---
title: Transpile fermionic circuits
description: Transpile fermionic circuits for the latest version of Qiskit Fermions
source: https://eu-de.quantum.cloud.ibm.com/docs/en/addons/qiskit-fermions/guides/transpilation
---

# Transpile fermionic circuits

> **Important**
>
> The concepts in this guide are currently available only in the Python API. Equivalent functionality will be made available in the C API in a future release.

This guide explains how to transpile a [`FermionicCircuit`](/docs/api/qiskit-fermions/circuit-fermionic-circuit#qiskit_fermions.circuit.FermionicCircuit "qiskit_fermions.circuit.FermionicCircuit") to a standard [`QuantumCircuit`](/docs/api/qiskit/qiskit.circuit.QuantumCircuit). It continues with the same time evolution example from the [fermionic circuits guide](/docs/addons/qiskit-fermions/guides/circuit#fermionic-circuit-explanation).

## Transpilation stages

As explained in [`qiskit_fermions.transpiler`](/docs/api/qiskit-fermions/transpiler#module-qiskit_fermions.transpiler "qiskit_fermions.transpiler"), the preset pass managers in this project split the transpilation into the following stages:

## **Input**

Converts the input circuit to a directed acyclic graph (DAG) data structure.

## **Optimization**

Keeps the circuit in fermionic space. These passes use fermionic structure and commutation relations while problem-aware knowledge remains fully available. [`FermionicTrotterization`](/docs/api/qiskit-fermions/transpiler-passes-fermionic-trotterization#qiskit_fermions.transpiler.passes.FermionicTrotterization "qiskit_fermions.transpiler.passes.FermionicTrotterization") and [`QDriftTrotterization`](/docs/api/qiskit-fermions/transpiler-passes-q-drift-trotterization#qiskit_fermions.transpiler.passes.QDriftTrotterization "qiskit_fermions.transpiler.passes.QDriftTrotterization") are the passes that Trotterize an [`Evolution`](/docs/api/qiskit-fermions/circuit-library-evolution#qiskit_fermions.circuit.library.Evolution "qiskit_fermions.circuit.library.Evolution") gate here; see [Optimization Passes](/docs/api/qiskit-fermions/transpiler-passes#qiskit-fermions-transpiler-passes-optimization) for the full set and [Synthesize an Evolution gate in fermionic space](/docs/addons/qiskit-fermions/guides/fermionic-synthesis#fermionic-synthesis-explanation) for how a product formula is chosen.

## **Layout**

Maps fermionic mode registers to quantum registers. For occupation-basis mappings like Jordan-Wigner, each fermionic mode maps to a single qubit. This stage also supports more general mappings where the number of qubits differs from the number of fermionic modes.

## **Synthesis**

Converts fermionic gates to qubit operations by using the chosen fermion-to-qubit mapping. [`FermionicGate`](/docs/api/qiskit-fermions/circuit-fermionic-gate#qiskit_fermions.circuit.FermionicGate "qiskit_fermions.circuit.FermionicGate") instances are transformed into sequences of standard quantum gates.

## **Qubit**

Transpiles the resulting qubit circuit by using standard Qiskit methods, including optimization, layout, and routing for your target hardware.

## **Output**

Converts the internal DAG data structure to the desired output format.

## A practical example: transpilation using Jordan-Wigner

Use the preset pass manager to transpile your fermionic circuit with the Jordan-Wigner fermion-to-qubit mapping:

\[x] Python

```python
>>> from qiskit_fermions.circuit import FermionicCircuit
>>> from qiskit_fermions.circuit.library import Evolution
>>> from qiskit_fermions.operators import FermionOperator, cre, ann
>>> from qiskit_fermions.transpiler.presets import generate_preset_jw_pass_manager
>>>
>>> # Create the same fermionic circuit from the previous guide
>>> circuit = FermionicCircuit(4)
>>> hamiltonian = FermionOperator.from_terms([
...     ([cre(0), ann(2)], 0.5),
...     ([cre(2), ann(0)], 0.5),
...     ([cre(1), ann(3)], 0.5),
...     ([cre(3), ann(1)], 0.5),
... ])
>>> hamiltonian.groups = [0, 0, 1, 1]
>>> evolution = Evolution(4, hamiltonian, time=1.0)
>>> circuit.append(evolution, circuit.register)
>>>
>>> # Generate the Jordan-Wigner transpilation pipeline
>>> pm = generate_preset_jw_pass_manager()
>>>
>>> # Transpile the fermionic circuit to a qubit circuit
>>> qubit_circuit = pm.run(circuit)
>>>
>>> # The result is a standard QuantumCircuit
>>> print(type(qubit_circuit))
<class 'qiskit.circuit.quantumcircuit.QuantumCircuit'>
```

\[ ] C

```c
// The C API for transpilation will be made available in a future release.
```

![The transpiled QuantumCircuit of the fermionic time evolution.](https://eu-de.quantum.cloud.ibm.com/docs/images/addons/qiskit-fermions/transpilation-2.avif)

### Compare with the traditional workflow

The [fermionic circuits](/docs/addons/qiskit-fermions/guides/circuit#fermionic-circuit-explanation) guide describes how the traditional workflow performs fermion-to-qubit encoding *before* building the [`QuantumCircuit`](/docs/api/qiskit/qiskit.circuit.QuantumCircuit). Compare the two approaches:

```python
>>> from qiskit_fermions.mappers.library import jordan_wigner
>>> from qiskit.circuit import QuantumCircuit
>>> from qiskit.circuit.library import PauliEvolutionGate
>>>
>>> # Map the fermionic Hamiltonian to a qubit operator
>>> qubit_hamiltonian = jordan_wigner(hamiltonian, 4).simplify()
>>>
>>> # Build the QuantumCircuit directly
>>> quantum_circuit = QuantumCircuit(4)
>>> pauli_evolution = PauliEvolutionGate(qubit_hamiltonian, time=1.0)
>>> quantum_circuit.append(pauli_evolution, quantum_circuit.qubits)
<qiskit.circuit.instructionset.InstructionSet object at ...>
```

![The directly constructed QuantumCircuit of the fermionic time evolution.](https://eu-de.quantum.cloud.ibm.com/docs/images/addons/qiskit-fermions/transpilation-4.avif)

Both workflows produce equivalent circuits. However, the traditional workflow requires you to implement optimization steps manually, whereas with the fermionic-first approach you can integrate problem-aware optimizations into the transpilation process.

## Advanced workflows

The preset pass manager provides a convenient starting point. For more advanced use cases, you can do the following:

- Customize the transpiler passes run during each stage.
- Choose the product formula that Trotterizes an [`Evolution`](/docs/api/qiskit-fermions/circuit-library-evolution#qiskit_fermions.circuit.library.Evolution "qiskit_fermions.circuit.library.Evolution") gate in fermionic space, either per gate or for a whole pipeline with [`FermionicTrotterization`](/docs/api/qiskit-fermions/transpiler-passes-fermionic-trotterization#qiskit_fermions.transpiler.passes.FermionicTrotterization "qiskit_fermions.transpiler.passes.FermionicTrotterization") (see [Synthesize an Evolution gate in fermionic space](/docs/addons/qiskit-fermions/guides/fermionic-synthesis#fermionic-synthesis-explanation)).
- Implement custom fermion-to-qubit mappings by creating synthesis plugins (see [`F2QSynthesisPlugin`](/docs/api/qiskit-fermions/transpiler-passes-synthesis-f-2-q-synthesis-plugin#qiskit_fermions.transpiler.passes.synthesis.F2QSynthesisPlugin "qiskit_fermions.transpiler.passes.synthesis.F2QSynthesisPlugin")).
- Build custom transpiler passes.