An overview of Quantum Cellular Automata

TL;DR

Quantum cellular automata are models of distributed quantum computation using arrays of identical quantum systems evolving through causal, translation-invariant unitary operations, with significant implications for quantum theory and simulation.

Contribution

This paper provides a comprehensive overview of quantum cellular automata, emphasizing their structure, computability, universality, and simulation capabilities.

Findings

Quantum cellular automata are capable of universal quantum computation.

They provide a framework for simulating quantum systems discretely.

Structure and computability results enhance understanding of quantum automata.

Abstract

Quantum cellular automata consist in arrays of identical finite-dimensional quantum systems, evolving in discrete-time steps by iterating a unitary operator G. Moreover the global evolution G is required to be causal (it propagates information at a bounded speed) and translation-invariant (it acts everywhere the same). Quantum cellular automata provide a model/architecture for distributed quantum computation. More generally, they encompass most of discrete-space discrete-time quantum theory. We give an overview of their theory, with particular focus on structure results; computability and universality results; and quantum simulation results.