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

Variational-Quantum-Eigensolver(VQE) method has been known as 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 the parameter landscape of the excited state has many local minimums, the results tend to be trapped by them. Therefore, we apply Genetic Algorithms and then Local Search(GA then LS) as the classical optimizer of the VQE method. We calculated ground and excited states and their energies on hydrogen molecules by modifying GA then LS. Here we used Powell, Broyden-Fletcher-Goldferb-Shanno, Nelder-Mead, and Newton's method as an optimizer of LS. We obtained that Newton's method can derive ground and excited states of hydrogen and helium hydride molecules and their energies with higher accuracy than others.