  Nonadiabatic holonomic quantum computation has robust feature in suppressing
control errors because of its holonomic feature. However, this kind of robust
feature is challenged since the usual way of realizing nonadiabatic holonomic
gates introduces errors due to systematic errors in the control parameters. To
resolve this problem, we here propose a composite scheme to realize
nonadiabatic holonomic gates. Our scheme can suppress systematic errors while
preserving holonomic robustness. It is particularly useful when the evolution
period is shorter than the coherence time. We further show that our composite
scheme can be protected by decoherence-free subspaces. In this case, the
strengthened robust feature of our composite gates and the coherence
stabilization virtue of decoherence-free subspaces are combined.
