Quantum cellular automata without particles

TL;DR

This paper constructs a non-trivial quantum cellular automaton in 1+1 dimensions that does not have a particle interpretation, challenging the usual particle-based perspective in quantum field theory models.

Contribution

It introduces a novel example of a quantum cellular automaton that is not a quantum lattice gas automaton, expanding the understanding of QCA models without particle interpretations.

Findings

Provides a simple 1+1 dimensional QCA without particle interpretation

Demonstrates the existence of non-QLGA QCA models

Challenges the particle-based view in quantum field theory simulations

Abstract

Quantum cellular automata (QCA) constitute space and time homogeneous discrete models for quantum field theories (QFTs). Although QFTs are defined without reference to particles, computations are done in terms of Feynman diagrams, which are explicitly interpreted in terms of interacting particles. Similarly, the easiest QCA to construct are quantum lattice gas automata (QLGA). A natural question then is, which QCA are not QLGA? Here we construct a non-trivial example of such a QCA; it provides a simple model in $1+1$ dimensions with no particle interpretation at the scale where the QCA dynamics are homogeneous.