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License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2017.42
URN: urn:nbn:de:0030-drops-69902
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/6990/
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Hoyer, Peter ; Komeili, Mojtaba

Efficient Quantum Walk on the Grid with Multiple Marked Elements

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LIPIcs-STACS-2017-42.pdf (0.5 MB)

Abstract

We give a quantum algorithm for finding a marked element on the grid when there are multiple marked elements. Our algorithm uses quadratically fewer steps than a random walk on the grid, ignoring logarithmic factors. This is the first known quantum walk that finds a marked element in a number of steps less than the square-root of the extended hitting time. We also give a new tighter upper bound on the extended hitting time of a marked subset, expressed in terms of the hitting times of its members.

BibTeX - Entry

@InProceedings{hoyer_et_al:LIPIcs:2017:6990,
  author =	{Peter Hoyer and Mojtaba Komeili},
  title =	{{Efficient Quantum Walk on the Grid with Multiple Marked Elements}},
  booktitle =	{34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)},
  pages =	{42:1--42:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-028-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{66},
  editor =	{Heribert Vollmer and Brigitte ValleĢe},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/6990},
  URN =		{urn:nbn:de:0030-drops-69902},
  doi =		{10.4230/LIPIcs.STACS.2017.42},
  annote =	{Keywords: Quantum walks, random walks, query complexity, spatial search}
}

Keywords: Quantum walks, random walks, query complexity, spatial search
Collection: 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)
Issue Date: 2017
Date of publication: 06.03.2017

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