Equivalence checking of quantum circuits via intermediary matrix product operator

TL;DR

This paper introduces a scalable method for quantum circuit equivalence checking using Matrix Product Operators, significantly improving efficiency for complex circuits and aiding in quantum system validation.

Contribution

The paper presents a novel MPO-based approach for quantum circuit equivalence checking, offering better scalability than existing methods.

Findings

Offers polynomial scaling in circuit width and depth

Demonstrates significant scalability improvements

Sets a new standard for quantum circuit validation

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 novel 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 non-equivalence. 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 sets the new standard for scalable equivalence checking of quantum circuits and will become a crucial tool for the validation of increasingly complex quantum systems.