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Model Checking Quantum Continuous-Time Markov Chains

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

Published in: LIPIcs, Volume 203, 32nd International Conference on Concurrency Theory (CONCUR 2021)


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

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)


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@InProceedings{xu_et_al:LIPIcs.CONCUR.2021.13,
  author =	{Xu, Ming and Mei, Jingyi and Guan, Ji and Yu, Nengkun},
  title =	{{Model Checking Quantum Continuous-Time Markov Chains}},
  booktitle =	{32nd International Conference on Concurrency Theory (CONCUR 2021)},
  pages =	{13:1--13:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-203-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{203},
  editor =	{Haddad, Serge and Varacca, Daniele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2021.13},
  URN =		{urn:nbn:de:0030-drops-143908},
  doi =		{10.4230/LIPIcs.CONCUR.2021.13},
  annote =	{Keywords: Model Checking, Formal Logic, Quantum Computing, Computer Algebra}
}
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