Error-resilient Floquet geometric quantum computation
Yuan-Sheng Wang, Bao-Jie Liu, Shi‐Lei Su, Man‐Hong Yung · Physical Review Research · 2021
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. Novi\ifmmode \check{c}\else \v{c}\fi{}enko and G. Juzeli\ifmmode \bar{u}\else \={u}\fi{}nas, 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 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, ${T}_{2}\ensuremath{\approx}32\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{s}$, 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.