  By using transitionless quantum driving algorithm (TQDA), we present an
efficient scheme for the shortcuts to the holonomic quantum computation (HQC).
It works in decoherence-free subspace (DFS) and the adiabatic process can be
speeded up in the shortest possible time. More interestingly, we give a
physical implementation for our shortcuts to HQC with nitrogen-vacancy centers
in diamonds dispersively coupled to a whispering-gallery mode microsphere
cavity. It can be efficiently realized by controlling appropriately the
frequencies of the external laser pulses. Also, our scheme has good scalability
with more qubits. Different from previous works, we first use TQDA to realize a
universal HQC in DFS, including not only two noncommuting accelerated
single-qubit holonomic gates but also a accelerated two-qubit holonomic
controlled-phase gate, which provides the necessary shortcuts for the complete
set of gates required for universal quantum computation. Moreover, our
experimentally realizable shortcuts require only two-body interactions, not
four-body ones, and they work in the dispersive regime, which relax greatly the
difficulty of their physical implementation in experiment. Our numerical
calculations show that the present scheme is robust against decoherence with
current experimental parameters.
