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Partitioned quantum cellular automata are intrinsically universal

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Abstract

There have been several non-axiomatic approaches taken to define quantum cellular automata (QCA). Partitioned QCA (PQCA) are the most canonical of these non-axiomatic definitions. In this work we show that any QCA can be put into the form of a PQCA. Our construction reconciles all the non-axiomatic definitions of QCA, showing that they can all simulate one another, and hence that they are all equivalent to the axiomatic definition. This is achieved by defining generalised n-dimensional intrinsic simulation, which brings the computer science based concepts of simulation and universality closer to theoretical physics. The result is not only an important simplification of the QCA model, it also plays a key role in the identification of a minimal n-dimensional intrinsically universal QCA.

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Acknowledgments

The authors would like to thank Jérôme Durand-Lose, Jacques Mazoyer, Nicolas Ollinger, Guillaume Theyssier and Philippe Jorrand.

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Authors and Affiliations

  1. Laboratoire LIG, Bâtiment IMAG C, University of Grenoble, 220 Rue de la Chimie, 38400, Saint-Martin-d’Hères, France

    Pablo Arrighi & Jonathan Grattage

  2. Laboratoire LIP, Ecole Normale Supérieure de Lyon, 46 Allée d’Italie, 69364, Lyon cedex 07, France

    Pablo Arrighi & Jonathan Grattage

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  1. Pablo Arrighi
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  2. Jonathan Grattage
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Correspondence to Pablo Arrighi.

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Arrighi, P., Grattage, J. Partitioned quantum cellular automata are intrinsically universal. Nat Comput 11, 13–22 (2012). https://doi.org/10.1007/s11047-011-9277-6

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