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Quantum Information Processing

Localization of a multi-dimensional quantum walk with one defect

  • 01-08-2017
Published in:
Authors
Toru Fuda
Daiju Funakawa
Akito Suzuki
Published in
Quantum Information Processing | Issue 8/2017

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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.

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previous article A subgradient approach for constrained binary optimization via quantum adiabatic evolution
next article Three-player conflicting interest games and nonlocality
Title
Localization of a multi-dimensional quantum walk with one defect
Authors
Toru Fuda
Daiju Funakawa
Akito Suzuki
Publication date
01-08-2017
Publisher
Springer US
Published in
Quantum Information Processing / Issue 8/2017
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-017-1653-4
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