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Genetic algorithms are heuristic optimization techniques inspired by Darwinian evolution, which are characterized by successfully finding robust solutions for optimization problems. Here, we propose a subroutine-based quantum genetic algorithm with individuals codified in independent registers. This distinctive codification allows our proposal to depict all the fundamental elements characterizing genetic algorithms, 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 firstly analyze the performance of two different quantum cloning machines, a key component of the crossover subroutine. Indeed, we study two paradigmatic examples, namely, the biomimetic cloning of quantum observables and the Bu\v zek-Hillery universal quantum cloning machine, observing 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. This tool could be extended to formally prove results on the convergence of general non-unitary iteration-based algorithms.