Resource-efficient quantum simulation of transport phenomena via Hamiltonian embedding
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Quantum Physics arXiv:2602.03099 (quant-ph) [Submitted on 3 Feb 2026] Title:Resource-efficient quantum simulation of transport phenomena via Hamiltonian embedding Authors:Joseph Li, Gengzhi Yang, Jiaqi Leng, Xiaodi Wu View a PDF of the paper titled Resource-efficient quantum simulation of transport phenomena via Hamiltonian embedding, by Joseph Li and 3 other authors View PDF HTML (experimental) Abstract:Transport phenomena play a key role in a variety of application domains, and efficient simulation of these dynamics remains an outstanding challenge. While quantum computers offer potential for significant speedups, existing algorithms either lack rigorous theoretical guarantees or demand substantial quantum resources, preventing scalable and efficient validation on realistic quantum hardware. To address this gap, we develop a comprehensive framework for simulating classes of transport equations, offering both rigorous theoretical guarantees -- including exponential speedups in specific cases -- and a systematic, hardware-efficient implementation. Central to our approach is the Hamiltonian embedding technique, a white-box approach for end-to-end simulation of sparse Hamiltonians that avoids abstract query models and retains near-optimal asymptotic complexity. Empirical resource estimates indicate that our approach can yield an order-of-magnitude (e.g., $42\times$) reduction in circuit depth given favorable problem structures. We then apply our framework to solve linear and nonlinear transport PDEs, including the first experimental demonstration of a 2D advection equation on a trapped-ion quantum computer. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2602.03099 [quant-ph] (or arXiv:2602.03099v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.03099 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Joseph Li [view email] [v1] Tue, 3 Feb 2026 04:44:10 UTC (3,646 KB) Full-text links: Access Paper: View a PDF of the paper titled Resource-efficient quantum simulation of transport phenomena via Hamiltonian embedding, by Joseph Li and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-02 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?)