Proposal of Variational Quantum Eigensolver method using Genetic Algorithm then Local Search

Abstract

We propose the novel method to calculate eigenenergies of quantum systems using Genetic Algorithms then Local search(GA then LS). It can calculate ground and excited energies in high accuracy. GA then LS is hybrid algorithm of Genetic Algorithms and local search algorithms such as newtonian methods e.g. Powell method. Genetic Algorithm(GA) is metaheuristic algorithms that solve problems by the lifecycle of creature, production, crossover, and inheritance. It can avoid local minimums in the case parameter landscapes don't have UV structure. GA then LS has been used to overcome such parameter landscapes that have UV structure. Variational Quantum Eigensolver(VQE) is very this case. Hence, calculating eigenenergies by this method using only GA or local search methods tend to be trapped by local minimums and failed. Therefore, we optimized the GA then LS for VQE method and calculated eigenenergies of some molecules. We call this new VQE method Genetic-Multi-Initial-Generalized VQE(GMIG-VQE). In general, this algorithm applies local search every crossover process. But, local search may quite a short time. Besides, GA must take 100N generations for the number of parameters N. Therefore, we apply local search for chosen 10 parameter sets at the end of GA. We calculated the eigenenergies of some kind of molecules for four algorithms of local search; Conjugate Gradient, BFGS, Nelder-Mead, SLSQP methods. We will show the result of them and the ideas to improving this GMIG-VQE.