Measurement-Efficient Variational Quantum Linear Solver for Carleman-Linearized Nonlinear Dynamics
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Quantum Physics arXiv:2605.15366 (quant-ph) [Submitted on 14 May 2026] Title:Measurement-Efficient Variational Quantum Linear Solver for Carleman-Linearized Nonlinear Dynamics Authors:Yunya Liu, Pai Wang View a PDF of the paper titled Measurement-Efficient Variational Quantum Linear Solver for Carleman-Linearized Nonlinear Dynamics, by Yunya Liu and Pai Wang View PDF HTML (experimental) Abstract:We present hybrid quantum-classical pipelines for solving the Duffing equation that leverage Carleman linearization and the Variational Quantum Linear Solver (VQLS). First, we demonstrate that Carleman linearization accurately approximates the weakly nonlinear Duffing equation, with errors diminishing as the truncation order increases. Next, across IBM and Xanadu platforms, we deploy VQLS with symmetry-grouped Hadamard Test evaluations under both global and local cost formulations, compare distinct Hermitianization within a common cost framework, and benchmark hardware-efficient ansatz architectures under a fixed Hermitianization. Across block-banded test cases, each method achieves near-unity fidelity and vanishing relative residuals. These results show that topology-agnostic ansatz, optimized Hermitianization, and efficient cost formulation enable VQLS to recover quantum states proportional to classical solutions for Carleman-structured systems, providing a portable recipe for quantum-in-the-loop simulation of nonlinear dynamics. Subjects: Quantum Physics (quant-ph); Computational Physics (physics.comp-ph) Cite as: arXiv:2605.15366 [quant-ph] (or arXiv:2605.15366v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.15366 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Yunya Liu [view email] [v1] Thu, 14 May 2026 19:45:27 UTC (8,717 KB) Full-text links: Access Paper: View a PDF of the paper titled Measurement-Efficient Variational Quantum Linear Solver for Carleman-Linearized Nonlinear Dynamics, by Yunya Liu and Pai WangView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 Change to browse by: 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?)