Temporal Complexity Hierarchies in Solvable Quantum Many-Body Dynamics

Quantum Physics arXiv:2510.21927 (quant-ph) [Submitted on 24 Oct 2025] Title:Temporal Complexity Hierarchies in Solvable Quantum Many-Body Dynamics Authors:He-Ran Wang, Ilya Vilkoviskiy, Dmitry A. Abanin View a PDF of the paper titled Temporal Complexity Hierarchies in Solvable Quantum Many-Body Dynamics, by He-Ran Wang and 2 other authors View PDF HTML (experimental) Abstract:The influence matrix (IM) provides a powerful framework for characterizing nonequilibrium quantum many-body dynamics by encoding multitime correlations into tensor-network states. Understanding how its computational complexity relates to underlying dynamics is crucial for both theoretical insight and practical utility, yet remains largely unexplored despite a few case studies. Here, we address this question for a family of brickwork quantum circuits ranging from integrable to chaotic regimes. Using tools from geometric group theory, we identify three qualitatively distinct scalings of temporal entanglement entropy, establishing a hierarchy of computational resources required for accurate tensor-network representations of the IM for these models. We further analyze the memory structure of the IM and distinguish between classical and quantum temporal correlations. In particular, for certain examples, we identify effectively classical IMs that admit an efficient Monte Carlo algorithm for computing multitime correlations. In more generic settings without an explicit classical description of the IM, we introduce an operational measure of quantum memory with an experimental protocol, and discuss examples exhibiting long-time genuinely quantum correlations. Our results establish a new connection between quantum many-body dynamics and group theory, providing fresh insights into the complexity of the IM and its intricate connection to the physical characteristics of the dynamics. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Exactly Solvable and Integrable Systems (nlin.SI) Cite as: arXiv:2510.21927 [quant-ph] (or arXiv:2510.21927v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2510.21927 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Ilya Vilkoviskiy [view email] [v1] Fri, 24 Oct 2025 18:00:08 UTC (2,042 KB) Full-text links: Access Paper: View a PDF of the paper titled Temporal Complexity Hierarchies in Solvable Quantum Many-Body Dynamics, by He-Ran Wang and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-10 Change to browse by: cond-mat cond-mat.stat-mech nlin nlin.SI 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?)