Fermionic and bosonic quantum field theories from quantum cellular automata in three spatial dimensions

TL;DR

This paper develops quantum cellular automata models for free fermions and bosons in three dimensions, successfully deriving relativistic quantum field theories like Dirac and Maxwell from lattice-based automata.

Contribution

It introduces a novel automaton-based approach to simulate multiparticle relativistic quantum fields in three dimensions, overcoming previous no-go theorems.

Findings

Recover Dirac field theory in the long-wavelength limit

Derive Maxwell field theory from automata models

Construct multiparticle automata for fermions and bosons

Abstract

Quantum walks on lattices can give rise to relativistic wave equations in the long-wavelength limit, but going beyond the single-particle case has proven challenging, especially in more than one spatial dimension. We construct quantum cellular automata for distinguishable particles based on two different quantum walks, and show that by restricting to the antisymmetric and symmetric subspaces, respectively, a multiparticle theory for free fermions and bosons in three spatial dimensions can be produced. This construction evades a no-go theorem that prohibits the usual fermionization constructions in more than one spatial dimension. In the long-wavelength limit, these recover Dirac field theory and Maxwell field theory, i.e., free QED.