  A fundamental requirement of quantum information processing is the protection
from the adverse effects of decoherence and noise. Decoherence-free subspaces
and geometric processing are important steps of quantum information protection.
Here, we provide a new experimentally feasible scheme to combine
decoherence-free subspaces with nonadiabatic geometric manipulations to attain
a universal quantum computation. The proposed scheme is different from previous
proposals and is based on the typical XY interaction coupling, which can be set
up in various nano-engineered systems and therefore open up for realization of
nonadiabatic holonomic quantum computation in decoherence-free subspaces.
