Reconstructing fluid velocity fields from sparse sensors using a variational quantum algorithm

Quantum Physics arXiv:2609.09268 (quant-ph) [Submitted on 8 Sep 2026] Title:Reconstructing fluid velocity fields from sparse sensors using a variational quantum algorithm Authors:Nhat-Quang Nguyen, Mohammad Mehedi Hasan Akash, Kourosh Shoele, Yanzhu Chen, Huixuan Wu View a PDF of the paper titled Reconstructing fluid velocity fields from sparse sensors using a variational quantum algorithm, by Nhat-Quang Nguyen and 4 other authors View PDF HTML (experimental) Abstract:Reconstructing fields governed by nonlinear partial differential equations (PDEs) from sparse measurements is a challenging task because the governing equations are strongly nonlinear and observations are available at only a few locations. Fluid velocity fields are a representative case. In this paper, we propose a variational quantum algorithm that reconstructs the solution over the entire spacetime domain at once. Rather than marching in time, the method encodes the full discrete spacetime solution in a single variational quantum state, so that all time points are optimized jointly. The cost function combines a sparse-measurement mismatch term with a physics-informed PDE violation term, letting data and the governing equation constrain the solution simultaneously. We demonstrate the method on the one-dimensional Burgers and Kuramoto--Sivashinsky equations using numerical simulations. The results suggest that variational quantum algorithms with a spacetime encoding scheme offer a compact framework for reconstructing nonlinear PDE dynamics. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2609.09268 [quant-ph] (or arXiv:2609.09268v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.09268 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Yanzhu Chen [view email] [v1] Tue, 8 Sep 2026 18:00:00 UTC (467 KB) Full-text links: Access Paper: View a PDF of the paper titled Reconstructing fluid velocity fields from sparse sensors using a variational quantum algorithm, by Nhat-Quang Nguyen and 4 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?)