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Decoherence in quantum walks – a review

Published online by Cambridge University Press:  01 December 2007

VIV KENDON
VIV KENDON*
Affiliation:
School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT, U.K. Email: v.kendon@leeds.ac.uk
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Abstract

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The development of quantum walks in the context of quantum computation, as generalisations of random walk techniques, has led rapidly to several new quantum algorithms. These all follow a unitary quantum evolution, apart from the final measurement. Since logical qubits in a quantum computer must be protected from decoherence by error correction, there is no need to consider decoherence at the level of algorithms. Nonetheless, enlarging the range of quantum dynamics to include non-unitary evolution provides a wider range of possibilities for tuning the properties of quantum walks. For example, small amounts of decoherence in a quantum walk on the line can produce more uniform spreading (a top-hat distribution), without losing the quantum speed up. This paper reviews the work on decoherence, and more generally on non-unitary evolution, in quantum walks and suggests what future questions might prove interesting to pursue in this area.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 17 , Issue 6 , December 2007 , pp. 1169 - 1220
Copyright
Copyright © Cambridge University Press 2007

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