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.
Highlights
The success of deep learning in artificial intelligence [1,2] has led to an outpouring of research into the use of neural networks for quantum physics and chemistry
We prove in Appendix B that a single determinant of this form is in theory general enough to represent any antisymmetric function, though in practice we require a small number of determinants to reach high accuracy
We have shown that antisymmetric neural networks can be constructed and optimized to enable high-accuracy quantum chemistry calculations of challenging systems
Summary
The success of deep learning in artificial intelligence [1,2] has led to an outpouring of research into the use of neural networks for quantum physics and chemistry. The FermiNet is an improvement over existing Ansatz for VMC, but is competitive with and in some cases superior to more sophisticated quantum chemistry algorithms Projector methods such as diffusion quantum Monte Carlo (DMC) [12] and auxiliary field quantum Monte Carlo (AFQMC) [28] generate stochastic trajectories that sample the ground-state wave function without the need for an explicit representation, accurate explicit trial wave functions are still required for good performance and numerical stability. Coupled cluster methods [8] use an Ansatz that multiplies a reference wave function by an exponential of a truncated sum of creation and annihilation operators This proves remarkably accurate for equilibrium geometries, but conventional reference wave functions are insufficient for systems with many low-lying excited states. We evaluate the FermiNet on a variety of stretched systems and find that it outperforms coupled cluster in all cases
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.