Error-resilient Floquet geometric quantum computation

We propose a 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 non-Abelian geometric phase proposed in a recent study [V. Novičenko and G. Juzeliūnas, Phys. Rev. A 100, 012127 (2019)]. Based on Rydberg atoms, we give possible implementations of universal FGQC single-qubit gates and a nontrivial FGQC two-qubit gate. By using numerical simulation, we evaluate the performance of the FGQC $Z$ and $\mathrm{X}$ gates in the presence of both decoherence and a certain kind of systematic control error. For the currently available coherence time of the Rydberg state, $T_2 \approx 32 \mu \mathrm{s}$, the numerical results show that the $X$ and $Z$ gate fidelities are about $0.900$ and $0.899$, respectively. In addition, we find that FGQC is robust against global control error; both analytical demonstration and numerical evidence are given. As the coherence time of various qubits grows, FGQC may provide a promising error-resilient quantum computation scheme in the future.

我们提出一种几何量子计算（GQC）方案，称为弗洛凯几何量子计算（FGQC），其中基于周期性驱动的二能级系统的抗误差几何门可以通过近期一项研究[V. 诺维琴科和G. 尤泽柳纳斯，《物理评论A》100，012127（2019）]中提出的非阿贝尔几何相位来构建。基于里德伯原子，我们给出了通用FGQC单量子比特门和一个非平凡的FGQC双量子比特门的可能实现方式。通过数值模拟，我们在存在退相干和某种系统控制误差的情况下评估了FGQC的$Z$门和$\mathrm{X}$门的性能。对于当前里德伯态可用的相干时间$T_2\approx32\ \mu\mathrm{s}$，数值结果表明$X$门和$Z$门的保真度分别约为$0.900$和$0.899$。此外，我们发现FGQC对全局控制误差具有鲁棒性；给出了分析论证和数值证据。随着各种量子比特的相干时间增加，FGQC未来可能会提供一种有前景的抗误差量子计算方案。