Sorting Out Quantum Monte Carlo

TL;DR

This paper introduces a scalable antisymmetrization method called 'sortlet' for quantum Monte Carlo simulations, enabling efficient wavefunction parameterization that achieves chemical accuracy for small molecules.

Contribution

The paper presents a novel antisymmetrization layer based on sorting, called 'sortlet', which reduces computational complexity from O(N^3) to O(N log N) for fermionic wavefunctions.

Findings

Sortlet scales as O(N log N), significantly faster than traditional determinants.

Applying sortlet on neural networks achieves chemical accuracy in small molecules.

The method is effective for approximating ground states of first-row atoms.

Abstract

Molecular modeling at the quantum level requires choosing a parameterization of the wavefunction that both respects the required particle symmetries, and is scalable to systems of many particles. For the simulation of fermions, valid parameterizations must be antisymmetric with respect to the exchange of particles. Typically, antisymmetry is enforced by leveraging the anti-symmetry of determinants with respect to the 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 $\textit{sortlet}$, which scales as $O(N \log N)$ with regards to the number of particles -- in contrast to $O(N^3)$ for the determinant. We show numerically 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 small molecules.