  Recently, nonadiabatic geometric quantum computation has been received great
attentions, due to its fast operation and intrinsic error resilience. However,
compared with the corresponding dynamical gates, the robustness of implemented
nonadiabatic geometric gates based on the conventional single-loop scheme still
has the same order of magnitude due to the requirement of strict multi-segment
geometric controls, and the inherent geometric fault-tolerance characteristic
is not fully explored. Here, we present an effective geometric scheme combined
with a general dynamical-corrected technique, with which the super-robust
nonadiabatic geometric quantum gates can be constructed over the conventional
single-loop and two-loop composite-pulse strategies, in terms of resisting the
systematic error, i.e., $\sigma_x$ error. In addition, combined with the
decoherence-free subspace (DFS) coding, the resulting geometric gates can also
effectively suppress the $\sigma_z$ error caused by the collective dephasing.
Notably, our protocol is a general one with simple experimental setups, which
can be potentially implemented in different quantum systems, such as Rydberg
atoms, trapped ions and superconducting qubits. These results indicate that our
scheme represents a promising way to explore large-scale fault-tolerant quantum
computation.
