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 to a standard QuantumCircuit. It continues with the same time evolution example from the fermionic circuits guide.

Transpilation stages

As explained in 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. F2FSynthesis is the pass that Trotterizes an Evolution gate here, with a product formula or with FermionicQDrift, and QDriftTrotterization its occupation-aware variant; see Optimization Passes for the full set and Synthesize an Evolution gate in fermionic space 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 instances are transformed into sequences of standard quantum gates. A barrier is carried through onto every qubit of each register it touched, so it continues to separate the gates on either side of it during the qubit stage.

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:

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

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

Compare with the traditional workflow

The fermionic circuits guide describes how the traditional workflow performs fermion-to-qubit encoding before building the QuantumCircuit. Compare the two approaches:

>>> 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 ...>

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 gate in fermionic space, either per gate or for a whole pipeline with F2FSynthesis (see Synthesize an Evolution gate in fermionic space).
• Implement custom fermion-to-qubit mappings by creating synthesis plugins (see F2QSynthesisPlugin).
• Build custom transpiler passes.