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An overview of quantum cellular automata

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Abstract

Quantum cellular automata are arrays of identical finite-dimensional quantum systems, evolving in discrete-time steps by iterating a unitary operator G. Moreover the global evolution G is required to be causal (it propagates information at a bounded speed) and translation-invariant (it acts everywhere the same). Quantum cellular automata provide a model/architecture for distributed quantum computation. More generally, they encompass most of discrete-space discrete-time quantum theory. We give an overview of their theory, with particular focus on structure results; computability and universality results; and quantum simulation results.

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Acknowledgements

I was lucky to have, as regular co-authors, great researchers such as Pablo Arnault, Cédric Bény, Gilles Dowek, Giuseppe Di Molfetta, Stefano Facchini, Terry Farrelly, Marcelo Forets, Jon Grattage, Iván Márquez, Vincent Nesme, Armando Péres, Zizhu Wang, Reinhard Werner. I would like to thank Jarkko Kari and Grzegorz Rozenberg for inviting me to write this overview, a task which I had been postponing for too long.

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  1. Aix-Marseille Univ, CNRS, LIS, and INRIA, ENS Paris-Saclay, LSV, Université Paris-Saclay, Paris-Saclay, France

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This paper is dedicated to my high school Mathematics teacher, Anne Lefèvre.

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Arrighi, P. An overview of quantum cellular automata. Nat Comput 18, 885–899 (2019). https://doi.org/10.1007/s11047-019-09762-6

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