AI 中文总结
研究量子最优控制，提出随机量子最优控制框架，通过在控制函数及其概率集合上优化，能更快达目标精度，开发基于对称性构造降低误差，引入随机GRAPE，还讨论了增强相干噪声鲁棒性的随机边界脉冲构造。
AI 中文摘要
量子最优控制旨在找到能将量子系统最优地导向目标操作的控制函数。我们引入了一个随机量子最优控制框架，其中优化是在控制函数及其概率的集合上进行，而非单一函数集。利用该框架，我们证明在相同资源约束下，随机量子最优控制能比任何确定性协议更快达到目标精度。我们还开发了基于对称性的通用构造，将给定控制转换为可系统降低误差的控制集合。通过对CNOT实现进行基准测试，发现所得随机协议能二次方地抑制优化后的确定性解的误差。此外，我们引入了随机GRAPE，它将GRAPE推广以直接优化控制集合及其相关概率。最后，作为相关应用，我们讨论了增强对相干噪声鲁棒性的随机边界脉冲构造。
英文摘要
Quantum optimal control (QOC) aims to find control functions that optimally steer a quantum system toward a target operation. We introduce a \emph{randomized} QOC framework where optimization is carried over an ensemble of control functions and their probabilities, instead of a single set of functions. Using this framework, we prove that randomized QOC can reach a target accuracy faster than any deterministic protocol under the same resource constraints. We also develop general symmetry-based constructions that convert a given control into an ensemble of controls that can systematically reduce the error. We benchmark these constructions for CNOT implementation and find that the resulting randomized protocol quadratically suppresses the error of the optimized deterministic solution. In addition, we introduce randomized GRAPE, which generalizes GRAPE to directly optimize control ensembles and their associated probabilities. Finally, as a related application, we discuss randomized boundary-pulse constructions {that enhance} robustness against coherent noise.
