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Quantum Markov chains: Description of hybrid systems, decidability of equivalence, and model checking linear-time properties
Li, Lvzhou1,2,4; Feng, Yuan2,3
2015-10-01
Source PublicationINFORMATION AND COMPUTATION
ISSN0890-5401
Volume244Pages:229-244
AbstractIn 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.
KeywordQuantum Markov chains Hybrid systems Quantum automata Equivalence Model checking Linear-time property
DOI10.1016/j.ic.2015.07.001
Language英语
Funding ProjectNational 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 Research AreaComputer Science ; Mathematics
WOS SubjectComputer Science, Theory & Methods ; Mathematics, Applied
WOS IDWOS:000362058100010
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
Citation statistics
Cited Times:3[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/20885
Collection中国科学院数学与系统科学研究院
Affiliation1.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
Recommended Citation
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.
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