Exact quantum circuits for lattice Boltzmann realization of the Dirac equation

Quantum Physics arXiv:2608.06570 (quant-ph) [Submitted on 6 Aug 2026] Title:Exact quantum circuits for lattice Boltzmann realization of the Dirac equation Authors:Nilesh Sawant, Ethan Young, Kevin Griffin, Michael Martin View a PDF of the paper titled Exact quantum circuits for lattice Boltzmann realization of the Dirac equation, by Nilesh Sawant and 3 other authors View PDF HTML (experimental) Abstract:The quantum lattice Boltzmann (QLB) scheme of Succi and Dellar advances a four-component Dirac spinor on a lattice by a fixed sequence of local, exactly norm-preserving operations: a basis rotation, a collision, a streaming shift, and the inverse rotation. This unitarity is a structural property of the scheme, not an approximation, which suggests that a QLB time step should map onto a sequence of quantum gates. Here we make that mapping explicit. We give a gate-level construction of every operation of the three-dimensional Dirac QLB scheme: the fixed rotation gates, the collision gate, the streaming shift as a controlled increment on a position register, the position-dependent potential as a phase oracle, and periodic and reflecting (bounce-back) boundary conditions as unitary circuits. We then compose them into single-axis, two- and three-dimensional time steps. On a state-vector emulator the resulting circuits reproduce the classical QLB solver to machine precision (maximum density deviation between $3.7\times10^{-12}$ and $1.0\times10^{-17}$ across the one-, two-, and three-dimensional tests), so the circuits are the scheme rather than an approximation of it. The scope is narrow: we establish that the Succi-Dellar theory can be implemented on a (gate-model) quantum computer, and report the associated gate counts. We make no claim of computational advantage; state preparation, measurement, and asymptotic cost are discussed as open questions. All operators, circuits, tests, and figures are reproducible from the open-source quantumKineticMethods library. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph); Computational Physics (physics.comp-ph) Cite as: arXiv:2608.06570 [quant-ph] (or arXiv:2608.06570v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2608.06570 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Nilesh Sawant [view email] [v1] Thu, 6 Aug 2026 20:26:27 UTC (976 KB) Full-text links: Access Paper: View a PDF of the paper titled Exact quantum circuits for lattice Boltzmann realization of the Dirac equation, by Nilesh Sawant and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-08 Change to browse by: cond-mat cond-mat.stat-mech math math-ph math.MP physics physics.comp-ph 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?)