https://doi.org/10.1140/epjd/s10053-023-00758-7
Regular Article – Quantum Information
Quantum walk search by Grover search on coin space
KDDI Research, Inc, Fujimino-shi, Saitama, Japan
Received:
28
July
2023
Accepted:
13
September
2023
Published online:
28
September
2023
Quantum walk followed by some amplitude amplification technique has been successfully used to search for marked vertices on various graphs. Lackadaisical quantum walk can search for target vertices on graphs without the help of any additional amplitude amplification technique. These studies either exploit AKR or SKW coin to distinguish the marked vertices from the unmarked vertices. The success of AKR coin-based quantum walk search algorithms highly depends on the arrangements of the set of marked vertices on the graph. For example, it fails to find adjacent vertices, diagonal vertices and other exceptional configurations of vertices on a two-dimensional periodic square lattice and on other graphs. These coins also suffer from low success probability while searching for marked vertices on a one-dimensional periodic lattice and on other graphs for certain arrangements for marked vertices. In this article, we propose a modified coin for the lackadaisical quantum walk search. It allows us to perform quantum walk search for the marked vertices by doing Grover search on the coin space. Our model finds the marked vertices by searching the self-loops associated with the marked vertices. It can search for marked vertices irrespective of their arrangement on the graph with high success probability. For all analysed arrangements of the marked vertices, the time complexity for 1d-lattice and 2d-lattice is 
and 
, respectively, with constant and high success probability.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
