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Quantum Walks

  • Norie Konno
Part of the Lecture Notes in Mathematics book series (LNM, volume 1954)

Abstract

Quantum walks can be considered as a generalized version of the classical random walk. There are two classes of quantum walks, that is, the discrete-time (or coined) and the continuous-time quantum walks. This manuscript treats the discrete case in Part I and continuous case in Part II, respectively. Most of the contents are based on our results. Furthermore, papers on quantum walks are listed in References. Studies of discrete-time walks appeared from the late 1980s from (1988), for example. (1996) investigated the model as a quantum lattice gas automaton. (2000) and (2001) studied intensively the behaviour of discrete-time walks, in particular, the Hadamard walk. In contrast with the central limit theorem for the classical random walks, (2002a), (2005a) showed a new type of weak limit theorems for the one-dimensional lattice. (2004) extended the limit theorem to a wider range of the walks. On the other hand, the continuous-time quantum walk was introduced and studied by (2002). Excellent reviews on quantum walks are found in (2003), (2003), (2003), (2007).

Keywords

Quantum Walk Ultrametric Space Quantum Random Walk Temporal Standard Deviation Classical Random Walk 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Norie Konno
    • 1
  1. 1.Department of Applied MathematicsYokohama National UniversityYokohamaJapan

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