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Optimal computation with non-unitary quantum walks

Kendon, V. and Maloyer, O. (2008) Optimal computation with non-unitary quantum walks. Theoretical Computer Science, 394 (3). pp. 187-196. ISSN 0304-3975

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Abstract

Quantum versions of random walks on the line and the cycle show a quadratic improvement over classical random walks in their spreading rates and mixing times, respectively. Non-unitary quantum walks can provide a useful optimisation of these properties, producing a more uniform distribution on the line, and faster mixing times on the cycle. We investigate the interplay between quantum and random dynamics by comparing the resources required, and examining numerically how the level of quantum correlations varies during the walk. We show numerically that the optimal non-unitary quantum walk proceeds such that the quantum correlations are nearly all removed at the point of the final measurement. This requires only O(logT) random bits for a quantum walk of T steps.

Item Type: Article
Copyright, Publisher and Additional Information: © 2008 Elsevier Science B.V. This is an author produced version of a paper published in Theoretical Computer Science. Uploaded in accordance with the publisher's self-archiving policy.
Academic Units: The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Physics and Astronomy (Leeds)
Depositing User: Sherpa Assistant
Date Deposited: 23 May 2008 13:35
Last Modified: 08 Feb 2013 16:56
Published Version: http://dx.doi.org/10.1016/j.tcs.2007.12.011
Status: Published
Publisher: Elsevier Science BV
Refereed: Yes
Identification Number: 10.1016/j.tcs.2007.12.011
URI: http://eprints.whiterose.ac.uk/id/eprint/3923

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