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DOI: 10.4230/LIPIcs.CONCUR.2021.13

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.

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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-dev.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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DOI: 10.4230/LIPIcs.ITCS.2021.11

Sample Efficient Identity Testing and Independence Testing of Quantum States

Authors: Nengkun Yu

Published in: LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)

Abstract

In this paper, we study the quantum identity testing problem, i.e., testing whether two given quantum states are identical, and quantum independence testing problem, i.e., testing whether a given multipartite quantum state is in tensor product form. For the quantum identity testing problem of 𝒟(ℂ^d) system, we provide a deterministic measurement scheme that uses 𝒪(d²/ε²) copies via independent measurements with d being the dimension of the state and ε being the additive error. For the independence testing problem 𝒟(ℂ^d₁⊗ℂ^{d₂}⊗⋯⊗ℂ^{d_m}) system, we show that the sample complexity is Θ̃((Π_{i = 1}^m d_i)/ε²) via collective measurements, and 𝒪((Π_{i = 1}^m d_i²)/ε²) via independent measurements. If randomized choice of independent measurements are allowed, the sample complexity is Θ(d^{3/2}/ε²) for the quantum identity testing problem, and Θ̃((Π_{i = 1}^m d_i^{3/2})/ε²) for the quantum independence testing problem.

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Nengkun Yu. Sample Efficient Identity Testing and Independence Testing of Quantum States. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 11:1-11:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{yu:LIPIcs.ITCS.2021.11,
  author =	{Yu, Nengkun},
  title =	{{Sample Efficient Identity Testing and Independence Testing of Quantum States}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{11:1--11:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-177-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{185},
  editor =	{Lee, James R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.11},
  URN =		{urn:nbn:de:0030-drops-135504},
  doi =		{10.4230/LIPIcs.ITCS.2021.11},
  annote =	{Keywords: Quantum property testing}
}

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Documents authored by Yu, Nengkun

Model Checking Quantum Continuous-Time Markov Chains

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Sample Efficient Identity Testing and Independence Testing of Quantum States

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