Autonomous Hamiltonian certification and changepoint detection

Quantum Physics [Submitted on 27 Mar 2026] Autonomous Hamiltonian certification and changepoint detection Steven T. Flammia, Dmitrii Khitrin, Muzhou Ma, Jamie Sikora, Yu Tong, Alice Zheng Modern quantum devices require high-precision Hamiltonian dynamics, but environmental noise can cause calibrated Hamiltonian parameters to drift over time, necessitating expensive recalibration. Detecting when recalibration is needed is challenging, especially since the very gates required for sophisticated verification protocols may themselves be miscalibrated. While cloud quantum computing services implement heuristic routines for triggering recalibration, the fundamental limits of optimal recalibration are not yet known. We develop efficient Hamiltonian certification and changepoint detection protocols in the autonomous setting, where we cannot rely on an external noiseless device and use only single-qubit gates and measurements, making the protocols robust to the calibration issues for multi-qubit operations they aim to detect. For unknown n-qubit Hamiltonians H and H_0 with operator norm bounded by M, our certification protocol distinguishes whether \|H-H_0\|_F\geq\epsilon or \|H-H_0\|_F\leq O(\epsilon/\sqrt{n}) with sample complexity O(nM^2\ln(1/\delta)/\epsilon^2) and total evolution time O(nM\ln(1/\delta)/\epsilon^2). We achieve this by evolving random stabilizer product states and performing adaptive single-qubit measurements based on a classically simulable hypothesis state. Extending this to continuous monitoring, we develop an online changepoint detection algorithm using the CUSUM procedure that achieves a detection delay time bound of O(nM\ln(M\mathbb{E}_\infty[T])/\epsilon^2), matching the known asymptotically optimal scaling with respect to false alarm run time \mathbb{E}_\infty[T]. Our approach enables quantum devices to autonomously monitor their own calibration status without requiring ancillary systems, entangling operations, or a trusted reference device, offering a practical solution for robust quantum computing with contemporary noisy devices. Comments: 26 pages, 4 figures. Comments welcome Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.26655 [quant-ph]   (or arXiv:2603.26655v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.26655 Focus to learn more Submission history From: Alice Zheng [view email] [v1] Fri, 27 Mar 2026 17:54:45 UTC (510 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)