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.
A method of quantization of classical soliton cellular automata (QSCA) is put forward that provides a description of their time evolution operator by means of quantum circuits that involve quantum gates from which the associated Hamiltonian describing a quantum chain model is constructed. The intrinsic parallelism of QSCA, a phenomenon first known from quantum computers, is also emphasized. Introduction. Soliton cellular automata (SCA), is a class of cellular automata[1] operating on binary sequences with an updating rule function f for each cell, that depends on past and present time cells, the number of which determines the radius r of the automaton[2]. Contrary to usual CA ( that evolve their cells by means of past time cells only), SCA exhibit a variety of evolution patterns[4, 5, 6] that is mainly known to characterize the temporal behavior of