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.
Calculation of binding energies for protein-ligand molecular systems requires accurate treatment of the electronic structure, a quantum chemistry problem that scales exponentially on classical hardware, while current quantum hardware remains too noisy for the required circuit depths. 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. First, we integrate the Linear Scaling CNOT UCCSD (LCNot-UCCSD) ansatz into the QSCI framework, replacing the $\mathcal{O}(N^6)$ CCSD parameter initialization of the competing LUCJ ansatz approach with $\mathcal{O}(N^4)$ MP2-amplitude initialization. Second, we introduce 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. Both are evaluated on eight different molecules in STO-3G across 14 controlled artificial error levels with 100 independent runs each, validated on potential energy surface scans of the N$_2$ molecule in cc-pVDZ, and embedded within DMET to treat the FDA-approved antiviral Amantadine (C$_{10}$H$_{17}$N, 11 DMET fragments) and the active region of the SARS-CoV-2 main protease complexed with its covalent inhibitor Carmofur (PDB: 7BUY, C$_{15}$H$_{28}$N$_4$O$_5$S, 10 fragments). To our knowledge, this is the first deployment of LCNot-UCCSD within QSCI on a quantum computing simulator, and the first DMET-QSCI(LCNot-UCCSD)-RBM application to an industry-relevant protein-ligand system. By utilizing a fraction of the classical computing resources required by the current state-of-the-art work by Cleveland Clinic, RIKEN, and IBM Quantum, this approach enables more efficient and economical drug discovery simulations for the industry.
V. AnuragK.S., A. Patra, M. Mukherjee et al.· arXiv.org· 3 citations
The geometric and topological structure of quantum cost landscapes (QCLs) governs the optimization and thus the predictive power of variational quantum algorithms (VQAs). We systematically analyze ravines - low-cost paths connecting local minima - using an adapted version of the nudged elastic band (NEB) algorithm, a method originating from theoretical chemistry. By training quantum neural networks (QNNs) to classify the concentratable entanglement of quantum states, we apply the NEB algorithm and numerically identify ravine structures in QCLs of hardware-efficient ansatzes. Beyond visualizing these ravines, we construct an ensemble prediction framework by averaging predictions from QNNs parameterized along the low-cost NEB path. We introduce a resource-light pre-training metric which quantifies local-prediction variability and serves as a strong performance indicator for VQAs, even beyond the scope of this study. When base classifiers are drawn from circuit and weight initializations exhibiting high local-prediction variability, the quantum-based NEB ensembles outperform both classical and naive quantum alternatives. Moreover, 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. A depth and qubit scaling analysis indicates that ravines persist across both scalings, and that, despite the expected growth in resource requirements with the qubit scaling, the NEB approach also accelerates convergence over the naive alternative.
The development of quantum chemistry has long been shaped by a central tension: while the laws governing electronic structure are known, their exact application quickly becomes computationally prohibitive for realistic molecular systems. Over decades, this challenge has driven the design of increasingly sophisticated approximations that balance predictive accuracy with computational affordability. More recently, machine learning (ML) has emerged as a new addition to this methodological landscape, offering the possibility of reproducing high-level quantum chemical results at a fraction of the cost.
This thesis explores how ML can contribute to this long-standing objective in a particularly resource-conscious way. Rather than treating ML purely as a black-box substitute for quantum chemistry, the work asks a broader methodological question: under finite budgets for data generation, training and inference, what is the most efficient way to use data-driven models to accelerate quantum chemical simulations? Across the different applications studied here, the guiding principle has been to identify the simplest effective strategy for the problem at hand while retaining as much physical structure and reusing as much existing data as possible.
A first key result of this thesis is that substantial acceleration can, in some settings, be achieved with remarkably simple models. In the context of basis set extrapolation for GW quasiparticle energies, a linear regression model based on molecular orbital descriptors was shown to recover near-complete basis set accuracy from finite-basis calculations. This demonstrates that when the underlying quantum chemical representations already contain the essential physical information, even lightweight statistical models can provide acceleration while maintaining high-level quantum chemical accuracy.
As many ML applications, especially neural networks, critically depend on sufficiently broad and reliable training data, part of this work focused on constructing a large-scale dataset of quasiparticle self-consistent GW (qsGW) quasiparticle energies, GW Bethe--Salpter equation (GW-BSE) neutral excitation energies, transition dipole moments and oscillator strengths across a chemically diverse space of organic molecules. Building on this foundation, a graph neural network was trained for the prediction of charged and neutral excitation energies. A central finding is that transfer learning from lower-fidelity but already widely available data sources, such as molecular orbital energies from density functional theory (DFT) and excitation energies from time-dependent DFT (TDDFT), can substantially improve the prediction of the high-fidelity qsGW and GW-BSE targets. In this way, previously generated computational data become a powerful resource for reducing the cost of expensive reference calculations.
The question of how simple ML models can remain while still being effective was further investigated for solvation energies and geometry optimization in solution. Here, the results show that relatively simple graph neural network architectures can already yield accurate predictions of Gibbs solvation energies for highly charged molecules. At the same time, ML was also used to parametrize and correct established physically grounded solvation models. These results suggest that, in such settings, 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.
Taken together, the work presented in this thesis shows that efficient ML for quantum chemistry does not rely on a single universally optimal model class. Instead, the most effective strategies arise from matching the complexity of the statistical model to the physical structure of the problem, reusing data across different levels of quantum chemical theory and retaining established physical models wherever they already provide reliable inductive bias. In this sense, ML serves not simply as a faster predictor but as a flexible methodological tool for extending the practical reach of quantum chemical simulations through resource-efficient acceleration.
Electronic structure calculations remain a major bottleneck in atomistic simulations and, not surprisingly, have attracted significant attention in machine learning (ML). Most existing approaches learn a direct map from molecular geometries, typically represented as graphs or encoded local environments, to molecular properties or use ML as a surrogate for electronic structure theory by targeting quantities, such as Fock or density matrices expressed in an atomic orbital (AO) basis. Inspired by the Hohenberg-Kohn theorem, in this work, we propose an operator-centric framework in which the external (nuclear) potential, expressed in an AO basis, serves as the model input. From this operator, we construct hierarchical, body-ordered representations of atomic configurations that closely mirror the principles underlying several popular atom-centered descriptors. At the same time, the matrix-valued nature of the external potential provides a natural connection to equivariant message-passing neural networks. In particular, we show that successive products of the external potential provide a scalable route to equivariant message passing and enable an efficient description of nonlocal effects. We demonstrate that this approach can be used to model molecular properties, such as energies and dipole moments, from the external potential or to learn effective operator-to-operator maps, including mappings to the Fock matrix from which multiple molecular observables can be simultaneously derived.
Jigyasa Nigam, T. Smidt, G. Dusson· Journal of Chemical Physics· 2 citations
No interatomic potential has offered universality across chemistry, near-first-principles accuracy and the speed of empirical potentials at once. Here we introduce DPA4C, an equivariant potential whose architecture and compressed CUDA operators are co-designed under deployment constraints to pursue accuracy and efficiency together. Five variants spanning a 49-fold parameter range form the high-throughput end of the measured accuracy--throughput frontier. The largest variant approaches the accuracy of the MACE-Omat models at about two orders of magnitude higher measured throughput. The most compact reduces the energy, force and stress errors of the fastest existing universal MLIP by 61.4%, 48.1% and 34.3% at 1.92 times its saturated throughput. All five variants complete multimillion-atom simulations on a single GPU and run molecular dynamics for 2.048 billion atoms on 1,024 16-GB NVIDIA V100 GPUs at 83.3--91.2% weak-scaling efficiency. Compared with the MEAM empirical potential, DPA4C-Nano reaches 1.8 and 2.5 times the saturated throughput in single-GPU scans on the same V100 hardware for diamond carbon and FCC copper, respectively. DPA4C therefore 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.