Exponentially-improved effective descriptions of physical bosonic systems
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Quantum Physics arXiv:2604.18720 (quant-ph) [Submitted on 20 Apr 2026] Title:Exponentially-improved effective descriptions of physical bosonic systems Authors:Varun Upreti, Nicolás Quesada, Ulysse Chabaud View a PDF of the paper titled Exponentially-improved effective descriptions of physical bosonic systems, by Varun Upreti and Nicol\'as Quesada and Ulysse Chabaud View PDF HTML (experimental) Abstract:The effective description of a bosonic quantum system identifies the minimum finite dimension required to capture its essential dynamics. This effective dimension plays an important role in the complexity of classical and quantum algorithms for learning and simulating bosonic systems. While generic bosonic states require a dimension scaling as $1/\epsilon^2$ for a precision of approximation $\epsilon$, here we identify a natural energy condition which allows us to improve this scaling exponentially to $\log(1/\epsilon)$. We then prove that most bosonic quantum states satisfy this condition, and in particular those produced by combining Gaussian dynamics with generic energy-preserving dynamics, which include the output states of universal bosonic quantum circuits. We apply this finding to enhance learning algorithms for bosonic quantum states and we further obtain new classical simulation algorithms for a large class of bosonic systems. Finally, using efficient decompositions of Kerr gates as sums of Gaussian gates, we significantly refine these classical simulation algorithms for universal bosonic quantum circuits. Our results demonstrate that physical bosonic systems are significantly more well-behaved than previously assumed, allowing for efficient descriptions even at high precision. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.18720 [quant-ph] (or arXiv:2604.18720v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.18720 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Varun Upreti [view email] [v1] Mon, 20 Apr 2026 18:20:13 UTC (1,837 KB) Full-text links: Access Paper: View a PDF of the paper titled Exponentially-improved effective descriptions of physical bosonic systems, by Varun Upreti and Nicol\'as Quesada and Ulysse ChabaudView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 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?)