Noise-induced Simulability Transition from Operator Scrambling
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Quantum Physics arXiv:2605.18943 (quant-ph) [Submitted on 18 May 2026] Title:Noise-induced Simulability Transition from Operator Scrambling Authors:Neil Dowling, Xhek Turkeshi, Jacopo De Nardis, Guglielmo Lami View a PDF of the paper titled Noise-induced Simulability Transition from Operator Scrambling, by Neil Dowling and Xhek Turkeshi and Jacopo De Nardis and Guglielmo Lami View PDF Abstract:The complexity of simulating quantum many-body dynamics, or quantum computations, in the Heisenberg picture is governed by the scrambling of initially simple operators into superpositions of exponentially many Pauli strings. The corresponding expansion coefficients define the Pauli spectrum, whose structure controls the performance of classical algorithms based on truncating Pauli expansions. Here we determine the finite-depth Pauli spectrum of random quantum circuits, both in the noiseless case and in the presence of local noise, through its moments, given by the operator stabilizer Rényi entropies. In noiseless circuits, we uncover a hierarchy in the approach to the fully scrambled regime: low moments equilibrate at relatively short depths, while higher moments, which are sensitive to rare, large-amplitude Pauli coefficients, require parametrically larger depths. In noisy circuits, scrambling competes with an effective suppression of operator spreading. Above a critical error per cycle $\gamma_c N=\mathcal{O}(1)$, the operator fails to reach the fully scrambled distribution and remains supported on an atypically sparse subset of Pauli strings. Conversely, below this scale, we rigorously show that classical simulation remains exponentially hard, demonstrating that finite noise does not automatically imply classical simulability. The resulting noise-induced transition in operator complexity therefore delineates the boundary between intrinsically hard quantum dynamics and those that remain classically accessible. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2605.18943 [quant-ph] (or arXiv:2605.18943v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.18943 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Neil Dowling [view email] [v1] Mon, 18 May 2026 18:00:00 UTC (4,662 KB) Full-text links: Access Paper: View a PDF of the paper titled Noise-induced Simulability Transition from Operator Scrambling, by Neil Dowling and Xhek Turkeshi and Jacopo De Nardis and Guglielmo LamiView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-05 Change to browse by: cond-mat cond-mat.stat-mech 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?)