  We proposed a new geometric quantum computation (GQC) scheme, called Floquet
GQC (FGQC), where error-resilient geometric gates based on periodically driven
two-level systems can be constructed via a new non-Abelian geometric phase
proposed in a recent study [V. Novi\^{c}enko \textit{et al}, Phys. Rev. A 100,
012127 (2019) ]. Based on Rydberg atoms, we gave possible implementations of
universal single-qubit gates and a nontrivial two-qubit gate for FGQC. By using
numerical simulation, we evaluated the performance of the FGQC Z and X gates in
the presence of both decoherence and a certain kind of systematic control
error. The gate fidelities of the Z and X gates are $F_{X,\text{gate}}\approx
F_{Z,\text{gate}}\approx 0.9992$. The numerical results provide evidence that
FGQC gates can achieve fairly high gate fidelities even in the presence of
noise and control imperfection. In addition, we found FGQC is robust against
global control error, both analytical demonstration and numerical evidence were
given. Consequently, this study makes an important step towards robust
geometric quantum computation.
