Experimental Realization of Nonadiabatic Holonomic Single-Qubit Quantum Gates with Optimal Control in a Trapped Ion

Quantum computation with quantum gates induced by geometric phases is regarded as a promising strategy in fault-tolerant quantum computation, owing to its robustness against operational noise. However, because of the parametric restrictions in previous schemes, the main robust advantage of holonomic quantum gates is reduced. Here, we experimentally demonstrate a solution scheme, obtaining nonadiabatic holonomic single-qubit quantum gates with optimal control in a trapped ¹⁷¹Yb⁺ ion based on a three-level system with resonant driving, which also has the advantages of rapid evolution and convenient implementation. Compared with previous geometric gates and conventional dynamical gates, the superiority of our scheme is that it is more robust against control amplitude errors, which is confirmed by the gate infidelity as measured by both quantum-process tomography and random benchmarking methods. In addition, we outline how nontrivial two-qubit holonomic gates can also be realized using currently available experimental technology. Thus, our experiment confirms the feasibility of this robust and fast holonomic quantum-computation strategy.