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  • Open Access

Equivalence checking of quantum circuits via intermediary matrix product operator

Aaron Sander1,*, Lukas Burgholzer1,2,†, and Robert Wille1,2,3,‡

  • *Contact author: aaron.sander@tum.de
  • †Contact author: lukas.burgholzer@tum.de
  • ‡Contact author: robert.wille@tum.de
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Phys. Rev. Research 7, 023261 – Published 13 June, 2025

DOI: https://doi.org/10.1103/3q71-y8cf

Abstract

As quantum computing advances, the complexity of quantum circuits is rapidly increasing, driving the need for robust methods to aid in their design. Equivalence checking plays a vital role in identifying errors that may arise during compilation and optimization of these circuits and is a critical step in quantum circuit verification. In this work, we introduce a method based on matrix product operators (MPOs) for determining the equivalence of quantum circuits. Our approach contracts tensorized quantum gates from two circuits into an intermediary MPO, exploiting their reversibility to determine their equivalence or nonequivalence. Our results show that this method offers significant scalability improvements over existing methods, with polynomial scaling in circuit width and depth for the practical use cases we explore. We expect that this work to set a standard for scalable equivalence checking of quantum circuits and will become a crucial tool for the validation of increasingly complex quantum systems.

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Outline

Information

Phys. Rev. Research 7, 023261– Published 13 June, 2025
  • Received 16 October 2024
  • Accepted 29 May 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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