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One-Dimensional quantum cellular automata

  • We define and study quantum cellular automata (QCA). We show that they are reversible and that the neighborhood of the inverse is the opposite of the neighborhood. We also show that QCA always admit, modulo shifts, a two-layered block representation. Note that the same two-layered block representation result applies also over infinite configurations, as was previously shown for one-dimensional systems in the more elaborate formalism of operators algebras [18]. Here the proof is simpler and self-contained, moreover we discuss a counterexample QCA in higher dimensions.

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Metadaten
Author:Pablo Arrighi, Vincent Nesme, Reinhard F. Werner
ISSN:1548-7199 (print)
Parent Title (English):International journal of unconventional computing : non-classical computation and cellular automata
Publisher:Old City Publishing Science
Place of publication:Philadelphia
Document Type:Article
Language:English
Year of first Publication:2011
Year of Completion:2011
Release Date:2017/03/26
Tag:block representation; cellular automata; neighborhood; quantum
Volume:7
Issue:4
Pagenumber:22
First Page:223
Last Page:244
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Informatik und Computational Science
Peer Review:Referiert
Institution name at the time of publication:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Informatik