Compression of Exact Wavefunctions with Restricted Boltzmann Machine Auto-Encoders

Abstract: Virtually, every ab-initio electronic structure method (Coupled Cluster, DMRG, etc.) can be viewed as an algorithm to compress the ground-state wavefunction. This compression is usually obtained by exploiting some physical structure of the wavefunction, which leads to issues when the system changes and that structure is lost. Compressions which are efficient near equilibrium (coupled cluster) or in 1-D systems (DMRG) often fail catastrophically elsewhere. To overcome these issues, we seek a scheme that compresses wavefunctions without any supervised physical information. In this manuscript, we introduce a scheme to compress molecular wavefunctions using a model for high dimensional functions from machine learning: a restricted Boltzmann machine (RBM). We show that, while maintaining chemical accuracy, the RBM can significantly compress the exact wavefunction.