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The quantum walk search algorithm: factors affecting efficiency

Published online by Cambridge University Press:  16 May 2018

NEIL B. LOVETT ,
MATTHEW EVERITT ,
ROBERT M. HEATH  and
VIV KENDON
NEIL B. LOVETT
Affiliation:
School of Physics and Astronomy, University of Leeds, Woodhouse Lane, Leeds, LS2 9JT, United Kingdom and Institute for Quantum Information Science, University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N 1N4, Canada
MATTHEW EVERITT
Affiliation:
School of Physics and Astronomy, University of Leeds, Woodhouse Lane, Leeds, LS2 9JT, United Kingdom
ROBERT M. HEATH
Affiliation:
School of Physics and Astronomy, University of Leeds, Woodhouse Lane, Leeds, LS2 9JT, United Kingdom Email: Robert.Heath@glasgow.ac.uk
VIV KENDON
Affiliation:
Department of Physics, Durham University, South Road, Durham, DH1 3LE, United Kingdom Email: viv.kendon@durham.ac.uk
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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.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 29 , Issue 3 , March 2019 , pp. 389 - 429
Copyright
Copyright © Cambridge University Press 2018 

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Footnotes

Unfortunately there has been an unintended delay in the publication of this article. Cambridge University Press apologises for the delay.

*

Neil Lovett was funded by the UK Engineering and Physical Sciences Research Council.

Viv Kendon was funded by a UK Royal Society University Research Fellowship.

§

Robert Heath's current address is School of Engineering, University of Glasgow, Glasgow, G12 8QQ, United Kingdom.

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