非均匀系综的最优控制
Optimal Control of Inhomogeneous Ensembles
AI总结：
针对物理系统中的非均匀性，本文利用系综控制概念提出一种基于多维伪谱近似的最优控制计算方法，用于设计量子脉冲，并证明了收敛性。
摘要：
非均匀性以其多种形式频繁出现在实际物理系统中。在量子系统中尤为明显，它由硬件缺陷、测量不准确和环境变化引起，进而限制了当前实验所能达到的性能和效率。在本文中，我们提供了一种系统性的方法，利用系综控制的概念对非均匀系综进行数学刻画和最优操控。特别地，我们开发了一种计算方法，基于多维伪谱近似，解决作为最优系综控制问题的实际量子脉冲设计问题。我们通过为标准应用和新颖应用设计脉冲来激发该方法的实用性。我们还证明了用于最优系综控制的伪谱方法的收敛性。这里开发的概念不仅适用于量子控制，还适用于神经元系统，以及具有参数不确定性的系统，这些系统遍及科学和工程的各个领域。
英文摘要：
Inhomogeneity, in its many forms, appears frequently in practical physical systems. Readily apparent in quantum systems, inhomogeneity is caused by hardware imperfections, measurement inaccuracies, and environmental variations, and subsequently limits the performance and efficiency achievable in current experiments. In this paper, we provide a systematic methodology to mathematically characterize and optimally manipulate inhomogeneous ensembles with concepts taken from ensemble control. In particular, we develop a computational method to solve practical quantum pulse design problems cast as optimal ensemble control problems, based on multidimensional pseudospectral approximations. We motivate the utility of this method by designing pulses for both standard and novel applications. We also show the convergence of the pseudospectral method for optimal ensemble control. The concepts developed here are applicable beyond quantum control, such as to neuron systems, and furthermore to systems with by parameter uncertainty, which pervade all areas of science and engineering.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
