In modern conditions of total digitalization of the entire world economy, the development of quantum algorithms is one of the topical areas of research. The advantage of quantum algorithms is to reduce the problem solving time by parallelizing operations by generating entangled quantum states and then using them. This advantage (quantum acceleration) is the most advantageous in solving the problem of modeling the dynamics of complex systems and enumerating mathematical problems. The island model of genetic algorithms gives a significant advantage in determining the computational load due to parallelization at the level of the main algorithm. Therefore, research into the possibilities of a quantum genetic algorithm is essential for solving many complex problems.