Catalytic Coherence Amplification for Quantum State Recovery: Theory, Numerical Validation, and Comparison with Conventional Error Correction
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Quantum Physics arXiv:2603.25774 (quant-ph) [Submitted on 26 Mar 2026] Title:Catalytic Coherence Amplification for Quantum State Recovery: Theory, Numerical Validation, and Comparison with Conventional Error Correction Authors:Hikaru Wakaura View a PDF of the paper titled Catalytic Coherence Amplification for Quantum State Recovery: Theory, Numerical Validation, and Comparison with Conventional Error Correction, by Hikaru Wakaura View PDF HTML (experimental) Abstract:We present Catalytic Quantum Error Correction (CQEC), a quantum state recovery protocol based on the arbitrary amplification of coherence in catalytic covariant transformations. Unlike conventional quantum error correction, CQEC requires knowledge of the target state and multiple noisy copies, but operates without an error threshold: recovery succeeds whenever the coherent modes of the target state are contained within those of the noisy state (mode inclusion), regardless of the noise magnitude. A reusable catalyst state mediates the transformation and its reduced state is preserved exactly after each cycle (correlated catalysis). We validate CQEC numerically across four quantum algorithms -- qDRIFT, quantum Kolmogorov--Arnold networks, control-free phase estimation, and Regev factoring -- and a tree tensor network cryptographic protocol, under dephasing, depolarizing, and combined noise. In the asymptotic (infinite-copy) limit, CQEC recovers the known algorithmic output state from fidelity $F = 0.07$ to $F > 0.999$ across 200 configurations; at finite copy number $n$, the fidelity gap scales as $1 - F \leq O(1/\sqrt{n})$. We compare with Steane and surface codes under their respectively different operational assumptions. Our results establish coherence resource theory as a complementary foundation for quantum state recovery. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.25774 [quant-ph] (or arXiv:2603.25774v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.25774 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Hikaru Wakaura [view email] [v1] Thu, 26 Mar 2026 12:03:20 UTC (187 KB) Full-text links: Access Paper: View a PDF of the paper titled Catalytic Coherence Amplification for Quantum State Recovery: Theory, Numerical Validation, and Comparison with Conventional Error Correction, by Hikaru WakauraView PDFHTML (experimental)TeX 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?)