Non-Abelian Geometric Phases in Triangular Structures And Universal SU(2) Control in Shape Space
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| author | Dai, J. Molochkov, A. Niemi, A. J. Westerholm, J. |
| author_facet | Dai, J. Molochkov, A. Niemi, A. J. Westerholm, J. |
| contents | We construct holonomic quantum gates for qubits that are encoded in the near-degenerate vibrational $E$-doublet of a deformable three-body system. Using Kendall's shape theory, we derive the Wilczek--Zee connection governing adiabatic transport within the $E$-manifold. We show that its restricted holonomy group is $\mathrm{SU}(2)$, implying universal single-qubit control by closed loops in shape space. We provide explicit loops implementing a $π/2$ phase gate and a Hadamard-type gate. For two-qubit operations, we outline how linked holonomic cycles in arrays generate a controlled Chern--Simons phase, enabling an entangling controlled-$X$ (CNOT) gate. We present a Ramsey/echo interferometric protocol that measures the Wilson loop trace of the Wilczek--Zee connection for a control cycle, providing a gauge-invariant signature of the non-Abelian holonomy. As a physically realizable demonstrator, we propose bond-length modulations of a Cs($6s$)--Cs($6s$)--Cs($nd_{3/2}$)
Rydberg trimer in optical tweezers and specify operating conditions that suppress leakage out of the $E$-manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24798 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-Abelian Geometric Phases in Triangular Structures And Universal SU(2) Control in Shape Space Dai, J. Molochkov, A. Niemi, A. J. Westerholm, J. Quantum Physics Other Condensed Matter We construct holonomic quantum gates for qubits that are encoded in the near-degenerate vibrational $E$-doublet of a deformable three-body system. Using Kendall's shape theory, we derive the Wilczek--Zee connection governing adiabatic transport within the $E$-manifold. We show that its restricted holonomy group is $\mathrm{SU}(2)$, implying universal single-qubit control by closed loops in shape space. We provide explicit loops implementing a $π/2$ phase gate and a Hadamard-type gate. For two-qubit operations, we outline how linked holonomic cycles in arrays generate a controlled Chern--Simons phase, enabling an entangling controlled-$X$ (CNOT) gate. We present a Ramsey/echo interferometric protocol that measures the Wilson loop trace of the Wilczek--Zee connection for a control cycle, providing a gauge-invariant signature of the non-Abelian holonomy. As a physically realizable demonstrator, we propose bond-length modulations of a Cs($6s$)--Cs($6s$)--Cs($nd_{3/2}$) Rydberg trimer in optical tweezers and specify operating conditions that suppress leakage out of the $E$-manifold. |
| title | Non-Abelian Geometric Phases in Triangular Structures And Universal SU(2) Control in Shape Space |
| topic | Quantum Physics Other Condensed Matter |
| url | https://arxiv.org/abs/2512.24798 |