We propose a fast mixed-state control scheme to transfer the quantum state along designable trajectories in Hilbert space, which is robust to multiple decoherence noises. Starting with the dynamical invariants of open quantum systems, we present the shortcuts to adiabaticity (STA) of open quantum systems at first, then apply the STA to speed up the adiabatic steady process. Our scheme drives open systems from a initial steady state to a target steady state by a controlled Liouvillian that possesses the same form as the reference (original) one that is accessible in present-day experiments. An experimental design with currently available parameters for the nitrogen-vacancy (N-$V$) center in diamond is suggested and discussed.

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• Adiabatic quantum optimization
• Open quantum systems & decoherence
• Quantum control
• Quantum information processing
• Quantum state engineering
• Quantum state transfer