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.
Author details: | Pablo Arrighi, Vincent Nesme, Reinhard F. Werner |
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ISSN: | 1548-7199 |
Title of parent work (English): | International journal of unconventional computing : non-classical computation and cellular automata |
Publisher: | Old City Publishing Science |
Place of publishing: | Philadelphia |
Publication type: | Article |
Language: | English |
Year of first publication: | 2011 |
Publication year: | 2011 |
Release date: | 2017/03/26 |
Tag: | block representation; cellular automata; neighborhood; quantum |
Volume: | 7 |
Issue: | 4 |
Number of pages: | 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 the publication: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Informatik |