ExtraFerm

ExtraFerm

pip install extraferm

Overview

This library can be used to estimate Born rule probabilities of measurement outcomes from particle-number conserving extended matchgate circuits:

• Extended matchgate: the universal gate set consisting of matchgates + controlled‑phase gates
• Particle-number conserving: the Hamming weight of initial state is preserved at all points by the circuit

Circuit Extent

Our simulator runs most efficiently when the circuit’s extent is close to one. The extent is defined as:

where is the angle of the -th controlled-phase gate.

Use

Users should interact with the simulator through the outcome_probabilities function in interface.py.

Example

import numpy as np
from qiskit import QuantumCircuit
from qiskit.circuit.library import XXPlusYYGate

from extraferm import outcome_probabilities

# Create a small circuit
seed = 123
rng = np.random.default_rng(seed=seed)
angles = rng.uniform(0, 2 * np.pi, size=12)
qc = QuantumCircuit(4)
qc.x([0, 2])
qc.append(XXPlusYYGate(theta=angles[0], beta=angles[1]), [0, 1])
qc.cp(theta=angles[3], control_qubit=1, target_qubit=2)
qc.append(XXPlusYYGate(theta=angles[4], beta=angles[5]), [1, 2])
qc.cp(theta=angles[6], control_qubit=0, target_qubit=1)
qc.p(theta=angles[7], qubit=0)
qc.append(XXPlusYYGate(theta=angles[8], beta=angles[9]), [2, 3])
qc.append(XXPlusYYGate(theta=angles[10], beta=angles[11]), [0, 1])

# Estimate a few bitstring probabilitites
bitstrings = [0b0101, 0b1100, 0b0011]
probs = outcome_probabilities(
    circuit=qc, outcome_states=bitstrings, trajectory_count=100_000, seed=seed
)

# Show results
print(probs)
qc.draw("mpl", scale=0.8, fold=-1)

[5.09355260e-01 1.56195696e-33 8.07714813e-02]

Citing ExtraFerm

You can cite ExtraFerm using the following BibTeX:

@misc{hassman2025enhancingchemistryquantumcomputers,
      title={Enhancing Chemistry on Quantum Computers with Fermionic Linear Optical Simulation}, 
      author={Zack Hassman and Oliver Reardon-Smith and Gokul Subramanian Ravi and Frederic T. Chong and Kevin J. Sung},
      year={2025},
      eprint={2511.12416},
      archivePrefix={arXiv},
      primaryClass={quant-ph},
      url={https://arxiv.org/abs/2511.12416}, 
}