Balancing Expressivity and Overfitting in Quantum Gaussian Process Regression

Quantum Physics arXiv:2609.09407 (quant-ph) [Submitted on 8 Sep 2026] Title:Balancing Expressivity and Overfitting in Quantum Gaussian Process Regression Authors:Saasha Joshi, Udson C. Mendes, Luke C. G. Govia View a PDF of the paper titled Balancing Expressivity and Overfitting in Quantum Gaussian Process Regression, by Saasha Joshi and 2 other authors View PDF HTML (experimental) Abstract:Active learning is a paradigm of machine learning that can be utilized to model expensive black-box functions by training a surrogate model from actively queried training points. The performance of this framework depends heavily on the choice of the surrogate model. When the surrogate is Gaussian Process Regression (GPR), its performance is largely determined by the expressivity of the underlying kernel. In this work, we investigate the peculiarities of using a quantum kernel to change the computational dynamics of active learning with GPR, focusing on the sensitivity to regularization by hyperparameter tuning. While generic, unstructured kernels suffer from exponential concentration at large scale, we empirically demonstrate that even at small scale overfitting can collapse GPR performance. Kernel regularization can be used to counteract this effect, but due to the smoothness of the quantum fidelity kernel, regularization must be carefully chosen to balance expressivity and overfitting. Our qualitative results transfer to the practical application of restricted quantum kernels designed to avoid exponential concentration and also present the kinds of noise that may be valuable to kernel training in near-term quantum devices. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2609.09407 [quant-ph] (or arXiv:2609.09407v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.09407 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Saasha Joshi [view email] [v1] Tue, 8 Sep 2026 20:01:22 UTC (334 KB) Full-text links: Access Paper: View a PDF of the paper titled Balancing Expressivity and Overfitting in Quantum Gaussian Process Regression, by Saasha Joshi and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 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?)