Toward DMC Accuracy Across Chemical Space with Scalable Δ‑QML

In the past decade, quantum diffusion Monte Carlo (DMC)
has been
demonstrated to successfully predict the energetics and properties
of a wide range of molecules and solids by numerically solving the
electronic many-body Schrödinger equation. With O(N3) scaling with the number of electrons N, DMC has the potential to be a reference method for larger
systems that are not accessible to more traditional methods such as
CCSD(T). Assessing the accuracy of DMC for smaller molecules becomes
the stepping stone in making the method a reference for larger systems.
We show that when coupled with quantum machine learning (QML)-based
surrogate methods, the computational burden can be alleviated such
that quantum Monte Carlo (QMC) shows clear potential to undergird
the formation of high-quality descriptions across chemical space.
We discuss three crucial approximations necessary to accomplish this:
the fixed-node approximation, universal and accurate references for
chemical bond dissociation energies, and scalable minimal amons-set-based
QML (AQML) models. Numerical evidence presented includes converged
DMC results for over 1000 small organic molecules with up to five
heavy atoms used as amons and 50 medium-sized organic molecules with
nine heavy atoms to validate the AQML predictions. Numerical evidence
collected for Δ-AQML models suggests that already modestly sized
QMC training data sets of amons suffice to predict total energies
with near chemical accuracy throughout chemical space.