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Model Checking Quantum Continuous-Time Markov Chains

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

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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).

Cite AsGet 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

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.

Subject Classification

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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