Self-learning projective quantum Monte Carlo simulations guided by restricted Boltzmann machines

Projective quantum Monte Carlo (QMC) simulations have been successfully used to simulate various relevant quantum many-body systems. They are systematically implemented in a two-step approach, in which a variational ansatz inspired by theory is first optimized using traditional variational optimization techniques. Later, the optimized ansatz is used as a guiding wave function in projective QMC simulations. In this work, we present a novel method that uses unsupervised machine learning techniques to combine the two steps above. It adaptively trains the guiding wave function (represented by a restricted Boltzmann machine) within QMC simulations, thus avoiding the need for separate variational optimization. On the one hand, this approach greatly increases the efficiency and accuracy of projective QMC simulations. On the other hand, it provides a new way to develop ground-state ansatzes, complementary to the common variational optimization schemes. We present extensive benchmarks that demonstrate the efficiency of our self-learning method.