Supervisory Control of Quantum Discrete Event Systems

TL;DR

This paper introduces a framework for quantum discrete event systems (QDES) using quantum finite automata, establishing supervisory control theorems and demonstrating advantages over classical systems in state complexity.

Contribution

It develops a basic framework for QDES with supervisory control theorems and provides polynomial-time algorithms for controllability, highlighting advantages over classical DES.

Findings

QDES can be modeled using quantum finite automata

Supervisory control theorems for QDES are established and proved

QDES show reduced state complexity compared to classical DES

Abstract

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.