  Genetic algorithms are heuristic optimization techniques inspired by
Darwinian evolution. Quantum computation is a new computational paradigm which
exploits quantum resources to speed up information processing tasks. Therefore,
it is sensible to explore the potential enhancement in the performance of
genetic algorithms by introducing quantum degrees of freedom. Along this line,
a modular quantum genetic algorithm has recently been proposed, with
individuals encoded in independent registers comprising exchangeable quantum
subroutines [arXiv:2203.15039], which leads to different variants. Here, we
address the numerical benchmarking of these algorithms against classical
genetic algorithms, a comparison missing from previous literature. To overcome
the severe limitations of simulating quantum algorithms, our approach focuses
on measuring the effect of quantum resources on the performance. In order to
isolate the effect of the quantum resources in the performance, the classical
variants have been selected to resemble the fundamental characteristics of the
quantum genetic algorithms. Under these conditions, we encode an optimization
problem in a two-qubit Hamiltonian and face the problem of finding its ground
state. A numerical analysis based on a sample of 200 random cases shows that
some quantum variants outperform all classical ones in convergence speed
towards a near-to-optimal result. Additionally, we have considered a diagonal
Hamiltonian and the Hamiltonian of the hydrogen molecule to complete the
analysis with two relevant use-cases. If this advantage holds for larger
systems, quantum genetic algorithms would provide a new tool to address
optimization problems with quantum computers.
