Localization of a multi-dimensional quantum walk with one defect

Localization of a multi-dimensional quantum walk with one defect In this paper, we introduce a multi-dimensional generalization of Kitagawa’s split-step discrete-time quantum walk, study the spectrum of its evolution operator for the case of one-defect coins, and prove localization of the walk. Using a spectral mapping theorem, we can reduce the spectral analysis of the evolution operator to that of a discrete Schrödinger operator with variable coefficients, which is analyzed using the Feshbach map. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Localization of a multi-dimensional quantum walk with one defect

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer Science+Business Media, LLC
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-017-1653-4
Publisher site
See Article on Publisher Site

Abstract

In this paper, we introduce a multi-dimensional generalization of Kitagawa’s split-step discrete-time quantum walk, study the spectrum of its evolution operator for the case of one-defect coins, and prove localization of the walk. Using a spectral mapping theorem, we can reduce the spectral analysis of the evolution operator to that of a discrete Schrödinger operator with variable coefficients, which is analyzed using the Feshbach map.

Journal

Quantum Information ProcessingSpringer Journals

Published: Jul 12, 2017

References

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