceptions.html#NotImplementedError "(in Python v3.13)") The interface does not implement this method.
</Attribute>
## Methods
### synthesize
<Function id="qiskit.synthesis.MatrixExponential.synthesize" github="https://github.com/Qiskit/qiskit/tree/stable/1.2/qiskit/synthesis/evolution/matrix_synthesis.py#L29-L47" signature="synthesize(evolution)">
Synthesize an `qiskit.circuit.library.PauliEvolutionGate`.
**Parameters**
**evolution** ([*PauliEvolutionGate*](qiskit.circuit.library.PauliEvolutionGate "qiskit.circuit.library.PauliEvolutionGate")) The evolution gate to synthesize.
**Returns**
A circuit implementing the evolution.
**Return type**
[QuantumCircuit](qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit")
</Function>
</Class>