Noise-Resistant Floquet Geometric Quantum Computation.

Non-adiabatic geometric quantum computation (NGQC) provides a promising way for implementing robust quantum gate operation. However, NGQC has no obvious advantage over the dynamical scheme in dealing with control errors. Here, we show a new geometric scheme, called Floquet geometric quantum computation (FGQC), in which error-resistant geometric gates based on periodically driven two-level systems can be constructed via a new non-Abelian geometric phase proposed in a recent work [V. Noviĉenko \emph{et al}, Phys. Rev. A 100, 012127 (2019) ]. Based on Rydberg atoms, the experimental feasibility of our proposal is demonstrated through numerical simulation using the recent experimental parameters. In addition, the numerical simulation of our geometric gates in the presence of global control error shows that the FGQC gates are more robust over NGQC and dynamical gate (DG). We further analytically prove the superiority of FGQC in terms of robustness against global control error. Consequently, our work makes an important step towards robust geometric quantum computation.