A Transferable Machine Learning Approach to Predict Optimized Orbitals for Electronic Structure Problems
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Quantum Physics arXiv:2605.04174 (quant-ph) [Submitted on 5 May 2026] Title:A Transferable Machine Learning Approach to Predict Optimized Orbitals for Electronic Structure Problems Authors:Lucas van der Horst, Maniraman Periyasamy, Abhishek Y. Dubey, Davide Bincoletto, Jakob S. Kottmann, Daniel D. Scherer View a PDF of the paper titled A Transferable Machine Learning Approach to Predict Optimized Orbitals for Electronic Structure Problems, by Lucas van der Horst and 5 other authors View PDF HTML (experimental) Abstract:Variational quantum eigensolver ansätze hold considerable promise for ground-state energy calculations on near-term quantum hardware, yet most promising ansatz designs currently strongly depend on how well the molecular orbital basis captures the electronic correlation of the system. Computing optimized orbital coefficients via classical routines is computationally expensive and must be performed independently for each molecular geometry -- a bottleneck that limits scalability across chemical space. We present a graph neural network framework that predicts optimized orbital coefficients directly from molecular geometry and pair-wise bonding structure. Trained on hydrogenic systems of modest size ($H_4$ and $H_6$) across tens of thousands of geometries, our model transfers to larger, unseen systems ($H_8$, $H_{10}$ and $H_{12}$) without retraining -- demonstrating strong out-of-distribution generalization with respect to system size. When evaluating on structured and random configurations, and comparing against energies obtained with full classical optimization, our model reaches mean absolute energy errors $\mathcal{O}(10^2)$ and $\mathcal{O}(10)$ milli-Hartrees, respectively. Beyond energy estimation, the predicted orbitals serve as high-quality warm-start initializations that substantially reduce optimizer iterations to ground-state energy convergence. These results establish graph neural networks as an effective and scalable strategy for accelerating orbital optimization in hybrid quantum-classical workflows, directly reducing the classical pre-processing overhead that currently limits the practical deployment of variational quantum eigensolver on near-term quantum hardware. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2605.04174 [quant-ph] (or arXiv:2605.04174v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.04174 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Abhishek Dubey [view email] [v1] Tue, 5 May 2026 18:12:05 UTC (2,261 KB) Full-text links: Access Paper: View a PDF of the paper titled A Transferable Machine Learning Approach to Predict Optimized Orbitals for Electronic Structure Problems, by Lucas van der Horst and 5 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)