ExtraFerm 0.1.0

Quantum circuit simulator for particle number conserving extended matchgate circuits

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:

$$ \xi^* = \prod_{j=1}^k \bigl(\cos(\theta_j/4) + \sin(\theta_j/4)\bigr)^2 $$

where $\theta_j$ is the angle of the $j$-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

# 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

from extraferm import outcome_probabilities
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]

Setup

Install this repository

git clone https://github.com/zhassman/Extended-Matchgate-Simulator.git
cd Extended-Matchgate-Simulator
pip install -e .