Efficient Quantum Simulation for Nonlinear Stochastic Differential Equations
Summarize this article with:
Quantum Physics arXiv:2603.12398 (quant-ph) [Submitted on 12 Mar 2026] Title:Efficient Quantum Simulation for Nonlinear Stochastic Differential Equations Authors:Xiangyu Li, Ahmet Burak Catli, Ho Kiat Lim, Matthew Pocrnic, Dong An, Jin-Peng Liu, Nathan Wiebe View a PDF of the paper titled Efficient Quantum Simulation for Nonlinear Stochastic Differential Equations, by Xiangyu Li and 6 other authors View PDF HTML (experimental) Abstract:Nonlinear stochastic differential equations (NSDEs) are a pillar of mathematical modeling for scientific and engineering applications. Accurate and efficient simulation of large-scale NSDEs is prohibitive on classical computers due to the large number of degrees of freedom, and it is challenging on quantum computers due to the linear and unitary nature of quantum mechanics. We develop a quantum algorithm to tackle nonlinear differential equations driven by the Ornstein-Uhlenbeck (OU) stochastic process. The query complexity of our algorithm scales logarithmically with the error tolerance and nearly quadratically with the simulation time. Our algorithmic framework comprises probabilistic Carleman linearization (PCL) to tackle nonlinearity coupled with stochasticity, and stochastic linear combination of Hamiltonian simulations (SLCHS) to simulate stochastic non-unitary dynamics. We obtain probabilistic exponential convergence for the Carleman linearization of Liu et al. [1], provided the NSDE is stable and reaches a steady state. We extend deterministic LCHS to stochastic linear differential equations, retaining near-optimal parameter scaling from An et al. [2] except for the nearly quadratic time scaling. This is achieved by using Monte Carlo integration for time discretization of both the stochastic inhomogeneous term in LCHS and the truncated Dyson series for each Hamiltonian simulation. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.12398 [quant-ph] (or arXiv:2603.12398v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.12398 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Xiangyu Li [view email] [v1] Thu, 12 Mar 2026 19:19:39 UTC (84 KB) Full-text links: Access Paper: View a PDF of the paper titled Efficient Quantum Simulation for Nonlinear Stochastic Differential Equations, by Xiangyu Li and 6 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 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?)