Application of neural network to sign problem via path optimization method

摘要

We introduce the feedforward neural network to attack the sign problem viathe path optimization method. The variables of integration is complexified andthe integration path is optimized in the complexified space by minimizing thecost function which reflects the seriousness of the sign problem. For thepreparation and optimization of the integral path in multi-dimensional systems,we utilize the feedforward neural network. We examine the validity andusefulness of the method in the two-dimensional complex $\lambda \phi^4$ theoryat finite chemical potential as an example of the quantum field theory havingthe sign problem. We show that the average phase factor is significantlyenhanced after the optimization and then we can safely perform the hybridMonte-Carlo method.