Self-Learning Proposal Machines for Fermionic Monte Carlo Simulations*

Despite the unparalleled applicability of Markov Chain Monte Carlo methods to sampling probability distributions which arise in a large number of problems in statistical physics, the resources required to obtain independent samples from the distributions related to problems of interest often becomes intractably large. This issue emerges notably in simulations of fermionic systems. Recently, the use of machine learning has been suggested as an approach to accelerate Monte Carlo simulations through the construction of “trained” non-local recommendation machines which can generate proposals of statistically independent samples in a tractable manner that can then be sampled from in such a way as to obtain unbiased samples from the probability distribution of interest. Here, we present such a machine to accelerate fermionic systems in general and apply it to study Quantum Electrodynamics in 1+1 dimensional spacetime.