  The adiabatic theorem and "shortcuts to adiabaticity" for the adiabatic
dynamics of time-dependent decoherence-free subspaces are explored in this
paper. Starting from the definition of the dynamical stable decoherence-free
subspaces, we show that, under a compact adiabatic condition, the quantum state
follows time-dependent decoherence-free subspaces (the adiabatic decoherence
free subspaces) into the target subspace with extremely high purity, even
though the dynamics of the quantum system may be non-adiabatic. The adiabatic
condition mentioned in the adiabatic theorem is very similar with the adiabatic
condition for closed quantum systems, except that the operators required to be
"slowness" is on the Lindblad operators. We also show that the adiabatic
decoherence-free subspaces program depends on the existence of instantaneous
decoherence-free subspaces, which requires that the Hamiltonian of open quantum
systems has to be engineered according to the incoherent control program.
Besides, "the shortcuts to adiabaticity" for the adiabatic decoherence-free
subspaces program is also presented based on the transitionless quantum driving
method. Finally, we provide an example of physical systems that support our
programs. Our approach employs Markovian master equations and applies primarily
to finite-dimensional quantum systems.
