Implementations of Quantum and Classical Topology-Aligned Architectures for Molecular Property Prediction
For quantum chemistry researchers in low-data regimes, this work demonstrates that topology-aligned inductive bias enables parameter-efficient learning, but the results are incremental as they only benchmark on QM9 with simple binary classification tasks.
The authors propose a topology-aligned inductive bias for molecular property prediction, where model architecture mirrors the molecular bond graph. Their quantum (Iso-QGNN) and classical (Iso-CGNN) models achieve test AUCs of ~0.88 and ~0.91 on HOMO-LUMO gap classification and ~0.78 on dipole moment classification with only 64 trainable parameters, reaching 90% of asymptotic performance within ~250 training molecules.
For low-data and resource-constrained regimes typical of quantum chemistry, parameter-efficient learning is a key objective. Here, we propose a topology-aligned inductive bias in which the model architecture mirrors the molecular bond graph: atoms map to a fixed register of computational units, and bonds determine which pairs interact through shared learnable parameters. This principle is instantiated in two architectures: a variational quantum circuit (Iso-QGNN), and a parameter-matched classical message-passing model (Iso-CGNN). The models are benchmarked on HOMO-LUMO and dipole moment binary classification tasks over the QM9 benchmark. With 64 trainable parameters, the implementations achieve test AUCs of approximately 0.88 (quantum) and 0.91 (classical) on the gap task, and close to 0.78 (both) on the dipole task. The models reach 90% of asymptotic performance within about 250 training molecules and gradient norms remain stable throughout training. These results indicate that the topology-aligned inductive bias is the active ingredient driving parameter efficiency at QM9 scale, with implications for matched-baseline benchmarking in quantum machine learning.