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

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