A gauge-invariant reversible cellular automaton

TL;DR

This paper introduces a method to implement gauge invariance in cellular automata, creating discrete models that mirror continuous gauge theories, with potential applications in quantum computing and numerical analysis.

Contribution

It provides a step-by-step gauging procedure to impose local symmetries on cellular automata, bridging gauge theory concepts with discrete computational models.

Findings

Developed a discrete gauge-invariance enforcement method.

Applied the method to a reversible cellular automaton.

Potential applications in quantum simulation and fault-tolerant computation.

Abstract

Gauge-invariance is a fundamental concept in physics---known to provide the mathematical justification for all four 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 applied to numerical analysis, quantum simulation, fault-tolerant (quantum) computation. From a mathematical perspective, discreteness provides a simple yet rigorous route straight to the core concepts.