Obstructions to universality in globally controlled qubit graphs

Quantum Physics [Submitted on 20 Apr 2026] Obstructions to universality in globally controlled qubit graphs Roberto Gargiulo, Roberto Menta, Vittorio Giovannetti, Robert Zeier Global control offers a promising route to scalable quantum computing. A recent conjecture by Hu et al. (arXiv:2508.19075) proposes that any connected qubit graph equipped with global Ising-type interactions and tunable global transverse fields achieves universality if and only if an additional control field breaks every non-trivial automorphism of the underlying graph. We disprove this conjecture by exhibiting explicit seven- and nine-qubit counterexamples: connected graphs with trivial automorphism group for which the generated Lie algebra is nonetheless not universal. Our analysis reveals that graph automorphisms capture only part of the Hamiltonian symmetry structure: there exist hidden symmetries beyond the automorphism group of the graph. Additionally, in the case of non-trivial automorphism group, we find control terms which break the graph symmetries but are still not universal. These findings sharpen the characterization of universality for globally controlled quantum systems. Comments: 5 pages, 5 figures. Comments are welcome! Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.18699 [quant-ph]   (or arXiv:2604.18699v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.18699 Focus to learn more Submission history From: Roberto Menta [view email] [v1] Mon, 20 Apr 2026 18:00:58 UTC (240 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?)