Error-Correction Transitions in Finite-Depth Quantum Channels
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Quantum Physics arXiv:2603.20369 (quant-ph) [Submitted on 20 Mar 2026] Title:Error-Correction Transitions in Finite-Depth Quantum Channels Authors:Arman Sauliere, Guglielmo Lami, Pedro Ribeiro, Andrea De Luca, Jacopo De Nardis View a PDF of the paper titled Error-Correction Transitions in Finite-Depth Quantum Channels, by Arman Sauliere and 4 other authors View PDF Abstract:We study error correction type protocols in which a quantum channel encodes logical information into an enlarged Hilbert space. Specifically, we consider channels realized by one dimensional random noisy quantum circuits with spatially local interaction gates. We analyze both noise acting after the encoding and noise affecting the encoding circuit itself. Using the coherent information as a metric, we show that in both cases the infinite depth limit is governed by random matrix theory, which predicts a universal phase transition at a critical noise rate. This critical point separates an error correcting phase, in which encoded information is preserved, from a phase in which it is irretrievably lost. Going beyond the infinite depth limit, we characterize the systematic finite depth deviations from random matrix universality. In particular, we show that these deviations behave parametrically differently depending on whether the noise acts after the encoding or also affects the encoding itself. For noiseless encoders, the approach is exponential in circuit depth, although boundary effects can delay perfect encoding relative to the circuit design time. For noisy encoders, we find that the circuit fidelity effectively replaces the Hashing bound, and perfect encoding is approached polynomially with depth. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.20369 [quant-ph] (or arXiv:2603.20369v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.20369 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Arman Sauliere [view email] [v1] Fri, 20 Mar 2026 18:00:00 UTC (1,202 KB) Full-text links: Access Paper: View a PDF of the paper titled Error-Correction Transitions in Finite-Depth Quantum Channels, by Arman Sauliere and 4 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-03 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?)