Quantum machine learning force fields

Abstract

An accurate knowledge of potential energy surfaces and local forces is of paramount importance to implement molecular dynamics (MD) calculations. As the exact solution of the Schrödinger equation for electrons and nuclei becomes quickly impractical with growing system size, approximate methods have been developed in a delicate balance between performance and accuracy. Besides density functional theory and empirical force fields, machine learning has emerged as a novel and effective framework, leading to the family of so-called neural network potentials (NNPs). The success of classical NNPs is nowadays testified by several high-impact scientific works and by the development of dedicated software libraries. At the same time, the quantum mechanical character of the relationship between molecular configurations, energies and forces immediately leads to the question whether quantum machine learning (QML) methods could provide even greater advantages. Inspired by this idea, our work aims at establishing a direct connection between quantum neural networks (QNNs) and molecular force fields. We carry out such program by designing a dedicated quantum neural network architecture and by applying it to different molecules of growing complexity. The quantum models exhibit a larger effective dimension with respect to classical counterparts, achieving competitive performances. Furthermore, we leverage the recently introduced framework of geometric QML to develop equivariant quantum neural networks that natively respect relevant sets of molecular symmetries upon input of cartesian coordinates, thus enhancing trainability and generalization power. Notably, QML is now reaching a level of maturity at which the quest for non-trivial candidate problems -- both practically relevant and suitable to showcase quantum advantage over classical counterparts -- becomes of paramount importance. With our present contribution, we not only show that QNNs can adequately serve the purpose of generating molecular force fields, but we suggest that this may constitute an appealing playground to test and understand the potential of QML techniques.