A Stable and General Quantum Fractional-Step Lattice Boltzmann Method for Incompressible Flows
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Quantum Physics arXiv:2603.00558 (quant-ph) [Submitted on 28 Feb 2026] Title:A Stable and General Quantum Fractional-Step Lattice Boltzmann Method for Incompressible Flows Authors:Yang Xiao, Liming Yang, Chang Shu, Yinjie Du View a PDF of the paper titled A Stable and General Quantum Fractional-Step Lattice Boltzmann Method for Incompressible Flows, by Yang Xiao and 3 other authors View PDF Abstract:Quantum computing shows substantial potential in accelerating simulations and alleviating memory bottlenecks in computational fluid dynamics (CFD), owing to its inherent properties of superposition and entanglement. The lattice Boltzmann method (LBM), being largely algebraic in nature, has inspired the development of various quantum LBMs. However, most existing approaches fix the relaxation time at $\tau$ = 1, thereby confining a given mesh resolution to simulations at a single Reynolds number. Although our earlier quantum lattice kinetic scheme (LKS) lifted this restriction, it suffers from instability at high Reynolds numbers. To address this challenge, we propose a quantum fractional-step LBM (FS-LBM). In this framework, the predictor step is implemented on a quantum circuit using the standard LBM formulation, while the corrector step is performed classically. The relaxation time is retained at $\tau$ = 1 to ensure seamless compatibility with existing quantum LBMs. Benchmark simulations of representative two- and three-dimensional incompressible isothermal and thermal flows demonstrate that the quantum FS-LBM achieves accuracy and convergence orders consistent with its classical counterpart, while significantly outperforming the quantum LKS in both precision and stability. Notably, this work presents the first quantum LBM simulation of three-dimensional incompressible thermal flows. Comments: Subjects: Quantum Physics (quant-ph); Fluid Dynamics (physics.flu-dyn) Cite as: arXiv:2603.00558 [quant-ph] (or arXiv:2603.00558v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.00558 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Yang Xiao [view email] [v1] Sat, 28 Feb 2026 09:16:45 UTC (20,202 KB) Full-text links: Access Paper: View a PDF of the paper titled A Stable and General Quantum Fractional-Step Lattice Boltzmann Method for Incompressible Flows, by Yang Xiao and 3 other authorsView PDF view license Current browse context: quant-ph new | recent | 2026-03 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?) 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?)