Encoding molecular structures in quantum machine learning

Abstract: Quantum machine learning (QML) has great potential for the analysis of chemical datasets. However, conventional quantum data-encoding schemes, such as fingerprint encoding, are generally unfeasible for the accurate representation of chemical moieties in such datasets. In this contribution, we introduce the quantum molecular structure encoding (QMSE) scheme, which encodes the molecular bond orders and interatomic couplings expressed as a hybrid Coulomb-adjacency matrix, directly as one- and two-qubit rotations within parameterised circuits. We show that this strategy provides an efficient and interpretable method in improving state separability between encoded molecules compared to other fingerprint encoding methods, which is especially crucial for the success in preparing feature maps in QML workflows. To benchmark our method, we train a parameterised ansatz on molecular datasets to perform classification of state phases and regression on boiling points, demonstrating the competitive trainability and generalisation capabilities of QMSE. We further prove a fidelity-preserving chain-contraction theorem that reuses common substructures to cut qubit counts, with an application to long-chain fatty acids. We expect this scalable and interpretable encoding framework to greatly pave the way for practical QML applications of molecular datasets.