Perfect quantum state engineering by the combination of the counterdiabatic driving and the reverse-engineering technique

We propose a method to design shortcuts to adiabaticity for implementing perfect quantum state engineering by the combination of the counterdiabatic driving and the reverse engineering technique. Based on the method, we can design simple schemes to realize the intended dynamics. For the sake of clearness, we apply this method to several examples including two-level, three-level and four-level system. We show that fast quantum state engineering can be realized by utilizing simply-designed auxiliary Hamiltonian. Furthermore, a suitable choice of the control parameters can eliminate the additional couplings in the introduced auxiliary Hamiltonian. Numerical simulation reveals that the constructed scheme is reliable and robust against various dissipation effects and the fluctuations of control parameters in current technology. - Highlights: • Fast and feasible quantum state engineering can be realized by using the method. • The method allows one to control accurately the evolution of the system. • The scheme is fast and robust against dissipation effects and parameter errors. • The scheme can be generalized to realize N-dimensional quantum state engineering.