Abstract: We consider the path-integral method for lattice quantum chromodynamics. Due to the presence

of the complex action, the numerical sign problem may cause large variance in the Monte Carlo method. To

tackle such a problem, the real Langevin method is complexified. However, the complexified Langevin

method may diverge due to excessive excursions to the imaginary part. To relax such a problem, complexified

gauge symmetry of the quantum field is applied to minimize the unitarity norm. In the current numerical

method, the gradient descent method may lead to an unsatisfactory reduction of the unitarity norm, and it

requires selection of the step length. By studying the one-dimensional Polyakov model, an optimal choice

of gauge can be analytically solved. The idea of the stochastic gradient method is applied to extend it the

method to the multi-dimensional case. The resulting method has no parameters and efficiently stabilizes the simulation.

Brief introduction: Zhenning Cai is now an assistant professor at National University of Singapore. His

research work mainly includes numerical computation for quantum mechanics and kinetic theory.