Approaching exact solutions of the electronic Schrödinger equation with deep quantum Monte Carlo

The electronic Schrödinger equation describes fundamental properties of molecules and materials, but cannot be solved exactly for larger systems than a hydrogen atom. Recently, deep variational quantum Monte Carlo has been established as a viable path towards highly accurate solutions with favorable scaling of the computational cost with system size [1,2]. Here, we present PauliNet, a deep-neural-network architecture that includes the Hartree–Fock solution and exact cusp conditions as a baseline, and uses the Jastrow factor and backflow transformation as entry points for a graph neural network which ensures permutational antisymmetry. PauliNet outperforms comparable state-of-the-art trial wave functions on atoms, small molecules, and a strongly correlated model system, and standard quantum chemistry methods on a difficult multireferential molecule. Convergence of the solution to a given fixed-node limit is analyzed with respect to the basis-set size and the Jastrow network size [3]. Numerically exact fixed-node solutions are obtained for LiH and H₄.

[1] J. Hermann, Z. Schätzle & F. Noé, Nat. Chem. 12, 891–897 (2020)
[2] D. Pfau, J. S. Spencer, A. G. D. G. Matthews & W. M. C. Foulkes, Phys. Rev. Research 2, 033429 (2020)
[3] Z. Schätzle, J. Hermann & F. Noé, arXiv:2010.05316