  Following a key idea of unconventional geometric quantum computation
developed earlier [Phys. Rev. Lett. 91, 197902 (2003)], here we propose a more
general scheme in such an intriguing way: $\gamma_{d}=\alpha_{g}+\eta \gamma
_{g}$, where $\gamma_{d}$ and $\gamma_{g}$ are respectively the dynamic and
geometric phases accumulated in the quantum gate operation, with $\eta$ as a
constant and $\alpha_{g}$ being dependent only on the geometric feature of the
operation. More arrestingly, we demonstrate the first experiment to implement a
universal set of such kind of generalized unconventional geometric quantum
gates with high fidelity in an NMR system.
