Boosting Quantum Machine Learning Models with a Multilevel Combination Technique: Pople Diagrams Revisited.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Machine Learning

Background:

• Accurate molecular energy calculations are crucial in chemistry.
• High-accuracy methods are computationally expensive, limiting their application.
• Quantum machine learning (QML) offers a data-driven approach to accelerate calculations.

Purpose of the Study:

• To develop a hierarchical scheme, termed multilevel combination (C) technique, to integrate various approximation levels in molecular energy calculations.
• To combine this scheme with QML models, creating a generalized unified recursive kernel ridge regression (CQML).
• To investigate the effectiveness of CQML in predicting molecular atomization energies across different dimensions.

Main Methods:

• Developed a hierarchical scheme based on the multilevel combination (C) technique.
• Integrated the C technique with quantum machine learning (QML) models to create the CQML model.
• Investigated three dimensions: chemical space, basis set, and electron correlation treatment.
• Applied the CQML model to predict atomization energies for organic molecules and constitutional isomers.

Main Results:

• The CQML model demonstrated a significant reduction in the number of required training samples for high-accuracy calculations.
• Achieved millisecond estimates of CCSD(T)/cc-pvdz atomization energies with prediction errors within chemical accuracy (∼1 kcal/mol) using only ∼100 training instances.
• Showed that fewer high-accuracy training instances are needed compared to conventional QML, while more are required at lower approximation levels.

Conclusions:

• The CQML approach offers a favorable trade-off between hierarchical approximations with different computational cost scaling.
• This method drastically reduces the computational burden for achieving highly accurate molecular energy predictions.
• CQML holds significant promise for accelerating quantum chemistry calculations and enabling the study of larger molecular systems.