Quantum Cellular Automata

TL;DR

This paper reviews the development of quantum cellular automata (QCA), discussing their definitions, properties like universality and reversibility, and highlighting challenges in early proposals.

Contribution

It provides a comprehensive overview of QCA definitions, properties, and the evolution of the field, including critical analysis of early shortcomings and recent advances.

Findings

Early QCA proposals had significant shortcomings.

Recent definitions of QCA address previous limitations.

QCA exhibit properties like universality and reversibility.

Abstract

Quantum cellular automata (QCA) are reviewed, including early and more recent proposals. QCA are a generalization of (classical) cellular automata (CA) and in particular of reversible CA. The latter are reviewed shortly. An overview is given over early attempts by various authors to define one-dimensional QCA. These turned out to have serious shortcomings which are discussed as well. Various proposals subsequently put forward by a number of authors for a general definition of one- and higher-dimensional QCA are reviewed and their properties such as universality and reversibility are discussed.