Experimental realization of nonadiabatic holonomic single‐qubit quantum gates with two dark paths in a trapped ion

For circuit-based quantum computation,experimental implementation of a universal set of quantum logic gates with high-fidelity and strong robustness is essential and central.Quantum gates induced by geometric phases,which depend only on global properties of the evolution paths,have built-in noise-resilience features.Here,we propose and experimentally demonstrate nonadiabatic holonomic single-qubit quantum gates on two dark paths in a trapped ^(171)γδ^(+)ion based on four-level systems with resonant drives.We confirm the implementation with measured gate fidelity through both quantum process tomography and randomized benchmarking methods.Meanwhile,we find that nontrivial holonomic two-qubit quantum gates can also be realized within current experimental technologies.Compared with previous implementations,our experiments share both the advantages of fast nonadiabatic evolution and robustness against systematic errors.Therefore,our experiments confirm a promising method for fast and robust holonomic quantum computation.