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Time-Efficient Quantum Walks for 3-Distinctness

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Automata, Languages, and Programming (ICALP 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7965))

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Abstract

We present two quantum walk algorithms for 3-Distinctness. Both algorithms have time complexity \(\tilde{O}(n^{5/7})\), improving the previous \(\tilde{O}(n^{3/4})\) and matching the best known upper bound for query complexity (obtained via learning graphs) up to log factors. The first algorithm is based on a connection between quantum walks and electric networks. The second algorithm uses an extension of the quantum walk search framework that facilitates quantum walks with nested updates.

This paper is a merge of two submitted papers, whose full versions are available at http://arxiv.org/abs/1302.3143 and http://arxiv.org/abs/1302.7316 . Support for this work was provided by European Social Fund within the project “Support for Doctoral Studies at University of Latvia”, the European Commission IST STREP project 25596 (QCS), NSERC, the Ontario Ministry of Research and Innovation, the US ARO, and the French ANR Blanc project ANR-12-BS02-005 (RDAM).

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Author information

Authors and Affiliations

  1. Faculty of Computing, University of Latvia, Latvia

    Aleksandrs Belovs

  2. Department of Combinatorics & Optimization, University of Waterloo, Canada

    Andrew M. Childs

  3. David R. Cheriton School of Computer Science, University of Waterloo, Canada

    Stacey Jeffery & Robin Kothari

  4. Institute for Quantum Computing, University of Waterloo, Canada

    Andrew M. Childs, Stacey Jeffery & Robin Kothari

  5. CNRS, LIAFA, Univ Paris Diderot, Sorbonne Paris-Cité, France

    Frédéric Magniez

Authors
  1. Aleksandrs Belovs
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  2. Andrew M. Childs
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  3. Stacey Jeffery
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  4. Robin Kothari
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  5. Frédéric Magniez
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Editor information

Editors and Affiliations

  1. Department of Informatics, University of Bergen, Postboks 7803, 5020, Bergen, Norway

    Fedor V. Fomin

  2. Faculty of Computing, University of Latvia, Raina bulv. 19, 1586, Riga, Latvia

    Rūsiņš Freivalds

  3. Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Marta Kwiatkowska

  4. Faculty of Mathematics and Computer Science, Weizmann Institute of Science, POB 26, 76100, Rehovot, Israel

    David Peleg

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© 2013 Springer-Verlag Berlin Heidelberg

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Belovs, A., Childs, A.M., Jeffery, S., Kothari, R., Magniez, F. (2013). Time-Efficient Quantum Walks for 3-Distinctness. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds) Automata, Languages, and Programming. ICALP 2013. Lecture Notes in Computer Science, vol 7965. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39206-1_10

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  • DOI: https://doi.org/10.1007/978-3-642-39206-1_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39205-4

  • Online ISBN: 978-3-642-39206-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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