Universal single-qubit operations based on purely geometric phase factors in adiabatic processes are demonstrated by utilizing a four-level system in a trapped single $^{40}$Ca$^+$ ion connected by three oscillating fields. Robustness against parameter variations is studied. The scheme demonstrated here can be employed as a building block for large-scale holonomic quantum computations, which may be useful for large qubit systems with statistical variations in system parameters

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We excited a transition between ground-state Zeeman sublevels in 40Ca+ using a radio frequency (RF) magnetic field. We discuss methods for generating an RF magnetic field of sufficiently large amplitude and for estimating the amplitude of the RF field to observe Rabi oscillations with high Rabi frequencies. A maximum Rabi frequency of ∼250 kHz was obtained. We also demonstrate a simple quantum gate operation on a combined system using the S1/2–D5/2 transition in 40Ca+.

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