Information-Theoretic Constraints on Variational Quantum Optimization: Efficiency Transitions and the Dynamical Lie Algebra
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Quantum Physics arXiv:2512.14701 (quant-ph) [Submitted on 2 Dec 2025] Title:Information-Theoretic Constraints on Variational Quantum Optimization: Efficiency Transitions and the Dynamical Lie Algebra Authors:Jun Liang Tan View a PDF of the paper titled Information-Theoretic Constraints on Variational Quantum Optimization: Efficiency Transitions and the Dynamical Lie Algebra, by Jun Liang Tan View PDF HTML (experimental) Abstract:Variational quantum algorithms are the leading candidates for near-term quantum advantage, yet their scalability is limited by the ``Barren Plateau'' phenomenon. While traditionally attributed to geometric vanishing gradients, we propose an information-theoretic perspective. Using ancilla-mediated coherent feedback, we demonstrate an empirical constitutive relation $\Delta E \leq \eta I(S:A)$ linking work extraction to mutual information, with quantum entanglement providing a factor-of-2 advantage over classical Landauer bounds. By scaling the system size, we identify a distinct efficiency transition governed by the dimension of the Dynamical Lie Algebra. Systems with polynomial algebraic complexity exhibit sustained positive efficiency, whereas systems with exponential complexity undergo an ``efficiency collapse'' ($\eta \to 0$) at $N \approx 6$ qubits. These results suggest that the trainability boundary in variational algorithms correlates with information-theoretic limits of quantum feedback control. Comments: Subjects: Quantum Physics (quant-ph); Emerging Technologies (cs.ET) MSC classes: 81P68, 82B26, 68Q12 ACM classes: F.1.1; F.2.2; J.2 Cite as: arXiv:2512.14701 [quant-ph] (or arXiv:2512.14701v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.14701 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Jun Liang Tan [view email] [v1] Tue, 2 Dec 2025 16:09:18 UTC (329 KB) Full-text links: Access Paper: View a PDF of the paper titled Information-Theoretic Constraints on Variational Quantum Optimization: Efficiency Transitions and the Dynamical Lie Algebra, by Jun Liang TanView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-12 Change to browse by: cs cs.ET 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?)