Boosting quantum machine learning models with multi-level combination technique: Pople diagrams revisited

TL;DR

This paper introduces a hierarchical multi-level combination technique integrated with quantum machine learning to efficiently predict molecular energies, significantly reducing training data needs for high-accuracy quantum chemistry calculations.

Contribution

It presents the CQML model, a recursive kernel ridge regression that combines multiple approximation levels across several dimensions, enhancing quantum machine learning for molecular energy predictions.

Findings

CQML reduces training data for accurate energy predictions.

Achieves chemical accuracy with only ~100 training samples.

Demonstrates efficient trade-offs in hierarchical quantum chemistry approximations.

Abstract

Inspired by Pople diagrams popular in quantum chemistry, we introduce a hierarchical scheme, based on the multi-level combination (C) technique, to combine various levels of approximations made when calculating molecular energies within quantum chemistry. When combined with quantum machine learning (QML) models, the resulting CQML model is a generalized unified recursive kernel ridge regression which exploits correlations implicitly encoded in training data comprised of multiple levels in multiple dimensions. Here, we have investigated up to three dimensions: Chemical space, basis set, and electron correlation treatment. Numerical results have been obtained for atomization energies of a set of $\sim$7'000 organic molecules with up to 7 atoms (not counting hydrogens) containing CHONFClS, as well as for $\sim$6'000 constitutional isomers of C$_7$H$_{10}$O$_2$. CQML learning curves for atomization energies suggest a dramatic reduction in necessary training samples calculated with the most accurate and costly method. In order to generate milli-second estimates of CCSD(T)/cc-pvdz atomization energies with prediction errors reaching chemical accuracy ($\sim$1 kcal/mol), the CQML model requires only $\sim$100 training instances at CCSD(T)/cc-pvdz level, rather than thousands within conventional QML, while more training molecules are required at lower levels. Our results suggest a possibly favourable trade-off between various hierarchical approximations whose computational cost scales differently with electron number.