Ab-Initio Solution of the Many-Electron Schr\"odinger Equation with Deep Neural Networks

TL;DR

This paper introduces a new deep neural network architecture called Fermionic Neural Network, which serves as an accurate wavefunction Ansatz for many-electron systems, outperforming traditional methods in quantum chemistry.

Contribution

The paper presents the Fermionic Neural Network, a novel deep learning architecture that accurately models many-electron wavefunctions obeying Fermi-Dirac statistics, advancing ab-initio quantum chemistry methods.

Findings

Achieves higher accuracy than other variational quantum Monte Carlo Ans"atze.

Predicts dissociation curves of challenging systems more accurately than coupled cluster methods.

Demonstrates deep neural networks can outperform traditional ab-initio quantum chemistry techniques.

Abstract

Given access to accurate solutions of the many-electron Schr\"odinger equation, nearly all chemistry could be derived from first principles. Exact wavefunctions of interesting chemical systems are out of reach because they are NP-hard to compute in general, but approximations can be found using polynomially-scaling algorithms. The key challenge for many of these algorithms is the choice of wavefunction approximation, or Ansatz, which must trade off between efficiency and accuracy. Neural networks have shown impressive power as accurate practical function approximators and promise as a compact wavefunction Ansatz for spin systems, but problems in electronic structure require wavefunctions that obey Fermi-Dirac statistics. Here we introduce a novel deep learning architecture, the Fermionic Neural Network, as a powerful wavefunction Ansatz for many-electron systems. The Fermionic Neural Network is able to achieve accuracy beyond other variational quantum Monte Carlo Ans\"atze on a variety of atoms and small molecules. Using no data other than atomic positions and charges, we predict the dissociation curves of the nitrogen molecule and hydrogen chain, two challenging strongly-correlated systems, to significantly higher accuracy than the coupled cluster method, widely considered the most accurate scalable method for quantum chemistry at equilibrium geometry. This demonstrates that deep neural networks can improve the accuracy of variational quantum Monte Carlo to the point where it outperforms other ab-initio quantum chemistry methods, opening the possibility of accurate direct optimization of wavefunctions for previously intractable many-electron systems.