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Matchgate benchmarking

Component-level

Scalable RB-style protocol that scores the continuous family of matchgate (XY-type, fermionic-simulation) gates by fitting decays of correlation functions over random matchgate circuits.

Measures
Fidelity of matchgate (XY-type) circuits, from SPAM-robust decays of correlation functions yielding per-mode Majorana fidelities and an average gate fidelity
Introduced by
Helsen, Nezami, Reagor & Walter (2020)
Also known as
Matchgate RB, Matchgate randomized benchmarking

Matchgate benchmarking scores a continuous family of gates rather than a discrete gate set: the matchgates, XY-type fermionic-simulation two-qubit gates that generate free-fermion dynamics. Introduced by Helsen, Nezami, Reagor and Walter in 2020 and published as Quantum 6, 657 (2022), it brings the SPAM-robust decay-fitting logic of randomized benchmarking to the gate family most relevant to fermionic quantum simulation, which Clifford-based RB cannot address directly.

How it works

Random circuits are drawn from the matchgate group at increasing depths and run on the device. Because matchgate circuits are free-fermionic and hence classically simulable, the ideal behavior can be computed at any width, which makes the protocol scalable. Measured correlation functions decay exponentially with depth; fitting the decays yields a “Majorana fidelity” per fermionic mode, robust to state-preparation and measurement error, and combining them gives an average fidelity over random matchgate circuits (gates of the form XY(θ)).

Strengths and limitations

Scalability comes precisely from classical simulability, so the certificate stays inside the family: reported fidelities cover matchgates only and say nothing about gates outside it. The hardware demonstration was small (two qubits on Rigetti’s Aspen-8, with an average random two-qubit matchgate fidelity of 0.88 ± 0.02), and the original protocol has seen limited hardware redeployment since. Naming needs care: Claes, Rieffel and Wang independently proposed a scalable matchgate RB scheme via character randomized benchmarking a few weeks earlier (PRX Quantum 2, 010351 (2021)), so “matchgate randomized benchmarking” can refer to either scheme. Note also that the GitHub repository named matchgate-benchmarking implements Burkat and Strelchuk’s 2024 lightweight variant; the original code lives on Zenodo.

Notable results

The line remains active through direct successors: a lightweight protocol for matchgate fidelity estimation (updated July 2026) and Free Fermion Volume (2025), a volumetric whole-processor benchmark built on the same free-fermion circuits; matchgate benchmarking itself outputs a gate-family fidelity rather than a holistic device score.

Key papers

Reference implementations

  • Randomized Benchmarking : Estimates average gate error from the exponential decay of survival probability over increasingly long random Clifford sequences, robust to state-preparation and measurement errors.
  • Character randomized benchmarking : Uses group character theory to isolate clean exponential decays, extending randomized benchmarking to gate sets that form groups beyond the multi-qubit Cliffords.
  • Free Fermion Volume : Proposed companion to Clifford Volume that scores a device by the largest random free-fermion circuit it executes faithfully, verified scalably through Majorana-mode expectation values.