Sound and Efficient Certification of High-Quality Qubit Operations: Theory and Experiment

Quantum Physics arXiv:2608.17005 (quant-ph) [Submitted on 17 Aug 2026] Title:Sound and Efficient Certification of High-Quality Qubit Operations: Theory and Experiment Authors:Nikolai Miklin, Jan Nöller, José Martínez, Lucas B. Vieira, Ulrich Poschinger, Ferdinand Schmidt-Kaler, Mariami Gachechiladze View a PDF of the paper titled Sound and Efficient Certification of High-Quality Qubit Operations: Theory and Experiment, by Nikolai Miklin and 6 other authors View PDF HTML (experimental) Abstract:Can a high-quality quantum gate be certified when uncharacterized state-preparation and measurement errors are dominant? Can this be achieved with low experimental overhead? Here, we introduce a sound black-box certification protocol for a single-qubit gate based on a small set of fixed, deterministic sequences. From the data, the protocol derives finite-sample bounds on the gate's rotation eigenvalue, a gauge-invariant property. Its phase reveals the accuracy of the rotation angle, while its modulus quantifies the loss of coherence under repeated gate applications. We implement the protocol on a $^{40}\mathrm{Ca}^{+}$ trapped-ion processor and certify the $\sqrt{\mathrm{X}}$-gate rotation eigenvalue using $22\,000$ circuit executions, and demonstrate the robustness of certification to state-preparation and measurement errors by deliberately degrading the readout. Finally, we prove that these spectral constraints imply, up to a physically meaningful unitary change of basis, a rigorous average gate-fidelity lower bound for every time-independent qubit model compatible with the data. In both readout settings, the spectral bounds yield the same fidelity certificate of $99.94(3)\%$ with $99\%$ confidence. Our results establish a new standard for quantum-gate certification by combining soundness and experimental efficiency without requiring trusted reference operations, randomized circuits, or model fitting. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2608.17005 [quant-ph] (or arXiv:2608.17005v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2608.17005 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Mariami Gachechiladze [view email] [v1] Mon, 17 Aug 2026 18:03:00 UTC (1,197 KB) Full-text links: Access Paper: View a PDF of the paper titled Sound and Efficient Certification of High-Quality Qubit Operations: Theory and Experiment, by Nikolai Miklin and 6 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-08 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?)