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Grover’s Search with Faults on Some Marked Elements

  • Dmitry Kravchenko
  • Nikolajs NahimovsEmail author
  • Alexander Rivosh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9587)

Abstract

Grover’s algorithm is a quantum query algorithm solving the unstructured search problem of size N using \(O(\sqrt{N})\) queries. It provides a significant speed-up over any classical algorithm [2].

The running time of the algorithm, however, is very sensitive to errors in queries. Multiple authors have analysed the algorithm using different models of query errors and showed the loss of quantum speed-up [1, 4].

We study the behavior of Grover’s algorithm in the model where the search space contains both faulty and non-faulty marked elements. We show that in this setting it is indeed possible to find one of marked elements in \(O(\sqrt{N})\) queries.

Keywords

Search Space Unit Sphere Spherical Triangle Slow State Horizontal Equator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Ambainis, A., Bačkurs, A., Nahimovs, N., Rivosh, A.: Grover’s algorithm with errors. In: Kučera, A., Henzinger, T.A., Nešetřil, J., Vojnar, T., Antoš, D. (eds.) MEMICS 2012. LNCS, vol. 7721, pp. 180–189. Springer, Heidelberg (2013)CrossRefGoogle Scholar
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    Grover, L.: A fast quantum mechanical algorithm for database search. In: Proceedings of the 28th ACM STOC, pp. 212–219 (1996)Google Scholar
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    Kaye, P., Laflamme, R.: An Introduction to Quantum Computing. Cambridge University Press, Cambridge (2007)zbMATHGoogle Scholar
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    Regev, O., Schiff, L.: Impossibility of a quantum speed-up with a faulty oracle. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 773–781. Springer, Heidelberg (2008)CrossRefGoogle Scholar
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    Todhunter, I.: Spherical Trigonometry, 5th edn. MacMillan, London (1886)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Dmitry Kravchenko
    • 1
  • Nikolajs Nahimovs
    • 1
    Email author
  • Alexander Rivosh
    • 1
  1. 1.Faculty of ComputingUniversity of LatviaRigaLatvia

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