Universal purification dynamics of monitored Clifford circuits
This result simplifies the analysis of purification in quantum circuits, offering an exact, solvable model that avoids complex analytic continuations, while revealing unique signatures of Clifford dynamics that generic monitored circuits lack.
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Quantum Physics arXiv:2607.06683 (quant-ph) [Submitted on 7 Jul 2026] Title:Universal purification dynamics of monitored Clifford circuits Authors:Beatrice Magni, Federico Gerbino, Xhek Turkeshi, Andrea De Luca View a PDF of the paper titled Universal purification dynamics of monitored Clifford circuits, by Beatrice Magni and 3 other authors View PDF HTML (experimental) Abstract:Quantum circuits under sufficiently weak monitoring purify on a timescale $T_P$ exponentially long in the system size. This slowness underlies a universal purification dynamics, whose quantitative description has so far required the replica trick, with a delicate analytic continuation. We show that monitored Clifford circuits on $L$ qudits of prime dimension $q$ bypass this construction entirely: in the scaling limit at fixed $x = t/T_P(L)$, purification reduces to the Markovian decay of the density-matrix rank, an exactly solvable death process descending from infinity. We compute the full scaling functions in compact form: all Rényi entropies collapse onto a universal curve $\langle S(x) \rangle$. Exact stabilizer simulations at $q=2,3,5$ confirm the predictions, with no fitting parameter for the global model and $T_P$ as the only fitted scale for local brick-wall circuits. Also, the replica problem amounts to a tilted version of the same Markov process, in agreement with exact computations from the Clifford commutant. Finally, the quantization of the rank leaves two hallmarks that distinguish Clifford dynamics from generic monitored circuits: the entropy fluctuations saturate at short scaled times $x\to0$ to an $O(1)$ variance, instead of vanishing, and observables develop a temporal modulation periodic in $\log_q x$, which cannot be captured by the replica approach. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2607.06683 [quant-ph] (or arXiv:2607.06683v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2607.06683 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Federico Gerbino [view email] [v1] Tue, 7 Jul 2026 18:02:16 UTC (567 KB) Full-text links: Access Paper: View a PDF of the paper titled Universal purification dynamics of monitored Clifford circuits, by Beatrice Magni and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-07 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?)