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Quantum Queries on Permutations

  • Taisia Mischenko-Slatenkova
  • Alina Vasilieva
  • Ilja Kucevalovs
  • Rūsiņš FreivaldsEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9118)

Abstract

K. Iwama and R. Freivalds considered query algorithms where the black box contains a permutation. Since then several authors have compared quantum and deterministic query algorithms for permutations. It turns out that the case of \(n\)-permutations where \(n\) is an odd number is difficult. There was no example of a permutation problem where quantization can save half of the queries for \((2m+1)\)-permutations if \(m\ge 2\). Even for \((2m)\)-permutations with \(m\ge 2\), the best proved advantage of quantum query algorithms is the result by Iwama/Freivalds where the quantum query complexity is \(m\) but the deterministic query complexity is \((2m-1)\). We present a group of \(5\)-permutations such that the deterministic query complexity is 4 and the quantum query complexity is 2.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Taisia Mischenko-Slatenkova
    • 1
  • Alina Vasilieva
    • 2
  • Ilja Kucevalovs
    • 2
  • Rūsiņš Freivalds
    • 1
    • 2
    Email author
  1. 1.Institute of Mathematics and Computer ScienceUniversity of LatviaRigaLatvia
  2. 2.Faculty of ComputingUniversity of LatviaRigaLatvia

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