Discrete event systems (DES) have been deeply developed and applied in practice, but state complexity in DES still is an important problem to be better solved with innovative methods. With the development of quantum computing and quantum control, a natural problem is to simulate DES by means of quantum computing models and to establish {\it quantum DES} (QDES). The motivation is twofold: on the one hand, QDES have potential applications when DES are simulated and processed by quantum computers, where quantum systems are employed to simulate the evolution of states driven by discrete events, and on the other hand, QDES may have essential advantages over DES concerning state complexity for imitating some practical problems. So, the goal of this paper is to establish a basic framework of QDES by using {\it quantum finite automata} (QFA) as the modelling formalisms, and the supervisory control theorems of QDES are established and proved. Then we present a polynomial-time algorithm to decide whether or not the controllability condition holds. In particular, we construct a number of new examples of QFA to illustrate the supervisory control of QDES and to verify the essential advantages of QDES over classical DES in state complexity.

翻译：离散事件系统（DES）已得到深入发展并在实践中广泛应用，但状态复杂性仍是亟待通过创新方法更好解决的重要问题。随着量子计算与量子控制的发展，一个自然的问题便是利用量子计算模型模拟DES，并建立量子离散事件系统（QDES）。该研究动机有二：一方面，当通过量子计算机模拟和处理DES时，QDES具有潜在应用前景——此时量子系统被用于模拟由离散事件驱动的状态演化；另一方面，在模拟某些实际问题时，QDES在状态复杂性方面可能比DES具有本质优势。因此，本文旨在利用量子有限自动机（QFA）作为建模形式化工具，建立QDES的基本框架，并提出并证明QDES的监督控制定理。随后，我们提出一个多项式时间算法以判定可控性条件是否成立。特别地，我们构造了多个QFA新实例来阐释QDES的监督控制，并验证了QDES在状态复杂性上相较经典DES的本质优势。