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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Cited by

[1] Martin Kliesch, "Randomized benchmarking with a tractable continuously generated group", Quantum Views 6, 64 (2022).

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

[3] 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).

[4] Jonas Helsen, Ingo Roth, Emilio Onorati, Albert H. Werner, and Jens Eisert, "A general framework for randomized benchmarking", arXiv:2010.07974, PRX Quantum 3 2, 020357 (2020).

[5] Jonas Helsen, Marios Ioannou, Ingo Roth, Jonas Kitzinger, Emilio Onorati, Albert H. Werner, and Jens Eisert, "Estimating gate-set properties from random sequences", arXiv:2110.13178.

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

[7] Timothy Proctor, Stefan Seritan, Kenneth Rudinger, Erik Nielsen, Robin Blume-Kohout, and Kevin Young, "Scalable randomized benchmarking of quantum computers using mirror circuits", arXiv:2112.09853.

[8] Ryotaro Suzuki, Kosuke Mitarai, and Keisuke Fujii, "Computational power of one- and two-dimensional dual-unitary quantum circuits", arXiv:2103.09211.

[9] Jordan Hines, Marie Lu, Ravi K. Naik, Akel Hashim, Jean-Loup Ville, Brad Mitchell, John Mark Kriekebaum, David I. Santiago, Stefan Seritan, Erik Nielsen, Robin Blume-Kohout, Kevin Young, Irfan Siddiqi, Birgitta Whaley, and Timothy Proctor, "Demonstrating scalable randomized benchmarking of universal gate sets", arXiv:2207.07272.

[10] Cupjin Huang, Tenghui Wang, Feng Wu, Dawei Ding, Qi Ye, Linghang Kong, Fang Zhang, Xiaotong Ni, Zhijun Song, Yaoyun Shi, Hui-Hai Zhao, Chunqing Deng, and Jianxin Chen, "Quantum Instruction Set Design for Performance", arXiv:2105.06074.

[11] 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.

[12] Peter W. Evans, Dominik Hangleiter, and Karim P. Y. Thébault, "How to engineer a quantum wavefunction", arXiv:2112.01105.

The above citations are from Crossref's cited-by service (last updated successfully 2022-10-05 01:23:36) and SAO/NASA ADS (last updated successfully 2022-10-05 01:23:37). The list may be incomplete as not all publishers provide suitable and complete citation data.

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