Lazy training of quantum physics informed neural networks

Quantum Physics arXiv:2609.19239 (quant-ph) [Submitted on 16 Sep 2026] Title:Lazy training of quantum physics informed neural networks Authors:Anderson Melchor Hernandez, Giacomo De Palma View a PDF of the paper titled Lazy training of quantum physics informed neural networks, by Anderson Melchor Hernandez and Giacomo De Palma View PDF HTML (experimental) Abstract:We study the gradient-flow training dynamics of quantum physics-informed neural networks (QPINNs) for the solution of second-order elliptic partial differential equations with Dirichlet boundary conditions. We consider parameterized quantum circuits as function approximators and analyze their overparameterized regime through the lens of the neural tangent kernel (NTK). Our contribution is a nonasymptotic lazy-training theory for QPINNs and their variational formulation: we prove that, for sufficiently large circuit width, the nonlinear gradient flow is quantitatively approximated by a linearized NTK model, with explicit bounds depending on the number of qubits, circuit depth, circuit light-cone geometry, and the dimension of the domain of the solution to the PDE. Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph); Probability (math.PR) MSC classes: 81P45, 49Q22, 60F05 Cite as: arXiv:2609.19239 [quant-ph] (or arXiv:2609.19239v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.19239 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Anderson Melchor Hernandez [view email] [v1] Wed, 16 Sep 2026 17:12:54 UTC (62 KB) Full-text links: Access Paper: View a PDF of the paper titled Lazy training of quantum physics informed neural networks, by Anderson Melchor Hernandez and Giacomo De PalmaView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 Change to browse by: math math-ph math.MP math.PR 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?)