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A simple yet versatile protocol to inversely engineer time-dependent Hamiltonian is proposed. By utilizing SU(2) transformation, a given speedup goal of gate operation can be achieved with larger freedom to select the control parameters. As an application, this protocol is adopted to realize conventional and unconventional nonadiabatic geometric quantum gates with any desired evolution paths by controlling the pulses in the diamond nitrogen-vacancy (NV) center system. We show that the designed gate can realize geometric quantum computation with a more economical evolution time that decreases the influence of noise on gate operation.

An interesting method of fast enantio-specific state transfer (ESST) is proposed for cyclic three-level systems of chiral molecules. We show that the fast population transfer via shortcut to adiabaticity can be accomplished for the cyclic three-level system of a general (chiral) molecule with invariant-based inverse engineering of the coupling strengths. By choosing appropriate parameters, the two enantiomers, which are initially prepared in their ground states in the three-level systems, will evolve respectively along their enantio-selective shortcut-to-adiabaticity paths to different-energy final states simultaneously, thereby achieving the fast ESST.