  High-fidelity quantum gates are essential for large-scale quantum
computation, which can naturally be realized in a noise-resilient way.
Geometric manipulation and decoherence-free subspace encoding are promising
ways toward robust quantum computation. Here, by combining the advantages of
both strategies, we propose and experimentally realize universal holonomic
quantum gates in both a singleloop scheme and a composite scheme, based on
nonadiabatic and non-Abelian geometric phases, in a decoherence-free subspace
with nuclear magnetic resonance. Our experiment uses only two-body resonant
spin-spin interactions and thus is experimental friendly. In particular, we
also experimentally verify that the composite scheme is more robust against the
pulse errors than the single-loop scheme. Therefore, our experiment provides a
promising way toward faithful and robust geometric quantum manipulation.
