Quantum computing of nonlinear reacting flows via the probability density function method

Quantum Physics arXiv:2512.07918 (quant-ph) [Submitted on 8 Dec 2025] Title:Quantum computing of nonlinear reacting flows via the probability density function method Authors:Jizhi Zhang, Ziang Yang, Zhaoyuan Meng, Zhen Lu, Yue Yang View a PDF of the paper titled Quantum computing of nonlinear reacting flows via the probability density function method, by Jizhi Zhang and 4 other authors View PDF HTML (experimental) Abstract:Quantum computing offers the promise of speedups for scientific computations, but its application to reacting flows is hindered by nonlinear source terms and the challenges of time-dependent simulations. We present a quantum framework to address these issues. We employ a probability density function (PDF) formulation to transform the nonlinear reacting-flow governing equations into high-dimensional linear ones. The entire temporal evolution is then solved as a single large linear system using the history state method, which avoids the measurement bottleneck of conventional time-marching schemes and fully leverages the advantages of quantum linear system algorithms. To extract the quantity of interest from the resulting quantum state, we develop an efficient algorithm to measure the statistical moments of the PDF, bypassing the need for costly full-state tomography. A computational complexity analysis indicates the potential for a near-exponential speedup over classical algorithms. We validate the framework by simulating a perfectly stirred reactor, demonstrating its capability to capture the PDF evolution and statistics of a nonlinear reactive system. This work establishes a pathway for applying quantum computing to nonlinear reacting flows. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2512.07918 [quant-ph] (or arXiv:2512.07918v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.07918 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Zhen Lu [view email] [v1] Mon, 8 Dec 2025 14:19:16 UTC (948 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum computing of nonlinear reacting flows via the probability density function method, by Jizhi Zhang and 4 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-12 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?)