Equivalence Checking of Quantum Finite-State Machines

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. They are applied in experiments of equivalence checking of quantum circuits. Moreover, it is shown that the minimisation problem is proved to be in \textbf{PSPACE}.