Exponentially-improved effective descriptions of physical bosonic systems

Quantum Physics [Submitted on 20 Apr 2026] Exponentially-improved effective descriptions of physical bosonic systems Varun Upreti, Nicolás Quesada, Ulysse Chabaud 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: 11 pages main text, 26 pages supplementary material and 1 figure 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 Submission history From: Varun Upreti [view email] [v1] Mon, 20 Apr 2026 18:20:13 UTC (1,837 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)