A universal scheme is introduced to speed up the dynamics of a driven open quantum system along a prescribed trajectory of interest. Shortcuts to adiabaticity (STA) designed in this fashion can be implemented in two alternative scenarios: one is characterized by the presence of balanced gain and loss, the second involves non-Markovian dynamics with time-dependent Lindblad operators. As an illustration we engineer superadiabatic cooling, heating, and isothermal strokes for a two-level system.

We also present a complementary approach to engineer STA in open systems that is specific for Gaussian states, e.g., of particles in a harmonic trap. An arbitrary thermal state can be prepared in a finite time by modulation of the trap frequency and the noise-induced dephasing strength. The implementation of such STA protocols is readily accessible via stochastic parametric driving in a variety of platforms.