AI 中文总结
该研究针对多能级系统，提出基于开关控制的时间最优量子门协议，以fluxonium电路为案例优化$X/2$和$Y/2$门，其性能优于标准谐振控制，可实现快速低误差量子操控。
AI 中文摘要
我们确定了实现高保真度、快速单量子比特门的最优量子操控协议。研究表明，时间最优脉冲序列为“开关（bang-bang）”序列：由正、负最大振幅或零值的离散脉冲构成。非绝热开关脉冲序列可最小化门持续时间，为低频架构提速。我们首先推导横向驱动二能级系统的协议，提取最小门时间的精确解析表达式；随后将该框架扩展至一般多能级架构，确定可相干抑制泄漏误差的条件。以fluxonium电路为代表性案例，我们通过离散开关序列与连续波形平滑结合，优化了$X/2$和$Y/2$门。该方法在保持近最优执行速度的同时，抑制了计算子空间外的跃迁。开放系统模拟显示，这些序列在不同fluxonium区域中优于等幅和谐振脉冲方案，即便存在$1/f$通量噪声和耗散，也能实现比标准谐振控制快得多的低误差操控。
英文摘要
We determine the optimal quantum manipulation protocols for implementing high-fidelity, fast single-qubit gates. We demonstrate that the time-optimal pulse sequence is a ``bang-bang'' sequence: discrete pulses of either positive or negative maximum amplitude or zero. The non-adiabatic bang-bang pulse sequence minimizes gate duration providing a speedup for low-frequency architectures. We first derive the protocol for a transversally driven two-level system, extracting exact analytic expressions for minimum gate times. We then extend this framework to general multilevel architectures, identifying conditions that enable the coherent suppression of leakage errors. Using the fluxonium circuit as a representative case study, we optimize $X/2$ and $Y/2$ gates through a combination of discrete bang sequences and continuous waveform smoothing. This approach preserves near-optimal execution speeds while mitigating transitions outside the computational subspace. Open-system simulations demonstrate that these sequences outperform commensurate and resonant pulse schemes across different fluxonium regimes, achieving low-error manipulation significantly faster than standard resonant control, even in the presence of $1/f$ flux noise and dissipation.
Comments18 pages, 5 figures
