Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks

David Pfau, James S. Spencer, Alex G. D. G. Matthews, W. M. C. Foulkes

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,1 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 approximators2,3 and
promise as a compact wavefunction Ansatz for spin systems,4 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,5 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 optimisation of wavefunctions for
previously intractable molecules and solids.