Work

Equivalence checking of quantum circuits via intermediary matrix product operator

Year: 2025

Type: article

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.

Source: Physical Review Research

DOI: 10.1103/3q71-y8cf

Authors: Aaron Sander, Lukas Burgholzer, Robert Wille

Institutions: Technical University of Munich, Software Competence Center Hagenberg (Austria)

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,625