Rabitz Herschel A, Hsieh Michael M, Rosenthal Carey M
Department of Chemistry, Princeton University, Princeton, NJ 08544, USA.
Science. 2004 Mar 26;303(5666):1998-2001. doi: 10.1126/science.1093649.
A large number of experimental studies and simulations show that it is surprisingly easy to find excellent quality control over broad classes of quantum systems. We now prove that for controllable quantum systems with no constraints placed on the controls, the only allowed extrema of the transition probability landscape correspond to perfect control or no control. Under these conditions, no suboptimal local extrema exist as traps that would impede the search for an optimal control. The identified landscape structure is universal for all controllable quantum systems of the same dimension when seeking to maximize the same transition probability, regardless of the detailed nature of the system Hamiltonian. The presence of weak control field noise or environmental decoherence is shown to preserve the general structure of the control landscape, but at lower resolution.
大量的实验研究和模拟表明，在广泛的量子系统类别中找到卓越的质量控制出奇地容易。我们现在证明，对于对控制没有限制的可控量子系统，跃迁概率景观中唯一允许的极值对应于完美控制或无控制。在这些条件下，不存在作为陷阱的次优局部极值来阻碍对最优控制的搜索。当试图最大化相同的跃迁概率时，所识别出的景观结构对于相同维度的所有可控量子系统都是通用的，而与系统哈密顿量的详细性质无关。结果表明，弱控制场噪声或环境退相干的存在会保留控制景观的一般结构，但分辨率较低。
