Nonadiabatic holonomic quantum computation and its optimal control

The geometric phase has the intrinsic property of being resistant to some types local noises as it only depends on global properties evolution path. Meanwhile, non-Abelian is in matrix form, and thus can naturally be used implement high performance quantum gates, i.e., so-called holonomic computation. This article reviews recent advances nonadiabatic computation, focuses various optimal control approaches that improve gate performance, terms fidelity robustness. Besides, we also pay special attention its possible physical realizations concrete examples experimental realizations. Finally, with all these efforts, within state-of-the-art technology, implemented gates outperform conventional dynamical ones, under certain conditions.