  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.
