Lie-Algebraic Classical Simulation of Bosonic Systems Beyond Gaussian Dynamics

Quantum Physics arXiv:2608.17094 (quant-ph) [Submitted on 17 Aug 2026] Title:Lie-Algebraic Classical Simulation of Bosonic Systems Beyond Gaussian Dynamics Authors:Adelina Bärligea, Timothy Heightman, Jakob S. Kottmann, Antonio Acín View a PDF of the paper titled Lie-Algebraic Classical Simulation of Bosonic Systems Beyond Gaussian Dynamics, by Adelina B\"arligea and 3 other authors View PDF HTML (experimental) Abstract:Classical simulability is ultimately determined by both the dynamics of a quantum system and the observables being evaluated. Lie-algebraic simulation exploits the latter to make exact polynomial-time classical simulations by propagating observables through low-dimensional invariant operator spaces. However, its conventional formulation in terms of polynomial-dimensional dynamical Lie algebras does not directly accommodate bosonic systems as their algebras are neither compact nor semisimple. In this contribution, we overcome this limitation, making bosonic systems accessible to the Lie-algebraic programme of exact polynomial-time classical simulation. We prove that expectation values, fixed-order correlation functions, including multi-time correlators and out-of-time-ordered correlators, and gradients are efficiently computable whenever their operator modules have polynomial dimension. This recovers Gaussian quantum optics and extends it to non-Gaussian input states, while identifying exact polynomial regimes of interacting non-Gaussian dynamics including bounded-photon Kerr and pair-hopping Hamiltonians and nilpotent polynomial phase dynamics. We show that unlike in the finite-dimensional spin and fermionic setting treated previously, a finite-dimensional bosonic generator algebra alone does not guarantee finite observable dynamics. We further derive a controlled perturbative hierarchy for squeezing beyond exact sector confinement and confirm the predicted error orders numerically. We also evaluate operator spreading on interacting chains of up to $400$ modes and connect a topological doublon band with flux-reversed edge motion. These results provide a unified formalism for classifying, discovering, and systematically approximating tractable bosonic quantum dynamics with classical polynomial-time simulation. Comments: Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph) MSC classes: 81P68, 17B81, 81V80 Cite as: arXiv:2608.17094 [quant-ph] (or arXiv:2608.17094v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2608.17094 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Adelina Bärligea [view email] [v1] Mon, 17 Aug 2026 20:01:15 UTC (760 KB) Full-text links: Access Paper: View a PDF of the paper titled Lie-Algebraic Classical Simulation of Bosonic Systems Beyond Gaussian Dynamics, by Adelina B\"arligea and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-08 Change to browse by: math math-ph math.MP 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?)