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Time-Efficient Quantum Walks for 3-Distinctness

  • Aleksandrs Belovs
  • Andrew M. Childs
  • Stacey Jeffery
  • Robin Kothari
  • Frédéric Magniez
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7965)

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Aleksandrs Belovs
    • 1
  • Andrew M. Childs
    • 2
    • 4
  • Stacey Jeffery
    • 3
    • 4
  • Robin Kothari
    • 3
    • 4
  • Frédéric Magniez
    • 5
  1. 1.Faculty of ComputingUniversity of LatviaLatvia
  2. 2.Department of Combinatorics & OptimizationUniversity of WaterlooCanada
  3. 3.David R. Cheriton School of Computer ScienceUniversity of WaterlooCanada
  4. 4.Institute for Quantum ComputingUniversity of WaterlooCanada
  5. 5.CNRS, LIAFAUniv Paris Diderot, Sorbonne Paris-CitéFrance

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