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 PSPACE.

中文翻译：

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量子有限状态机的等效检查

在本文中，我们介绍了量子计量机的模型，并研究了它们的等效检查和最小化问题。开发了两种有效的算法来检查同一台机器中两个状态的等效性并检查两台机器的等效性。作为一种应用，它们可用于量子电路的等效检查。此外，最小化问题被证明是在PSPACE中。