Cellular Automata on Quantum Annealing Systems

TL;DR

This paper explores how to implement 2-color cellular automata, including Rule 110 and Conway's Game of Life, on quantum annealing systems like D-Wave, enabling new computational approaches using quantum hardware.

Contribution

It introduces methods to encode cellular automata as QUBO problems suitable for quantum annealers, including complex rules like Rule 110 and 2D automata.

Findings

Successfully implemented Rule 110 as a QUBO for quantum annealing.

Demonstrated back-propagation to find initial states for desired automaton outcomes.

Expressed 2D cellular automata, such as Conway's Game of Life, for quantum annealing systems.

Abstract

We present herein an introduction to implementing 2-color cellular automata on quantum annealing systems, such as the D-Wave quantum computer. We show that implementing nearest-neighbor cellular automata is possible. We present an implementation of Wolfram's cellular automata Rule 110, which has previously been shown to be a universal Turing machine, as a QUBO suitable for use on quantum annealing systems. We demonstrate back-propagation of cellular automata rule sets to determine initial cell states for a desired later system state. We show 2-D 2-color cellular automata, such as Conway's Game of Life, can be expressed for quantum annealing systems.