Efficient Treatment of Non-Linearity in Quantum Computational Fluid Dynamics Using Hybrid Tensor Networks

Quantum Physics arXiv:2608.24150 (quant-ph) [Submitted on 25 Aug 2026] Title:Efficient Treatment of Non-Linearity in Quantum Computational Fluid Dynamics Using Hybrid Tensor Networks Authors:Pia Siegl, Nis-Luca van Hülst, Maximilian Mandelt Buxadé, Tomohiro Hashizume, Dieter Jaksch View a PDF of the paper titled Efficient Treatment of Non-Linearity in Quantum Computational Fluid Dynamics Using Hybrid Tensor Networks, by Pia Siegl and Nis-Luca van H\"ulst and Maximilian Mandelt Buxad\'e and Tomohiro Hashizume and Dieter Jaksch View PDF HTML (experimental) Abstract:Nonlinear terms present a fundamental challenge for quantum computational fluid dynamics, as their implementation on inherently linear quantum hardware typically requires resource-intensive workarounds that limit scalability to large-scale simulations. We present a hybrid quantum-classical tensor network algorithm that addresses this bottleneck by combining variational time-stepping with quantum tensor programming to efficiently compile operators and time-dependent fields into quantum circuits. Within a probabilistic framework, we replace prior state-based nonlinear implementations with tensor-based block encodings, stabilizing success probabilities that otherwise decay exponentially with system size. Benchmarking on turbulent flow fields demonstrates that the algorithm maintains high success probabilities and moderate measurement overhead across increasing Reynolds numbers and grid resolutions. Compared to fully classical tensor network solvers, our hybrid approach yields substantial reductions in both memory footprint and computational cost, establishing a scalable pathway toward practical quantum advantage in scale-resolving CFD simulations. Comments: Subjects: Quantum Physics (quant-ph); Fluid Dynamics (physics.flu-dyn) Cite as: arXiv:2608.24150 [quant-ph] (or arXiv:2608.24150v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2608.24150 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Pia Siegl [view email] [v1] Tue, 25 Aug 2026 07:13:00 UTC (280 KB) Full-text links: Access Paper: View a PDF of the paper titled Efficient Treatment of Non-Linearity in Quantum Computational Fluid Dynamics Using Hybrid Tensor Networks, by Pia Siegl and Nis-Luca van H\"ulst and Maximilian Mandelt Buxad\'e and Tomohiro Hashizume and Dieter JakschView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-08 Change to browse by: physics physics.flu-dyn 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?)