Direct sampling of projected entangled-pair states

Direct sampling of high-dimensional probability distributions provides an important improvement over Markov Chains in Variational Monte Carlo algorithms for many-body quantum systems. They alleviate the burden of large autocorrelation times in Markov Chains by providing independent samples drawn according to the probability distribution. On one hand, probability distributions can be designed such that they can be easily sampled directly, e.g. in the case of autoregressive neural networks. On the other hand, a given distribution can in some cases be cast in a form such that they can be sampled directly. We show how to do this approximately for projected entangled-pair states (PEPS) by adding an importance sampling step. We show that this procedure is efficient and provides signifficant improvements over the widely used Markov Chain sampling of PEPS with local updates.