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A Gauge-Invariant Reversible Cellular Automaton

Abstract : Gauge-invariance is a fundamental concept in physics—known to provide mathematical justifications for the fundamental forces. In this paper, we provide discrete counterparts to the main gauge theoretical concepts, directly in terms of Cellular Automata. More precisely, we describe a step-by-step gauging procedure to enforce local symmetries upon a given Cellular Automaton. We apply it to a simple Reversible Cellular Automaton for concreteness. From a Computer Science perspective, discretized gauge theories may be of use in numerical analysis, quantum simulation, fault-tolerant (quantum) computation. From a mathematical perspective, discreteness provides a simple yet rigorous route straight to the core concepts.
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Pablo Arrighi, Giuseppe Molfetta, Nathanaël Eon. A Gauge-Invariant Reversible Cellular Automaton. 24th International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA), Jun 2018, Ghent, Belgium. pp.1-12, ⟨10.1007/978-3-319-92675-9_1⟩. ⟨hal-01824869⟩

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