Equivalence Checking of Quantum Finite-State Machines

TL;DR

This paper introduces quantum Mealy machines, develops algorithms for checking their state and machine equivalence, and applies these methods to quantum circuit verification, with minimisation shown to be PSPACE-complete.

Contribution

It presents the first algorithms for equivalence checking of quantum Mealy machines and applies them to quantum circuit verification, advancing quantum automata theory.

Findings

Algorithms for state and machine equivalence checking

Application to quantum circuit equivalence

Minimisation problem is PSPACE-complete

Abstract

In this paper, we introduce the model of quantum Mealy machines and study the equivalence checking and minimisation problems of them. Two efficient algorithms are developed for checking equivalence of two states in the same machine and for checking equivalence of two machines. As an application, they are used in equivalence checking of quantum circuits. Moreover, the minimisation problem is proved to be in $\textbf{PSPACE}$.