Sorting Out Quantum Monte Carlo
Jack Richter-Powell Luca Thiede Alán Asparu-Guzik David Duvenaud
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.