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On the Probability of Finding Marked Connected Components Using Quantum Walks


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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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).

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Keywords and phrases

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