The Complexity of Dynamical Correlators: Operator Shadows and Exponential Learning Separations

Quantum Physics arXiv:2607.15493 (quant-ph) [Submitted on 16 Jul 2026] Title:The Complexity of Dynamical Correlators: Operator Shadows and Exponential Learning Separations Authors:Shao-Hen Chiew, Armando Angrisani, Zoe Holmes View a PDF of the paper titled The Complexity of Dynamical Correlators: Operator Shadows and Exponential Learning Separations, by Shao-Hen Chiew and 2 other authors View PDF Abstract:Quantum platforms can realize many-body dynamics beyond classical simulation yet complete readout remains intractable: the cost of extracting accessible information scales exponentially with system size. Classical shadows and Bell sampling offer scalable, multi-observable estimation from randomized or entanglement-assisted measurements. Here we aim to push these ideas beyond static snapshots to dynamical correlators, including out-of-time-ordered correlators (OTOCs) and two-point functions. In particular, we introduce the notion of the shadow of an operator, defined as the classical shadow of the vectorized time-evolved operator. Pauli operator-shadows enable simultaneous estimation of all local OTOCs, while Clifford operator-shadows enable efficient simultaneous estimation of all two-point correlators. Alternatively, Bell sampling allows one to simultaneously compute all diagonal OTOCs. We also prove information-theoretic lower bounds for learning OTOCs, fully characterizing their query complexities in many cases, and yielding exponential separations that formalize when the vectorized approach provides measurement-efficiency advantages. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2607.15493 [quant-ph] (or arXiv:2607.15493v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2607.15493 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Shao-Hen Chiew Mr [view email] [v1] Thu, 16 Jul 2026 22:44:25 UTC (625 KB) Full-text links: Access Paper: View a PDF of the paper titled The Complexity of Dynamical Correlators: Operator Shadows and Exponential Learning Separations, by Shao-Hen Chiew and 2 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-07 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?)