论文标题
通过分析谎言代数衍生物对旋转的最佳控制
Optimal Control of Spins by Analytical Lie Algebraic Derivatives
论文作者
论文摘要
在许多优化算法中，忠诚度函数的衍生物（梯度和黑森）的计算是最关键的步骤之一。在优化过程需要在许多步骤中传播这些计算的情况下，可以访问准确的方法来计算这些衍生物，这在最佳控制旋转系统中特别重要。在这里，我们提出了一种新型的数值方法，升华（使用分析性谎言代数衍生物进行有效的自旋控制），该方法通过利用$ 2 \ times 2 $ hermitian矩阵的谎言组的特性，$ \\ mathrm {surm {surm {suge}（2）$ and lie alge algebra，seke a al al algebra，ske a al a al a algebra，ske a a al a al a al a al a algebra，ske a al a al a al lie a al a al a algebra seke fifelity函数的确切第一和第二个衍生物。 $ \ mathfrak {su}（2）$。提出了对所提出的方法的完整数学处理以及一些数值示例。
Computation of derivatives (gradient and Hessian) of a fidelity function is one of the most crucial steps in many optimization algorithms. Having access to accurate methods to calculate these derivatives is even more desired where the optimization process requires propagation of these calculations over many steps, which is in particular important in optimal control of spin systems. Here we propose a novel numerical approach, ESCALADE (Efficient Spin Control using Analytical Lie Algebraic Derivatives) that offers the exact first and second derivatives of the fidelity function by taking advantage of the properties of the Lie group of $2\times 2$ Hermitian matrices, $\mathrm{SU}(2)$, and its Lie algebra, the Lie algebra of skew-Hermitian matrices, $\mathfrak{su}(2)$. A full mathematical treatment of the proposed method along with some numerical examples are presented.
