Explicit Quantum Circuit Simulation of Nonlinear 1-Dimensional Fluid with Carleman-linearized Boltzmann Method
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Quantum Physics arXiv:2606.12770 (quant-ph) [Submitted on 11 Jun 2026] Title:Explicit Quantum Circuit Simulation of Nonlinear 1-Dimensional Fluid with Carleman-linearized Boltzmann Method Authors:Keita Kanno, Kazumasa Ueno, Hayato Higuchi, Morimasa Okamoto, Yuya Yoshizuru, Ryoya Ishimaru, Towa Takagi, Kentaro Sakamoto View a PDF of the paper titled Explicit Quantum Circuit Simulation of Nonlinear 1-Dimensional Fluid with Carleman-linearized Boltzmann Method, by Keita Kanno and 7 other authors View PDF Abstract:Quantum computation of fluid dynamics has attracted growing attention as a key application of fault-tolerant quantum computers anticipated in the coming decade, with lattice Boltzmann methods emerging as a particularly promising approach. Explicit and efficient elementary-gate-level circuit simulations, however, have so far been demonstrated only in the linear case. Here we include the leading nonlinearity through second-order Carleman linearization of the one-dimensional Boltzmann equation, and demonstrate, via explicit quantum-circuit simulation, the preparation of the final-time state using a Taylor-expansion-based ODE solver based on the quantum singular value transformation. With this construction, we analyze the gate and qubit complexities, which scale logarithmically with the grid size, the nonlinearity captured by the higher-order Carleman linearization, and the practical utility of higher-order expansions in the Taylor ODE solver. The construction provides a concrete baseline for computational cost reduction and further developments such as extensions to higher dimensions, complex geometries, and the extraction of physical quantities, towards industrially useful quantum CFD. Comments: Subjects: Quantum Physics (quant-ph); Fluid Dynamics (physics.flu-dyn) Cite as: arXiv:2606.12770 [quant-ph] (or arXiv:2606.12770v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.12770 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Keita Kanno [view email] [v1] Thu, 11 Jun 2026 00:25:13 UTC (275 KB) Full-text links: Access Paper: View a PDF of the paper titled Explicit Quantum Circuit Simulation of Nonlinear 1-Dimensional Fluid with Carleman-linearized Boltzmann Method, by Keita Kanno and 7 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-06 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?)