Theory of Magic Phase Transitions in Encoding-Decoding Circuits
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Quantum Physics arXiv:2603.00235 (quant-ph) [Submitted on 27 Feb 2026] Title:Theory of Magic Phase Transitions in Encoding-Decoding Circuits Authors:Piotr Sierant, Xhek Turkeshi View a PDF of the paper titled Theory of Magic Phase Transitions in Encoding-Decoding Circuits, by Piotr Sierant and 1 other authors View PDF HTML (experimental) Abstract:Quantum magic resources, or nonstabilizerness, are a central ingredient for universal quantum computation. In noisy many-body systems, the interplay between these resources and errors leads to sharp magic phase transitions. However, the microscopic mechanism behind these critical phenomena is still an open question, especially since early empirical evidence showed conflicting results regarding their universality classes. In this work, we provide a comprehensive picture of magic phase transitions for the class of encoding-decoding quantum circuits to resolve these ambiguities. We analytically show that the behavior of magic resources is fundamentally dictated by the chosen measurement protocol. When we fix, or post-select, the class of measurement syndromes, the magic transition inherits the universal features of the error-resilience phase transition in the circuits. Interestingly, this clean transition survives even for fully random Haar encoders showing that it is a consequence of initial's state retrieval, and not an artifact of the Clifford encoders. On the other hand, if we consider realistic Born-rule sampling, the intrinsic statistical fluctuations of a given syndrome measurement act as a relevant perturbation. This brings in strong finite-size drifts and an apparent multifractality, which end up altering the critical behavior of the system. We reveal that magic phase transitions are actually direct manifestations of error-resilience thresholds, rather than independent critical phenomena, reconciling conflicting observations from the earlier literature. Ultimately, our framework clarifies how the quantum computational power can survive, or be irreversibly destroyed, due to the competition between scrambling, measurements, and errors. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2603.00235 [quant-ph] (or arXiv:2603.00235v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.00235 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Piotr Sierant [view email] [v1] Fri, 27 Feb 2026 19:00:03 UTC (2,816 KB) Full-text links: Access Paper: View a PDF of the paper titled Theory of Magic Phase Transitions in Encoding-Decoding Circuits, by Piotr Sierant and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 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?) 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?)