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

Jonas Helsen1,2, Sepehr Nezami3, Matthew Reagor4, and Michael Walter1,5,6

1QuSoft & Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Science Park 123, 1098 XG Amsterdam, The Netherlands
2Centrum Wiskunde & Informatica (CWI), Science Park 123, 1098 XG Amsterdam, The Netherlands
3Institute for Quantum Information and Matter, Caltech, Pasadena, CA 91125, USA
4Rigetti Computing, 775 Heinz Ave, Berkeley, CA 94710, USA
5Institute for Theoretical Physics & ILLC, University of Amsterdam, Science Park 123, 1098 XG Amsterdam, The Netherlands
6Faculty of Computer Science, Ruhr University Bochum, Universitätsstraße 150, 44801 Bochum, Germany

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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.

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[14] Michał Oszmaniec, Ninnat Dangniam, Mauro E. S. Morales, and Zoltán Zimborás, "Fermion Sampling: A Robust Quantum Computational Advantage Scheme Using Fermionic Linear Optics and Magic Input States", PRX Quantum 3 2, 020328 (2022).

[15] Yunchao Liu, Matthew Otten, Roozbeh Bassirianjahromi, Liang Jiang, and Bill Fefferman, "Benchmarking near-term quantum computers via random circuit sampling", arXiv:2105.05232, (2021).

[16] Jonas Helsen, Ingo Roth, Emilio Onorati, Albert H. Werner, and Jens Eisert, "A general framework for randomized benchmarking", arXiv:2010.07974, (2020).

[17] Ashley Montanaro and Stasja Stanisic, "Error mitigation by training with fermionic linear optics", arXiv:2102.02120, (2021).

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[19] Markus Heinrich, Martin Kliesch, and Ingo Roth, "Randomized benchmarking with random quantum circuits", arXiv:2212.06181, (2022).

[20] Jahan Claes, Eleanor Rieffel, and Zhihui Wang, "Character randomized benchmarking for non-multiplicity-free groups with applications to subspace, leakage, and matchgate randomized benchmarking", arXiv:2011.00007, (2020).

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