Genetic-Multi-initial Generalized VQE: Advanced VQE method using Genetic Algorithms then Local Search

Variational-Quantum-Eigensolver (VQE) method has been known as the method of chemical calculation using quantum computers and classical computers. This method also can derive the energy levels of excited states by Variational-Quantum-Deflation (VQD) method. Although, parameter landscape of excited state have many local minimums that the results are tend to be trapped by them. Therefore, we apply Genetic Algorithms then Local Search (GA then LS) as the classical optimizer of VQE method. We performed the calculation of ground and excited states and their energies on hydrogen molecule by modified GA then LS. Here we uses Powell, Broyden-Fletcher-Goldfarb-Shanno, Nelder-Mead and Newton method as an optimizer of LS. We obtained the result that Newton method can derive ground and excited states and their energies in higher accuracy than others. We are predicting that newton method is more effective for seed up and be more accurate.