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.
Abstract
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 network (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 0.89 (quantum) and 0.92 (classical) on the gap task, and close to 0.78 (both) on the dipole task. The models reach 90% of asymptotic performance within about 300 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.
This report presents a hybrid quantum-classical workflow performed on the Fujitsu FX700 ideal state-vector simulator using QARP that addresses two structural inefficiencies in quantum-sampling-based diagonalization workflows and introduces QSCI-RBM, a variant that replaces the configuration recovery of the SQD framework with a Restricted Boltzmann Machine (RBM) acting as a compact generative subspace expansion model.
V. AnuragK.S., A. Patra, M. Mukherjee et al.· arXiv.org· 3 citations
A complexity analysis shows that leveraging the ravine-like structure of QCLs with the QNN NEB approach substantially reduces computational costs compared to naive QNN ensembling, and that the NEB approach also accelerates convergence over the naive alternative.
The work presented in this thesis shows that efficient ML for quantum chemistry does not rely on a single universally optimal model class, and hybrid strategies that combine explicit physical models with learned components can be as effective as fully data-driven approaches while retaining the robustness and interpretability of the underlying physical description.
This work proposes an operator-centric framework in which the external (nuclear) potential, expressed in an AO basis, serves as the model input and builds hierarchical, body-ordered representations of atomic configurations that closely mirror the principles underlying several popular atom-centered descriptors.
Jigyasa Nigam, T. Smidt, G. Dusson· Journal of Chemical Physics· 2 citations
DPA4C is introduced, an equivariant potential whose architecture and compressed CUDA operators are co-designed under deployment constraints to pursue accuracy and efficiency together and brings quantum-trained universal accuracy into a regime of speed and system size previously associated with empirical potentials.
Tian Li, Jianming Xue, Linfeng Zhang et al.· 0 citations
Coupled-cluster theory defines the accuracy standard for molecular electronic-structure properties but scales too steeply for routine application, whereas density-functional theory is affordable yet systematically biased. We resolve this trade-off with a single equivariant network, MEHnet-MG, that predicts an effective one-electron Hamiltonian from one inexpensive B3LYP/def2-SVP calculation and derives a broad suite of properties from it (energy, optical gap, dipole, quadrupole, polarizability, Mulliken atomic charges, and Mayer bond orders) at coupled-cluster accuracy across nine main-group elements, including the under-served phosphorus, sulfur, and chlorine chemistries. The model is trained on a new in-house dataset of multi-property labels computed at the CCSD(T) level for all nine elements. On a held-out test set, it reduces the error of every property by a factor of 3.8 to 230 relative to semi-local, hybrid, and double-hybrid DFT (referenced to composite CCSD(T)/cc-pVTZ; Methods), while adding only ~25 ms wall time per molecule, delivering coupled-cluster-quality predictions at the cost of a single DFT calculation. Critically, deriving every property from a predicted Hamiltonian rather than pooling per-atom features builds the correct size-scaling into the model architecture: on pi-conjugated oligothiophenes it matches finite-field CCSD polarizability and the EOM-CCSD optical gap to ~2% at the largest sizes where those references remain affordable (44 and 37 atoms, where a single CCSD field point already costs ~500x the model's entire inference) and extrapolates the corrected trends to 58-atom chains, a regime where pooling-based architectures fail by construction. Accurate extrapolation is therefore set by the model's inductive bias rather than by the training data.