Stopping Reliability in Adaptive Krylov-Shadow Quantum Fisher Information Estimation
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Quantum Physics arXiv:2605.14338 (quant-ph) [Submitted on 14 May 2026] Title:Stopping Reliability in Adaptive Krylov-Shadow Quantum Fisher Information Estimation Authors:Erjie Liu, Yangshuai Wang View a PDF of the paper titled Stopping Reliability in Adaptive Krylov-Shadow Quantum Fisher Information Estimation, by Erjie Liu and Yangshuai Wang View PDF HTML (experimental) Abstract:Adaptive quantum Fisher information (QFI) estimation requires a stopping rule that distinguishes accuracy from apparent numerical stability. For Krylov-shadow QFI estimators, finite Krylov order $K$ produces truncation bias, while finite sample budget $M$ produces finite-$M$ sampling-side error. We show that a width-only empirical stopping rule, based on interval width and local Krylov stability, can declare convergence at small $(K,M)$ even when the post hoc error exceeds the requested tolerance; we call this event a \emph{false stop}. The mechanism is a narrow empirical interval centered on a biased low-$K$ estimate. We give a two-component stopping analysis that separates the Krylov and sampling terms, and we implement a guarded rule that permits a success declaration only after minimum thresholds in $K$ and $M$ and a persistence condition are satisfied. On a five-level dephasing benchmark at $n=4$ qubits, the guarded rule suppresses the false success declarations produced by the width-only empirical rule, whose false-stop rates range from $0.16$ to $0.68$ across the tested noise levels. Under the main fixed resource limit, the guarded rule refuses to make success declarations rather than accepting biased low-$K$ estimates; a separate true-relative-tolerance sampling-budget sequence then shows that, after Krylov and sampling recalibration, the same decision principle can make success declarations without observed false stops. These results show that stopping reliability is a distinct design requirement for adaptive QFI estimation: sampling precision at fixed $K$ does not by itself establish that Krylov truncation bias is controlled. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2605.14338 [quant-ph] (or arXiv:2605.14338v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.14338 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Yangshuai Wang [view email] [v1] Thu, 14 May 2026 04:02:23 UTC (171 KB) Full-text links: Access Paper: View a PDF of the paper titled Stopping Reliability in Adaptive Krylov-Shadow Quantum Fisher Information Estimation, by Erjie Liu and Yangshuai WangView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 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?)