Toward DMC Accuracy Across Chemical Space with Scalable ?-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 Schro''dinger 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 Delta-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.

Automated summary

Quantum diffusion Monte Carlo (DMC) has shown great potential in predicting the energetics and properties of molecules and solids through solving the electronic many-body Schrödinger equation. When coupled with quantum machine learning (QML), DMC can alleviate computational burden, making it a promising method for large systems. Three crucial approximations, including fixed-node approximation, universal reference for chemical bond dissociation energies, and scalable minimal amons-set-based QML (AQML) models, are discussed. Numerical evidence suggests that even modestly sized QMC training data sets can accurately predict total energies throughout chemical space.