Measurement and reload costs in direct quantum simulation of nonlinear waves

Quantum Physics arXiv:2608.21647 (quant-ph) [Submitted on 21 Aug 2026] Title:Measurement and reload costs in direct quantum simulation of nonlinear waves Authors:Ziqing Guo, Viraj Dsouza, Alex Khan, Abhishek Chopra, Rut Lineswala, Ziwen Pan View a PDF of the paper titled Measurement and reload costs in direct quantum simulation of nonlinear waves, by Ziqing Guo and 5 other authors View PDF HTML (experimental) Abstract:Quantum processors encode an N-point field in log_2(N) qubits, which renders nonlinear wave equations an important application for quantum simulation. Nonlinear evolution, however, requires the field values themselves, and these are not directly accessible without quantum measurement. Existing algorithms circumvent this measurement through linear embeddings and state copies, thereby obscuring its cost within the truncation order, the auxiliary dimensions, and the state preparation. In order to expose this cost, a hybrid split-step solver is proposed in which the field is measured, updated classically, and reloaded at every step, with all shots and gates accounted for in a single cost-and-error model. Since the entire field is available at every step, a property unavailable to linear approximations in strongly nonlinear regimes, the design of the solver reduces to a budgeting problem over the timestep, the polynomial degree, and the shot count. The coherent kernels of the solver are validated on superconducting hardware. An identical structure and bottleneck govern the viscous Burgers' equation in one and two dimensions. Because every step reads the full field, the quantum cost per step, measured as circuit depth multiplied by measurement shots, exceeds the classical cost with increasing grid size. The framework consequently identifies a coherent, measurement-free nonlinear update as the quantitative target that any end-to-end advantage must meet. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2608.21647 [quant-ph] (or arXiv:2608.21647v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2608.21647 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Ziqing Guo [view email] [v1] Fri, 21 Aug 2026 21:36:39 UTC (2,775 KB) Full-text links: Access Paper: View a PDF of the paper titled Measurement and reload costs in direct quantum simulation of nonlinear waves, by Ziqing Guo and 5 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-08 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?)