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Model Checking Quantum Continuous-Time Markov Chains

Authors Ming Xu , Jingyi Mei , Ji Guan , Nengkun Yu

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ACM Subject Classification
  • Theory of computation → Verification by model checking
  • Computing methodologies → Symbolic and algebraic algorithms
  • Theory of computation → Quantum computation theory
Keywords
  • Model Checking
  • Formal Logic
  • Quantum Computing
  • Computer Algebra

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Abstract

Verifying quantum systems has attracted a lot of interests in the last decades. In this paper, we initialise the model checking of quantum continuous-time Markov chain (QCTMC). As a real-time system, we specify the temporal properties on QCTMC by signal temporal logic (STL). To effectively check the atomic propositions in STL, we develop a state-of-the-art real root isolation algorithm under Schanuel’s conjecture; further, we check the general STL formula by interval operations with a bottom-up fashion, whose query complexity turns out to be linear in the size of the input formula by calling the real root isolation algorithm. A running example of an open quantum walk is provided to demonstrate our method.

Cite As Get BibTex

Ming Xu, Jingyi Mei, Ji Guan, and Nengkun Yu. Model Checking Quantum Continuous-Time Markov Chains. In 32nd International Conference on Concurrency Theory (CONCUR 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 203, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.CONCUR.2021.13

Author Details

Ming Xu
  • Shanghai Key Lab of Trustworthy Computing, MoE Engineering Research Center of Software/Hardware Co-design Technology and Application, East China Normal University, Shanghai, China
Jingyi Mei
  • Shanghai Key Lab of Trustworthy Computing, East China Normal University, Shanghai, China
Ji Guan
  • State Key Lab of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China
Nengkun Yu
  • Centre for Quantum Software and Information, Faculty of Engineering and Information Technology, University of Technology, Sydney, Australia

Funding

  • Xu, Ming: The corresponding author M. X. is supported by the National Natural Science Foundation of China (No. 11871221), the National Key R&D Program of China (No. 2018YFA0306704), the Fundamental Research Funds for the Central Universities, and the Research Funds of Happiness Flower ECNU (No. 2020ECNU-XFZH005).
  • Guan, Ji: The corresponding author J. G. is supported by the National Key R&D Program of China (No. 2018YFA0306701) and the National Natural Science Foundation of China (No. 61832015).
  • Yu, Nengkun: N. Y. is supported by ARC Discovery Early Career Researcher Award (No. DE180100156) and ARC Discovery Program (No. DP210102449).

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