We develop a systematic and efficient approach for numerically solving the non-Markovian quantum state diffusion equations for open quantum systems coupled to an environment up to arbitrary orders of noises or coupling strengths. As an important appl
ication, we consider a real-time simulation of a spin-boson model in a strong coupling regime that is difficult to deal with using conventional methods. We show that the non-Markovian stochastic Schr{o}dinger equation can be efficiently implemented as a real--time simulation for this model, so as to give an accurate description of spin-boson dynamics beyond the rotating-wave approximation.
