# A quantum cellular automaton for one-dimensional QED

## TL;DR

This paper introduces a quantum cellular automaton framework for simulating one-dimensional quantum electrodynamics, capturing gauge invariance and information propagation limits, and providing a basis for quantum simulation and continuum limit analysis.

## Contribution

It presents a novel discrete spacetime model of 1D QED using quantum cellular automata with exact gauge covariance and a built-in maximum information speed.

## Key findings

- Defines a convergent sequence of automata for continuum limit
- Provides a quantum simulation algorithm for 1D QED dynamics
- Ensures exact gauge invariance in the automaton model

## Abstract

We propose a discrete spacetime formulation of quantum electrodynamics in one-dimension (a.k.a the Schwinger model) in terms of quantum cellular automata, i.e. translationally invariant circuits of local quantum gates. These have exact gauge covariance and a maximum speed of information propagation. In this picture, the interacting quantum field theory is defined as a "convergent" sequence of quantum cellular automata, parameterized by the spacetime lattice spacing---encompassing the notions of continuum limit and renormalization, and at the same time providing a quantum simulation algorithm for the dynamics.