Quantum Genetic Algorithm with Individuals in Multiple Registers

Abstract

Genetic algorithms (GAs) are heuristic optimization techniques inspired by Darwinian evolution, which are characterized by successfully finding robust solutions for optimization problems. While quantum resources have allowed for the acceleration of many computational tasks, it remains an open question whether they can enhance the efficacy of evolutionary algorithms, particularly GAs. Here, we propose a subroutine-based quantum GA with individuals codified in independent registers. This distinctive codification allows our proposal to depict all the fundamental elements characterizing GAs, i.e., population-based search with selection of many individuals, crossover, and mutation. Our subroutine-based construction permits us to consider several variants of the algorithm. For instance, we first analyze the performance of two different quantum cloning machines (QCMs), a key component of the crossover subroutine. Indeed, we study two paradigmatic examples, namely, the biomimetic cloning of quantum observables and the Bužek-Hillery universal QCM. We observed a faster average convergence of the former, but better-final populations of the latter. Additionally, we analyzed the effect of introducing a mutation subroutine, concluding a minor impact on the average performance. Furthermore, we introduce a quantum channel analysis to prove the exponential convergence of our algorithm and even predict its convergence ratio.