Estimating Green's functions with a robust quantum Arnoldi method
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Quantum Physics arXiv:2605.22920 (quant-ph) [Submitted on 21 May 2026] Title:Estimating Green's functions with a robust quantum Arnoldi method Authors:Jacob S. Nelson, Andrew B. Baczewski View a PDF of the paper titled Estimating Green's functions with a robust quantum Arnoldi method, by Jacob S. Nelson and Andrew B. Baczewski View PDF HTML (experimental) Abstract:Many applications of Green's functions (GFs) require their evaluation over intervals or at multiple points, motivating quantum algorithms that return an efficiently computable functional representation rather than mere point estimates. We introduce a robust quantum Arnoldi method (ROQAM) that achieves this goal. Its robustness is derived from formulation in terms of orthogonal polynomials, which preserves the upper-Hessenberg structure of the projected matrices despite finite-precision estimation. We also show that as the iteration depth increases, the precision required for matrix-element estimation can be reduced. Resource estimates for the spectral function of a quantum impurity model indicate that ROQAM outperforms pointwise estimation via quantum singular value transformation by multiple orders of magnitude. Finally, we show that the ROQAM can be used to estimate GFs at nonzero temperatures using only a single Krylov subspace. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2605.22920 [quant-ph] (or arXiv:2605.22920v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.22920 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Jacob Nelson [view email] [v1] Thu, 21 May 2026 18:00:41 UTC (1,108 KB) Full-text links: Access Paper: View a PDF of the paper titled Estimating Green's functions with a robust quantum Arnoldi method, by Jacob S. Nelson and Andrew B. BaczewskiView 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?)