Discrete-time quantum walks as fermions of lattice gauge theory

TL;DR

This paper demonstrates that discrete-time quantum walks can effectively digitize fermionic models in lattice gauge theory, preserving unitarity and ultralocality, but losing certain symmetries in a (1+1)-dimensional setting.

Contribution

It introduces a method to use discrete-time quantum walks for fermionic lattice gauge theories, highlighting their unitarity and ultralocality properties.

Findings

Quantum walks can digitize fermionic models in lattice gauge theory.

Ultralocality bounds particle speed, aligning with relativistic theories.

Lattice chiral symmetry is lost due to ultralocality constraints.

Abstract

It is shown that discrete-time quantum walks can be used to digitize, i.e., to time discretize fermionic models of continuous-time lattice gauge theory. The resulting discrete-time dynamics is thus not only manifestly unitary, but also ultralocal, i.e. the particle's speed is upper bounded, as in standard relativistic quantum field theories. The lattice chiral symmetry of staggered fermions, which corresponds to a translational invariance, is lost after the requirement of ultralocality of the evolution; this fact is an instance of Meyer's 1996 no-go lemma stating that no non-trivial one-dimensional scalar quantum cellular automaton can be translationally invariant [1]. All results are presented in a single-particle framework and for a (1+1)-dimensional spacetime.