A quantum advection-diffusion solver using the quantum singular value transform

Quantum Physics arXiv:2512.22163 (quant-ph) [Submitted on 16 Dec 2025] Title:A quantum advection-diffusion solver using the quantum singular value transform Authors:Gard Olav Helle, Tommaso Benacchio, Anna Bomme Ousager, Jørgen Ellegaard Andersen View a PDF of the paper titled A quantum advection-diffusion solver using the quantum singular value transform, by Gard Olav Helle and Tommaso Benacchio and Anna Bomme Ousager and J{\o}rgen Ellegaard Andersen View PDF Abstract:We present a quantum algorithm for the simulation of the linear advection-diffusion equation based on block encodings of high order finite-difference operators and the quantum singular value transform. Our complexity analysis shows that the higher order methods significantly reduce the number of gates and qubits required to reach a given accuracy. The theoretical results are supported by numerical simulations of one- and two-dimensional benchmarks. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2512.22163 [quant-ph] (or arXiv:2512.22163v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.22163 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Tommaso Benacchio [view email] [v1] Tue, 16 Dec 2025 19:06:27 UTC (541 KB) Full-text links: Access Paper: View a PDF of the paper titled A quantum advection-diffusion solver using the quantum singular value transform, by Gard Olav Helle and Tommaso Benacchio and Anna Bomme Ousager and J{\o}rgen Ellegaard AndersenView PDFTeX Source view license Current browse context: quant-ph new | recent | 2025-12 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)