Sorting Out Quantum Monte Carlo

Abstract

Molecular modeling at the quantum level requires choosing a parameterization of the wavefunction that both respects the required symmetries, and is scalable to systems of many particles. For the simulation of fermions, valid parameterizations must be antisymmetric with the transposition of particles. Typically, antisymmetry is enforced by leveraging the anti-symmetry of determinants with respect to exchange of matrix rows, but this involves computing a full determinant each time the wavefunction is evaluated. Instead, we introduce a new antisymmetrization layer derived from sorting, the $\text{\emph{sortlet}}$, which scales as $O(N \log N )$ in the number of particles, in contrast to the $O(N^3)$ of the determinant. We show experimentally that applying this anti-symmeterization layer on top of an attention based neural-network backbone yields a flexible wavefunction parameterization capable of reaching chemical accuracy when approximating the ground state of first-row atoms and molecules.