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

Abstract

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-Goldferb-Shanno, Nelder-Mead, and Newton's method as an optimizer of LS. We obtained the result that Newton's 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 speedup and be more accurate.

Evaluation on Genetic Algorithms as an optimizer of Variational Quantum Eigensolver(VQE) method

“…Novel methods for crossover and offspring are necessary for the improvement of the accuracy of rcGA as an optimizer of the VQE method. Although, novel VQE method using the combining method of rcGA and local search method denotes the high accuracy su-perior to that of BFGS method we demonstrated [25]. It means that rcGA makes many individuals as parameter sets.…”

“…7 shows the results for the initial population according to the beta distribution with a=b=0. 25. First, the computed potential surface is shown.…”