  Pure-state inverse engineering among the schemes of shortcuts to adiabaticity
is a widespread utility in applications to quantum computation and quantum
simulation. While in principle it can realise the fast control of quantum
systems with high fidelity, in practice this fast control is severely hindered
by infinite energy gaps and impractical control fields. To circumvent this
problem, we propose a scheme of shortcuts to adiabaticity of mixed state based
on the dynamical invariant of open quantum system. Our scheme can drives a
steady state to a target steady state of the open system by a controlled
Liouvillian that possesses the same form as the reference (original) one. We
apply this scheme to stimulated Raman adiabatic passage (STIRAP) and find that
an almost perfect population transfer can be obtained. The experimental
observation with currently available parameters for the nitrogen-vacancy (NV)
center in diamond is suggested and discussed.
