Fast implementation of four-dimensional entangled state via transitionless quantum driving

In comparison to low-dimensional entangled states, multi-dimensional entangled states are more security for quantum communication and more efficient and error-tolerant for quantum computation. Using transitionless quantum driving to construct shortcuts to adiabatic passage, we propose an efficient scheme to fast implement a four-dimensional entangled state of two atoms. The rigorous numerical simulations are showed. The results represent that the proposed generation scheme takes less time than traditional adiabatic scheme, and more robust against atomic spontaneous emission. Furthermore, this scheme is insensitive to the instability of experiment parameters.