  Besides the intrinsic noise resilience property, nonadiabatic geometric
phases are of the fast evolution nature, and thus can naturally be used in
constructing quantum gates with excellent performance, i.e., the so-called
nonadiabatic geometric quantum computation (NGQC). However, previous
single-loop NGQC schemes are sensitive to the operational control error, i.e.,
the $X$ error, due to the limitations of the implementation. Here, we propose a
robust scheme for NGQC combining with the dynamical correction technique, which
still uses only simplified pulses, and thus being experimental friendly. We
numerically show that our scheme can greatly improve the gate robustness in
previous protocols, retaining the intrinsic merit of geometric phases.
Furthermore, to fight against the dephasing noise, due to the $Z$ error, we can
incorporate the decoherence-free subspace encoding strategy. In this way, our
scheme can be robust against both types of errors. Finally, we also propose how
to implement the scheme with encoding on superconducting quantum circuits with
experimentally demonstrated technology. Therefore, due to the intrinsic
robustness, our scheme provides a promising alternation for the future scalable
fault-tolerant quantum computation.
