Kernel based quantum machine learning at record rate: Many-body distribution functionals as compact representations.

Area of Science:

• Computational chemistry
• Quantum machine learning
• Materials science

Background:

• Kernel-based quantum machine learning (QML) models demonstrate high data efficiency for chemical systems.
• Accurate chemical representations often require high-dimensional feature mapping, leading to significant computational burdens.
• Efficient and accurate molecular representations are crucial for advancing QML in chemical compound space.

Purpose of the Study:

• To introduce novel, compact, and accurate linear scaling quantum machine learning representations.
• To develop representations that are invariant to the number of atoms, reducing computational complexity.
• To evaluate the performance and data efficiency of these new representations against state-of-the-art methods.

Main Methods:

• Development of compact, linear scaling QML representations using atomic Gaussian many-body distribution functionals (MBDF) and their derivatives.
• Utilizing weighted density functions of MBDF values as global, fixed-size representations.
• Testing the representations on QM9 and QMugs datasets for various molecular properties.

Main Results:

• The proposed MBDF-based representations achieve predictive performance and training data efficiency competitive with state-of-the-art methods.
• These representations demonstrate generalization capabilities for diverse molecular properties including energies, electronic properties, and thermodynamic parameters.
• MBDF-based models significantly improve the trade-off between sampling and training costs, enabling faster exploration of chemical space.

Conclusions:

• Compact MBDF-based QML representations offer a computationally efficient and accurate alternative for modeling chemical systems.
• These representations facilitate rapid and accurate sampling of chemical compound space, accelerating materials discovery.
• The developed method provides a pathway to achieve chemical accuracy at a significantly reduced computational cost.