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We introduce a simple yet versatile protocol to inverse engineer thetime-dependent Hamiltonian in two- and three level systems. In the protocol, byutilizing a universal SU(2) transformation, a given speedup goal can beobtained with large freedom to select the control parameters. As anillustration example, the protocol is applied to perform population transferbetween nitrogen-vacancy (NV) centers in diamond. Numerical simulation showsthat the speed of the present protocol is fast compared with that of theadiabatic process. Moreover, the protocol is also tolerant to decoherence andexperimental parameter fluctuations. Therefore, the protocol may be useful fordesigning an experimental feasible Hamiltonian to engineer a quantum system.

Fast quantum state engineering via universal SU(2) transformation