Blind Catalytic Quantum Error Correction: Target-State Estimation and Fidelity Recovery Without \textit{A Priori} Knowledge
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Quantum Physics arXiv:2604.11857 (quant-ph) [Submitted on 13 Apr 2026] Title:Blind Catalytic Quantum Error Correction: Target-State Estimation and Fidelity Recovery Without \textit{A Priori} Knowledge Authors:Hikaru Wakaura View a PDF of the paper titled Blind Catalytic Quantum Error Correction: Target-State Estimation and Fidelity Recovery Without \textit{A Priori} Knowledge, by Hikaru Wakaura View PDF HTML (experimental) Abstract:Catalytic quantum error correction (CQEC) recovers quantum states via catalytic covariant transformations but requires full knowledge of the target state. We introduce \emph{blind CQEC}, which estimates the target from the noisy output alone before catalytic recovery. Five estimation strategies are benchmarked across three noise models (dephasing, depolarizing, amplitude damping), four quantum algorithms ($d = 4$--$64$), Haar-random states up to $d = 256$, and mixed-state targets with variable purity. Key results: (i)~coherence maximization achieves $ F_{ rec } > 0.95$ for $d \leq 16$ without noise-model knowledge, matching the oracle to within $4\%$; (ii)~channel inversion is required at $d = 64$ ($ F_{ rec } = 0.905$); (iii)~estimation and recovery fidelities are linearly correlated ($r > 0.99$), identifying target estimation as the sole bottleneck; (iv)~an analytical crossover dimension $d^* \approx 25$--$40$ separates noise-model-free and noise-informed regimes, bridged by a hybrid interpolation strategy; (v)~copy scaling follows $1 - F(n) \sim n^{-\alpha}$ with $\alpha \in [0.4, 2.2]$, spanning the statistical averaging and denoising synergy limits. Standard linear inversion tomography fails as a CQEC target estimator, validating the need for decoherence-aware strategies. An end-to-end VQE demonstration for H$_2$ shows $3.4\times$ energy-error reduction with channel-inversion blind CQEC. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.11857 [quant-ph] (or arXiv:2604.11857v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.11857 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Hikaru Wakaura [view email] [v1] Mon, 13 Apr 2026 08:27:08 UTC (371 KB) Full-text links: Access Paper: View a PDF of the paper titled Blind Catalytic Quantum Error Correction: Target-State Estimation and Fidelity Recovery Without \textit{A Priori} Knowledge, by Hikaru WakauraView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 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?)