Obstructions to universality in globally controlled qubit graphs

Fuente: arXiv
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Main Authors: Gargiulo, Roberto, Menta, Roberto, Giovannetti, Vittorio, Zeier, Robert
Format: Preprint
Published: 2026
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author Gargiulo, Roberto
Menta, Roberto
Giovannetti, Vittorio
Zeier, Robert
author_facet Gargiulo, Roberto
Menta, Roberto
Giovannetti, Vittorio
Zeier, Robert
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2604_18699
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Obstructions to universality in globally controlled qubit graphs
Gargiulo, Roberto
Menta, Roberto
Giovannetti, Vittorio
Zeier, Robert
Quantum Physics
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.
title Obstructions to universality in globally controlled qubit graphs
topic Quantum Physics
url https://arxiv.org/abs/2604.18699