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Quantum Walks

  • Chapter
Quantum Potential Theory

Part of the book series: Lecture Notes in Mathematics ((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).

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Authors and Affiliations

  1. Department of Applied Mathematics, Yokohama National University, 79-5 Tokiwadai, Yokohama, 240-8501, Japan

    Norie Konno

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  1. Norie Konno
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Editors and Affiliations

  1. Département de mathématiques de Besancon, Université de Franche-Comté, 16, route de Gray, 25030, Besancon cedex, France

    Uwe Franz

  2. Graduate School of Information Sciences, Tohoku University, 6-3-09 Aramaki-Aza-Aoba, Aoba-ku, Sendai, 980-8579, Japan

    Uwe Franz

  3. Institut für Mathematik und Informatik, Ernst-Moritz-Arndt-Universität Greifswald, Jahnstrasse 15a, 17487, Greifswald, Germany

    Michael Schürmann

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© 2008 Springer-Verlag Berlin Heidelberg

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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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