Universal Robust Quantum Gates via Doubly Geometric Control

Quantum Physics [Submitted on 3 Apr 2026] Universal Robust Quantum Gates via Doubly Geometric Control Hai Xu, Tao Chen, Junkai Zeng, Xiu-Hao Deng, Fang Gao, Xin Wang, Zheng-Yuan Xue, Chengxian Zhang Geometric quantum computation offers a potential route to fault-tolerant quantum information processing by exploiting the global nature of geometric phases. However, achieving controlled high-order suppression of multiple error sources remains a long-standing limitation, particularly in realistic large-scale circuits with complex noise environments. This limitation is largely due to the absence of a general framework that directly characterizes error accumulation and enables systematic improvement. Here we establish such a framework for universal doubly geometric gates by embedding target operations into a hierarchy of level-n identity constructions. This approach enables direct quantification of error accumulation while removing structural constraints inherent in previous schemes. We analytically show that the defining conditions lead to simultaneous fourth-order suppression of control errors, with a systematic extension to sixth-order suppression via higher-level constructions. Our results establish doubly geometric control as a general and scalable route toward high-order robust quantum gates, with potential implications for fault-tolerant quantum information processing. Comments: 6 pages, 3 figures Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.02962 [quant-ph]   (or arXiv:2604.02962v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.02962 Focus to learn more Submission history From: Chengxian Zhang [view email] [v1] Fri, 3 Apr 2026 10:53:26 UTC (1,041 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 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?)