Matchgate benchmarking: Scalable benchmarking of a continuous family of many-qubit gates

Abstract

We propose a method to reliably and efficiently extract the fidelity of many-qubit quantum circuits composed of continuously parametrized two-qubit gates called matchgates. This method, which we call $\textit{matchgate benchmarking}$, relies on advanced techniques from randomized benchmarking as well as insights from the representation theory of matchgate circuits. We argue the formal correctness and scalability of the protocol, and moreover deploy it to estimate the performance of matchgate circuits generated by two-qubit XY spin interactions on a quantum processor.