Local Unitary Quantum Cellular Automata

TL;DR

This paper introduces a quantum cellular automaton model based on local unitary operators, serving as a framework for quantum computation and simulating space-homogeneous quantum phenomena with practical advantages.

Contribution

It formalizes a quantization of cellular automata using local unitary operators, bridging quantum computation and physical quantum systems.

Findings

Demonstrates universality of the model

Shows strong connection to quantum circuit model

Highlights ease of implementation on quantum hardware

Abstract

In this paper we present a quantization of Cellular Automata. Our formalism is based on a lattice of qudits, and an update rule consisting of local unitary operators that commute with their own lattice translations. One purpose of this model is to act as a theoretical model of quantum computation, similar to the quantum circuit model. It is also shown to be an appropriate abstraction for space-homogeneous quantum phenomena, such as quantum lattice gases, spin chains and others. Some results that show the benefits of basing the model on local unitary operators are shown: universality, strong connections to the circuit model, simple implementation on quantum hardware, and a wealth of applications.