Computational techniques for a quantum control problem with H1-cost
Computational techniques for a quantum control problem with H1-cost
复制标题
具有 H1 成本的量子控制问题的计算技术
DOI：
10.1088/0266-5611/24/3/034007
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发表时间：
2008
期刊：
影响因子：
2.1
通讯作者：
A. Borzì
中科院分区：
文献类型：
--
作者：
G. V. Winckel;A. Borzì
无限维量子控制问题最优控制的精确数值计算是一项非常困难的任务，需要我们考虑到原始无限维问题的特征。一个重要的问题是定义最小化过程的功能空间的选择。 L2 最小化与基于 H1 最小化的系统比较表明，适当功能空间的选择很重要，并且在某些优化技术的实施中会产生许多后果。在 L2 和 H1 设置中引入了无矩阵级联 BFGS 算法，并且证明选择 H1 而不是 L2 会带来性能和鲁棒性的显着提高。比较了函数空间最小化产生的最优控制与切比雪夫最小化和适当正交分解基函数系数获得的控制。
The accurate numerical computation of optimal controls of infinite-dimensional quantum control problems is a very difficult task that requires us to take into account the features of the original infinite-dimensional problem. An important issue is the choice of the functional space where the minimization process is defined. A systematic comparison of L2- versus H1-based minimization shows that the choice of the appropriate functional space matters and has many consequences in the implementation of some optimization techniques. A matrix-free cascadic BFGS algorithm is introduced in the L2 and H1 settings, and it is demonstrated that the choice of H1 over L2 results in a substantial performance and robustness increase. A comparison between optimal control resulting from function space minimization and the control obtained by minimization over Chebyshev and proper orthogonal decomposition basis function coefficients is presented.