Classification of qubit cellular automata on hypercubic lattices

TL;DR

This paper classifies qubit cellular automata on hypercubic lattices, analyzing their structure, realizability as finite-depth circuits, and entanglement dynamics to advance understanding of quantum automata behavior.

Contribution

It provides a comprehensive classification of quantum cellular automata on hypercubic lattices and characterizes their structure and entanglement properties.

Findings

Most general structure of qubit cellular automata identified

Automata realizability as finite-depth quantum circuits established

Entanglement production rate between cells evaluated

Abstract

We classify quantum cellular automata whose cells are qubits, on hypercubic lattices $\mathbb Z^s$, with the von Neumann neighborhood scheme, in terms of realizability as finite-depth quantum circuits. We show the most general structure of such automata and use its characterisation to simulate a few steps of evolution and evaluate the rate of entanglement production between one cell and its surroundings.