Fermionic neural-network states for ab-initio electronic structure

Kenny Choo,Antonio Mezzacapo,Giuseppe Carleo

doi:10.1038/s41467-020-15724-9

Abstract

Neural-network quantum states have been successfully used to study a variety of lattice and continuous-space problems. Despite a great deal of general methodological developments, representing fermionic matter is however still early research activity. Here we present an extension of neural-network quantum states to model interacting fermionic problems. Borrowing techniques from quantum simulation, we directly map fermionic degrees of freedom to spin ones, and then use neural-network quantum states to perform electronic structure calculations. For several diatomic molecules in a minimal basis set, we benchmark our approach against widely used coupled cluster methods, as well as many-body variational states. On some test molecules, we systematically improve upon coupled cluster methods and Jastrow wave functions, reaching chemical accuracy or better. Finally, we discuss routes for future developments and improvements of the methods presented.

Highlights

Neural-network quantum states have been successfully used to study a variety of lattice and continuous-space problems
We show results for several diatomic molecules in minimal Gaussian basis sets, where our approach reaches chemical accuracy (
We have shown that relatively simple shallow neural networks can be used to compactly encode, with high precision, the electronic wave function of model molecular problems in quantum chemistry

Summary

Introduction

Neural-network quantum states have been successfully used to study a variety of lattice and continuous-space problems. CC techniques are routinely adopted in QC electronic calculations, and they are often considered the “gold standard” in ab-initio electronic structure Despite this success, the accuracy of CC is intrinsically limited in the presence of strong quantum correlations, in turn restricting the applicability of the method to regimes of relative weak correlations. For strongly correlated molecules and materials, alternative, non-perturbative approaches have been introduced Most notably, both stochastic and non-stochastic methods based on variational representations of many-body wave-functions have been developed and constantly improved in the past decades of research. Stochastic projection methods systematically improving upon variational starting points are for example the fixed-node Green’s function Monte Carlo[8] and constrained-path auxiliary field Monte Carlo[9]. Variational forms considered so-far for higher dimensional systems typically rely on rigid variational classes and do not provide a systematic and computationally efficient way to increase their expressive power

Methods

Results

Conclusion