Lackadaisical quantum walks with multiple marked vertices
Abstract
The concept of lackadaisical quantum walk -- quantum walk with self loops -- was first introduced for discrete-time quantum walk on one-dimensional line. Later it was successfully applied to improve the running time of the spacial search on two-dimensional grid. 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 the previous papers 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.
Keywords
Cite
@article{arxiv.1808.00672,
title = {Lackadaisical quantum walks with multiple marked vertices},
author = {Nikolajs Nahimovs},
journal= {arXiv preprint arXiv:1808.00672},
year = {2018}
}