The quantum walk search algorithm: factors affecting efficiency

Lovett, N. B., Everitt, M., Heath, R. M. and Kendon, V. (2019) The quantum walk search algorithm: factors affecting efficiency. Mathematical Structures in Computer Science, 29(3), pp. 389-429. (doi: 10.1017/S0960129518000051)

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Abstract

We carry out a numerical study of the quantum walk search algorithm of Shenvi, Kempe and Whaley Shenvi et al. (2003) and the factors that affect its efficiency in finding an individual state from an unsorted set. Previous work has focused purely on the effects of the dimensionality of the dataset to be searched. In the current paper we consider the effects of interpolating between dimensions, the connectivity of the dataset and the possibility of disorder in the underlying substrate: all these factors affect the efficiency of the search algorithm. We show that in addition to the strong dependence on the spatial dimension of the structure to be searched, there are also secondary dependencies on the connectivity and symmetry of the lattice, with greater connectivity providing a more efficient algorithm. We also show that the algorithm can tolerate a non-trivial level of disorder in the underlying substrate.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Heath, Mr Robert
Authors: Lovett, N. B., Everitt, M., Heath, R. M., and Kendon, V.
College/School:College of Science and Engineering > School of Engineering > Electronics and Nanoscale Engineering
Journal Name:Mathematical Structures in Computer Science
Publisher:Cambridge University Press
ISSN:0960-1295
ISSN (Online):1469-8072
Published Online:16 May 2018
Copyright Holders:Copyright © 2018 Cambridge University Press
First Published:First published in Mathematical Structures in Computer Science 29(3): 389-429
Publisher Policy:Reproduced in accordance with the publisher copyright policy

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