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We propose a new approach to circumvent the sign problem in which theintegration path is optimized to control the sign problem. We give a trialfunction specifying the integration path in the complex plane and tune it tooptimize the cost function which represents the seriousness of the signproblem. We call it the path optimization method. In this method, we do notneed to solve the gradient flow required in the Lefschetz-thimble method andthen the construction of the integration-path contour arrives at theoptimization problem where several efficient methods can be applied. In asimple model with a serious sign problem, the path optimization method isdemonstrated to work well; the residual sign problem is resolved and preciseresults can be obtained even in the region where the global sign problem isserious.

Toward solving the sign problem with path optimization method