Breaking the Curse of Dimensionality in Quantum PDE Solvers via Gevrey Regularity

Quantum Physics arXiv:2608.07893 (quant-ph) [Submitted on 8 Aug 2026] Title:Breaking the Curse of Dimensionality in Quantum PDE Solvers via Gevrey Regularity Authors:Pooya Ronagh, Mariia Sobchuk, Xiaoran Li, Arsalan Motamedi, Grecia Castelazo, Ala Shayeghi View a PDF of the paper titled Breaking the Curse of Dimensionality in Quantum PDE Solvers via Gevrey Regularity, by Pooya Ronagh and 5 other authors View PDF HTML (experimental) Abstract:We connect different degrees of smoothness of real-valued periodic functions to the cost of preparing their high-precision Fourier-basis amplitude encodings as quantum states. Our central observation is that the Gevrey hierarchy, which stratifies the space between smooth and analytic functions, provides a natural class for high-precision quantum algorithms. We then specialize to solving general linear partial differential equations (PDEs), showing how our Fourier methods do so efficiently at varying target precisions on a quantum computer. This also demonstrates how our framework enables passage from query-complexity results to explicit elementary gate counts. As an application, we introduce a hierarchy of many-body quantum simulation pipelines that harness these high-precision algorithms to probe the linear response of atomistic systems in first quantization. Each level of the hierarchy unlocks a further polynomial-degree quantum speedup, yielding a gradual improvement in simulation efficiency as quantum computers scale. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2608.07893 [quant-ph] (or arXiv:2608.07893v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2608.07893 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Pooya Ronagh [view email] [v1] Sat, 8 Aug 2026 03:40:25 UTC (59 KB) Full-text links: Access Paper: View a PDF of the paper titled Breaking the Curse of Dimensionality in Quantum PDE Solvers via Gevrey Regularity, by Pooya Ronagh and 5 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-08 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?)