A Gauge-Invariant Reversible Cellular Automaton

  • Pablo Arrighi
  • Giuseppe Di Molfetta
  • Nathanaël EonEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10875)


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.



The authors would like to thank Cédric Bény, Thomas Krajewski, Terry Farrelly and Pablo Arnault, for very instructive conversations about gauge theories. This work was partially supported by the CNRS PEPS JCJC GQNet and the CNRS PEPS Défi InFinitTI “Lattice Quantum Simulation Theory” LaQuST.


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Copyright information

© IFIP International Federation for Information Processing 2018

Authors and Affiliations

  • Pablo Arrighi
    • 1
    • 2
  • Giuseppe Di Molfetta
    • 1
    • 3
  • Nathanaël Eon
    • 1
    • 4
    Email author
  1. 1.Aix-Marseille Univ, Université de Toulon, CNRS, LISMarseilleFrance
  2. 2.IXXILyonFrance
  3. 3.Departamento de Física Terica and IFICUniversidad de Valencia-CSICBurjassotSpain
  4. 4.École CentraleMarseilleFrance

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