Ground-state wave functions of two-particle systems determined using quantum genetic algorithms

We apply a quantum genetic algorithm to calculate ground-state wave functions of two-particle systems in one and two dimensions. The method is based on the application of evolutionary operations (copy, crossover, mutation) on trial wave functions. The quantum version of genetic algorithms, presented in a previous work for single-particle problems in one dimension [Grigorenko and Garcia, Physica A 284 (2000) 131], has been extended to two-particle systems and two dimensions by conveniently redefining the mutation and cross-over operations. We test the method by determining the exact ground state for noninteracting two-particle systems in two dimensions under different external potentials. We also use the method to calculate the Hartree–Fock ground state of interacting two-particles systems in one and two dimensions. In all cases our calculated electron distributions are in good agreement with both exact analytical and numerical results.