Solving the electronic Schrödinger equation with deep learning

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The electronic Schrödinger equation describes fundamental properties of molecules and materials, but cannot be solved exactly for larger systems than a hydrogen atom. Variational quantum Monte Carlo (QMC) provides a computationally efficient platform for arbitrarily accurate solutions of the electronic Schrödinger equation, but until recently its accuracy has been limited by the expressiveness of the available wave function ansatzes. In this talk, I will present a new class of ansatzes based on deep learning that has been established as a viable path towards highly accurate solutions of the electronic structure with favorable scaling of the computational cost with system size. Unlike machine learning approaches based on supervised learning from large chemical datasets, deep QMC is an ab-initio approach, just as standard QMC, and requires no external data. Our deep-learning ansatz, PauliNet, has been constructed with 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.