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Lackadaisical Quantum Walks with Multiple Marked Vertices

  • Nikolajs Nahimovs
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11376)

Abstract

The concept of lackadaisical quantum walk – quantum walk with self loops – was first introduced for discrete-time quantum walk on one-dimensional line [8]. Later it was successfully applied to improve the running time of the spacial search on two-dimensional grid [16].

In this paper we study search by lackadaisical quantum walk on the two-dimensional grid with multiple marked vertices. First, we show that the lackadaisical quantum walk, similarly to the regular (non-lackadaisical) quantum walk, has exceptional configuration, i.e. placements of marked vertices for which the walk has no speed-up over the classical exhaustive search. Next, we demonstrate that the weight of the self-loop suggested in [16] is not optimal for multiple marked vertices. And, last, we show how to adjust the weight of the self-loop to overcome the aforementioned problem.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Center for Quantum Computer Science, Faculty of ComputingUniversity of LatviaRigaLatvia

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