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On the Probability of Finding Marked Connected Components Using Quantum Walks

Lobachevskii Journal of Mathematics volume 39, pages 1016–1023 (2018)Cite this article

Abstract

Finding a marked vertex in a graph can be a complicated task when using quantum walks. Recent results show that for two or more adjacent marked vertices search by quantum walk with Grover’s coin may have no speed-up over classical exhaustive search. In this paper, we analyze the probability of finding a marked vertex for a set of connected components of marked vertices. We prove two upper bounds on the probability of finding a marked vertex and sketch further research directions.

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Authors and Affiliations

  1. Center for Quantum Computer Science, Faculty of Computing, University of Latvia, Raina bulv. 19, Riga, LV-1586, Latvia

    K. Khadiev, N. Nahimovs & R. A. M. Santos

  2. Institute of Computational Mathematics and Information Technologies, Kazan (Volga region) Federal University, ul. Kremlevskaya 35, Kazan, Tatarstan, 420008, Russia

    K. Khadiev

Authors
  1. K. Khadiev
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  2. N. Nahimovs
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  3. R. A. M. Santos
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Correspondence to K. Khadiev.

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Submitted by F.M. Ablayev

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Khadiev, K., Nahimovs, N. & Santos, R.A.M. On the Probability of Finding Marked Connected Components Using Quantum Walks. Lobachevskii J Math 39, 1016–1023 (2018). https://doi.org/10.1134/S1995080218070144

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  • DOI: https://doi.org/10.1134/S1995080218070144

Keywords and phrases

  • Quantum computing
  • quantum walks
  • exceptional configurations
  • stationary states