QGoL: Quantum Game of Life

This paper proposes a novel probabilistic version of the Game of Life and a quantum model for it. Based on the study and formalisation of the traditional deterministic case, the quantum paradigm is presented as a good candidate for modelling probabilistic behaviour, providing a convenient description of the problem and efficient calculation of the necessary probabilities in an intrinsic way. To illustrate the advantages of quantum computing for this calculation, two implementations are presented: a classical version developed in Rust and a quantum version built using IBM’s Qiskit quantum circuit software. The particularities of this model are presented, its applications are discussed, and optimisations are suggested for the general case, where different neighbourhood sizes and geometries or an increased number of dimensions can be considered. For the particular case of the traditional Game of Life and for all these extended cases, competitive complexity is demonstrated through the quantum paradigm, with respect to the exhaustive classical calculation of probabilities or approximate methods. This allows cases with many dimensions or complex conditions to be executed efficiently.