Quantum Markov chains: Description of hybrid systems, decidability of equivalence, and model checking linear-time properties

doi:10.1016/j.ic.2015.07.001

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	Quantum Markov chains: Description of hybrid systems, decidability of equivalence, and model checking linear-time properties
	Li, Lvzhou 1,2,4; Feng, Yuan 2,3
	2015-10-01
发表期刊	INFORMATION AND COMPUTATION
ISSN	0890-5401
卷号	244 页码:229-244
摘要	In this paper, we study a model of quantum Markov chains that is a quantum analogue of Markov chains and is obtained by replacing probabilities in transition matrices with quantum operations. We show that this model is very suited to describe hybrid systems that consist of a quantum component and a classical one. Indeed, hybrid systems are often encountered in quantum information processing. Thus, we further propose a model called hybrid quantum automata (HQA) that can be used to describe the hybrid systems receiving inputs (actions) from the outer world. We show the language equivalence problem of HQA is decidable in polynomial time. Furthermore, we apply this result to the trace equivalence problem of quantum Markov chains, and thus it is also decidable in polynomial time. Finally, we discuss model checking linear-time properties of quantum Markov chains, and show the quantitative analysis of regular safety properties can be addressed successfully. (C) 2015 Elsevier Inc. All rights reserved.
关键词	Quantum Markov chains Hybrid systems Quantum automata Equivalence Model checking Linear-time property
DOI	10.1016/j.ic.2015.07.001
语种	英语
资助项目	National Natural Science Foundation of China[61100001] ; National Natural Science Foundation of China[61472452] ; National Natural Science Foundation of China[61272058] ; National Natural Science Foundation of China[61428208] ; National Natural Science Foundation of China[61472412] ; National Natural Science Foundation of Guangdong Province of China[2014A030313157] ; Australian Research Council[DP130102764] ; CAS-SAFEA International Partnership Program for Creative Research Teams
WOS研究方向	Computer Science ; Mathematics
WOS类目	Computer Science, Theory & Methods ; Mathematics, Applied
WOS记录号	WOS:000362058100010
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/20885
专题	中国科学院数学与系统科学研究院
通讯作者	Li, Lvzhou
作者单位	1.Sun Yat Sen Univ, Dept Comp Sci, Guangzhou 510006, Guangdong, Peoples R China 2.Univ Technol Sydney, FEIT, Ctr Quantum Computat & Intelligent Syst, Sydney, NSW 2007, Australia 3.Chinese Acad Sci, AMSS UTS Joint Res Lab Quantum Computat, Beijing, Peoples R China 4.Sun Yat Sen Univ, Guangdong Key Lab Informat Secur Technol, Guangzhou 510006, Guangdong, Peoples R China
推荐引用方式 GB/T 7714	Li, Lvzhou,Feng, Yuan. Quantum Markov chains: Description of hybrid systems, decidability of equivalence, and model checking linear-time properties[J]. INFORMATION AND COMPUTATION,2015,244:229-244.
APA	Li, Lvzhou,&Feng, Yuan.(2015).Quantum Markov chains: Description of hybrid systems, decidability of equivalence, and model checking linear-time properties.INFORMATION AND COMPUTATION,244,229-244.
MLA	Li, Lvzhou,et al."Quantum Markov chains: Description of hybrid systems, decidability of equivalence, and model checking linear-time properties".INFORMATION AND COMPUTATION 244(2015):229-244.