Topological phenomena in quantum walks: elementary introduction to the physics of topological phases

Topological phenomena in quantum walks: elementary introduction to the physics of topological phases Discrete quantum walks are dynamical protocols for controlling a single quantum particle. Despite of its simplicity, quantum walks display rich topological phenomena and provide one of the simplest systems to study and understand topological phases. In this article, we review the physics of discrete quantum walks in one and two dimensions in light of topological phenomena and provide elementary explanations of topological phases and their physical consequence, namely the existence of boundary states. We demonstrate that quantum walks are versatile systems that simulate many topological phases whose classifications are known for static Hamiltonians. Furthermore, topological phenomena appearing in quantum walks go beyond what has been known in static systems; there are phenomena unique to quantum walks, being an example of periodically driven systems, that do not exist in static systems. Thus the quantum walks not only provide a powerful tool as a quantum simulator for static topological phases but also give unique opportunity to study topological phenomena in driven systems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Topological phenomena in quantum walks: elementary introduction to the physics of topological phases

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Publisher
Springer US
Copyright
Copyright © 2012 by Springer Science+Business Media, LLC
Subject
Physics; Data Structures, Cryptology and Information Theory; Quantum Physics; Quantum Information Technology, Spintronics; Mathematical Physics; Quantum Computing
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-012-0425-4
Publisher site
See Article on Publisher Site

Abstract

Discrete quantum walks are dynamical protocols for controlling a single quantum particle. Despite of its simplicity, quantum walks display rich topological phenomena and provide one of the simplest systems to study and understand topological phases. In this article, we review the physics of discrete quantum walks in one and two dimensions in light of topological phenomena and provide elementary explanations of topological phases and their physical consequence, namely the existence of boundary states. We demonstrate that quantum walks are versatile systems that simulate many topological phases whose classifications are known for static Hamiltonians. Furthermore, topological phenomena appearing in quantum walks go beyond what has been known in static systems; there are phenomena unique to quantum walks, being an example of periodically driven systems, that do not exist in static systems. Thus the quantum walks not only provide a powerful tool as a quantum simulator for static topological phases but also give unique opportunity to study topological phenomena in driven systems.

Journal

Quantum Information ProcessingSpringer Journals

Published: Aug 4, 2012

References

  • Quantized hall conductance, current-carrying edge states, and the existence of extended states in a two-dimensional disordered potential
    Halperin, B.I.
  • Colloquium: topological insulators
    Hasan, M.Z.; Kane, C.L.
  • Solitons with fermion number 12 in condensed matter and relativistic field theories
    Jackiw, R.; Schrieffer, J.
  • Classification of topological insulators and superconductors in three spatial dimensions
    Schnyder, A.P.; Ryu, S.; Furusaki, A.; Ludwig, A.W.W.

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