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arXiv:2509.26397

Are neural scaling laws leading quantum chemistry astray?

Siwoo Lee, Adji Bousso Dieng

Published Sep 30, 2025• 1 citation
arXivHTMLPDF

Abstract

Neural scaling laws are driving the machine learning community toward training ever-larger foundation models across domains, assuring high accuracy and transferable representations for extrapolative tasks. We test this promise in quantum chemistry by scaling model capacity and training data from quantum chemical calculations. As a generalization task, we evaluate the resulting models' predictions of the bond dissociation energy of neutral H$_2$, the simplest possible molecule. We find that, regardless of dataset size or model capacity, models trained only on stable structures fail dramatically to even qualitatively reproduce the H$_2$ energy curve. Only when compressed and stretched geometries are explicitly included in training do the predictions roughly resemble the correct shape. Nonetheless, the largest foundation models trained on the largest and most diverse datasets containing dissociating diatomics exhibit serious failures on simple diatomic molecules. Most strikingly, they cannot reproduce the trivial repulsive energy curve of two bare protons, revealing their failure to learn the basic Coulomb's law involved in electronic structure theory. These results suggest that scaling alone is insufficient for building reliable quantum chemical models.

DOI
10.48550/arxiv.2509.26397

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physics.chem-phCross-listedarXiv:2606.17077•Jun 11, 2026
Neural scaling laws are driving the machine learning community toward training ever-larger foundation models across domains, assuring high accuracy and transferable representations for extrapolative tasks. We test this promise in quantum chemistry by scaling model capacity and training data from quantum chemical calculations. As a generalization task, we evaluate the resulting models' predictions of the bond dissociation energy of neutral H2_22​, the simplest possible molecule. We find that, regardless of dataset size or model capacity, models trained only on stable structures fail dramatically to even qualitatively reproduce the H2_22​ energy curve. Only when compressed and stretched geometries are explicitly included in training do the predictions roughly resemble the correct shape. Nonetheless, the largest foundation models trained on the largest and most diverse datasets containing dissociating diatomics exhibit serious failures on simple diatomic molecules. Most strikingly, they cannot reproduce the trivial repulsive energy curve of two bare protons, revealing their failure to learn the basic Coulomb's law involved in electronic structure theory. These results suggest that scaling alone is insufficient for building reliable quantum chemical models.
A long-standing goal of science is to accurately solve the Schrödinger equation for large molecular systems. The poor scaling of current quantum chemistry algorithms on classical computers imposes an effective limit of about a few dozen atoms for which we can calculate molecular electronic structure. We present a machine learning (ML) method to break through this scaling limit and make quantum chemistry calculations of very large systems possible. We show that Euclidean Neural Networks can be trained to predict the electron density with high fidelity from limited data. Learning the electron density allows us to train a machine learning model on small systems and make accurate predictions on large ones. We show that this ML electron density model can break through the quantum scaling limit and calculate the electron density of systems of thousands of atoms with quantum accuracy.
Neural-network quantum states (NNQSs) can represent many-electron wave functions without explicitly enumerating the determinant space, but their accuracy depends jointly on model size and variational-optimization effort. Here we characterize this dependence for a physics-conditioned autoregressive NNQS trained separately on two six-molecule source benchmarks. Across eight model sizes and five optimization milestones, we find that model size and optimization steps jointly shape the energy error. The capacity advantage of larger models becomes more apparent with sufficient optimization, while the returns from additional optimization vary with model size. We capture this coupling using an interaction scaling law and quantify the cumulative compute of each evaluated configuration. The resulting error-compute Pareto frontiers provide a practical decision rule for jointly selecting model size and optimization steps under a given compute budget within the evaluated range. Furthermore, we find that this beneficial scaling trend persists during fine-tuning on held-out N2_22​. Pretrained models show decreasing error with increasing model size, with a steeper reduction following pretraining on the Hard benchmark. Together, these results place autoregressive neural quantum states within the broader landscape of empirical neural scaling and open a quantitative route toward the systematic scaling of neural quantum solvers for ab initio quantum chemistry.
The ability to perform ab initio molecular dynamics simulations using potential energies calculated on quantum computers would allow virtually exact dynamics for chemical and biochemical systems, with substantial impacts on the fields of catalysis and biophysics. However, noisy hardware, the costs of computing gradients, and the number of qubits required to simulate large systems present major challenges to realizing the potential of dynamical simulations using quantum hardware. Here, we demonstrate that some of these issues can be mitigated by recent advances in machine learning. By combining transfer learning with techniques for building machine-learned potential energy surfaces, we propose a new path forward for molecular dynamics simulations on quantum hardware. We use transfer learning to reduce the number of energy evaluations that use quantum hardware by first training models on larger, less accurate classical datasets and then refining them on smaller, more accurate quantum datasets. We demonstrate this approach by training machine learning models to predict a molecule's potential energy using Behler-Parrinello neural networks. When successfully trained, the model enables energy gradient predictions necessary for dynamics simulations that cannot be readily obtained directly from quantum hardware. To reduce the quantum resources needed, the model is initially trained with data derived from low-cost techniques, such as Density Functional Theory, and subsequently refined with a smaller dataset obtained from the optimization of the Unitary Coupled Cluster ansatz. We show that this approach significantly reduces the size of the quantum training dataset while capturing the high accuracies needed for quantum chemistry simulations.
In the past decade, quantum diffusion Monte Carlo (DMC) has been demonstrated to successfully predict the energetics and properties of a wide range of molecules and solids by numerically solving the electronic many-body Schrödinger equation. With O ( N 3 ) scaling with the number of electrons N, DMC has the potential to be a reference method for larger systems that are not accessible to more traditional methods such as CCSD(T). Assessing the accuracy of DMC for smaller molecules becomes the stepping stone in making the method a reference for larger systems. We show that when coupled with quantum machine learning (QML)-based surrogate methods, the computational burden can be alleviated such that quantum Monte Carlo (QMC) shows clear potential to undergird the formation of high-quality descriptions across chemical space. We discuss three crucial approximations necessary to accomplish this: the fixed-node approximation, universal and accurate references for chemical bond dissociation energies, and scalable minimal amons-set-based QML (AQML) models. Numerical evidence presented includes converged DMC results for over 1000 small organic molecules with up to five heavy atoms used as amons and 50 medium-sized organic molecules with nine heavy atoms to validate the AQML predictions. Numerical evidence collected for Δ-AQML models suggests that already modestly sized QMC training data sets of amons suffice to predict total energies with near chemical accuracy throughout chemical space.
Abstract Ab‐initio quantum chemistry simulations are essential for understanding electronic structure of molecules and materials in almost all areas of chemistry. A broad variety of electronic structure theories and implementations has been developed in the past decades to hopefully solve the many‐body Schrödinger equation in an approximate manner on modern computers. In this review, we present recent progress in advancing low‐rank electronic structure methodologies that rely on the wavefunction sparsity and compressibility to select the important subset of electronic configurations for both weakly and strongly correlated molecules. Representative chemistry applications that require the many‐body treatment beyond traditional density functional approximations are discussed. The low‐rank electronic structure theories have further prompted us to highlight compressive and expressive principles that are useful to catalyze idea of quantum learning models. The intersection of the low‐rank correlated feature design and the modern deep neural network learning provides new feasibilities to predict chemically accurate correlation energies of unknown molecules that are not represented in the training dataset. The results by others and us are discussed to reveal that the electronic feature sets from an extremely low‐rank correlation representation, which is very poor for explicit energy computation, are however sufficiently expressive for capturing and transferring electron correlation patterns across distinct molecular compositions, bond types and geometries. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Software > Quantum Chemistry Software > Simulation Methods
Proton dissociation constants (pKa) are critical for functional molecule discovery and molecular modeling. Building on iBonD, the largest experimental pKa database established, we and other researchers have developed several methods including machine-learning-based empirical prediction and high-accuracy energy calculations. Despite this foundation, the rapid augmentation of high-quality pKa data remains fundamentally constrained. As part of this work, we performed large-scale regression-based pKa prediction on unlabeled molecular datasets using a collection of extensively optimized machine-learning models. The results indicate that, since the feature distributions of unlabeled molecular datasets, the pKa data distribution approximates normality, with extreme scarcity of tail-region samples. Although such augmentation is highly valuable for improving overall data availability and predictive modeling, it remains insufficient for efficiently discovering molecules with broad-spectrum pKa properties. To address this, we explore the targeted generation of molecules with sparse pKa properties from the vast chemical space. Given that traditional continuous latent space VAE-RNN methods for molecular generation suffer from insufficient stability and fail to demonstrate clear advantages in complementing sparse data, we design and implement a quantum-assisted sparse-pKa molecular generation. Feasibility is validated on a simulated quantum annealer, and superior extreme-value sampling is further achieved on physical coherent Ising machines (CIMs). (to be continued)