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Quantum Walks

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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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Konno, N. (2008). Quantum Walks. In: Franz, U., Schürmann, M. (eds) Quantum Potential Theory. Lecture Notes in Mathematics, vol 1954. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69365-9_7

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