Quantum walks: a comprehensive review

Quantum walks: a comprehensive review Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete-time quantum walks. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Quantum walks: a comprehensive review

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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/s11128-012-0432-5
Publisher site
See Article on Publisher Site

Abstract

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete-time quantum walks.

Journal

Quantum Information ProcessingSpringer Journals

Published: Jul 8, 2012

References

  • Disordered quantum walks in one lattice dimension
    Ahlbrecht, A.; Scholz, V.B.; Werner, A.H.
  • Asymptotic evolution of quantum walks with random coin
    Ahlbrecht, A.; Vogts, H.; Werner, A.H.; Werner, R.F.
  • Quantum search algorithms
    Ambainis, A.
  • Perfect state transfer on quotient graphs
    Bachman, R.; Fredette, E.; Fuller, J.; Landry, M.; Opperman, M.; Tamon, C.; Tollefson, A.
  • Two-dimensional quantum random walk
    Baryshnikov, Y.; Brady, W.; Bressler, A.; Pemantle, R.

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