The complexity of the selection procedure of a genetic algorithm that requires reordering, if we restrict the class of the possible fitness functions to non–local or time–dependent fitness functions, is O (N log N) where N is the size of the population. Quantum Genetic Algorithm (QGA) exploits the power of quantum computation in order to speed up genetic procedures. In QGA the classical fitness evaluation and selection procedures are replaced by a single quantum procedure. QGA outperforms a typical classical genetic algorithm. We show that the complexity of our QGA is O (1) in terms of number of oracle calls in the selection procedure. Such theoretical results are confirmed by the simulations of the algorithm.