Realization of universal nonadiabatic holonomic quantum gates in trapped ion system

The implementation of holonomic quantum computation is meaningful. We can effectively resist local and collective noise in the process of physical implementation by using the advantage of non-Abelian geometric phase. In this paper, we set out from the simplest and most fundamental Jaynes-Cummings model of ion trap system to implement single-qubit logical operations, and taking advantage of the interaction of two ions with a pair of laser pulses to implement two-qubit logical operations, respectively. Compared with the previous proposal, the whole process of our proposal are in tunable way and the universal holonomic quantum qubit gates can be made robust to systematic error and decay which pushes the gate fidelities in the presence of decoherence and systematic error to well high level. Thus our scheme affords an experimentally feasible and simple way to make realizing the robust nonadiabatic holonomic quantum computation.