Experimental demonstration of a brachistochrone nonadiabatic holonomic single-qubit gate scheme in a trapped ion
Phys. Rev. A 114, 022472 – Published 31 August, 2026
DOI: https://doi.org/10.1103/n1wm-93dv
Abstract
Nonadiabatic holonomic quantum computation (NHQC) offers intrinsic resilience to certain control imperfections. However, conventional nonadiabatic holonomic protocols are constrained by the fixed-pulse-area condition, which limits flexibility and prolongs duration of small-angle gates. Here we experimentally demonstrate a brachistochrone nonadiabatic holonomic single-qubit gate scheme in a trapped ion and realize the construction of the gate under the conventional NHQC, brachistochrone NHQC (BNHQC), and composite BNHQC (CBNHQC) protocols. By characterizing the performance of the gate in the presence of dissipation, Rabi-frequency errors and detuning errors, we show that BNHQC and CBNHQC outperform conventional NHQC, and BNHQC can offer a favorable balance between operation speed and robustness. It further shows that keeping high fidelity and strong robustness requires a reduction of the accumulated population of excited state in the evolution process. These results demonstrate the favorable balance between operation speed and robustness offered by time-optimal holonomic control, and they support further exploration of such schemes in trapped-ion platforms.
