Russell Benjamin, Rabitz Herschel
Department of Chemistry, Princeton University, Princeton, NJ 08540, USA
Department of Chemistry, Princeton University, Princeton, NJ 08540, USA.
Philos Trans A Math Phys Eng Sci. 2017 Mar 6;375(2088). doi: 10.1098/rsta.2016.0210.
A common goal in the sciences is optimization of an objective function by selecting control variables such that a desired outcome is achieved. This scenario can be expressed in terms of a control landscape of an objective considered as a function of the control variables. At the most basic level, it is known that the vast majority of quantum control landscapes possess no traps, whose presence would hinder reaching the objective. This paper reviews and extends the quantum control landscape assessment, presenting evidence that the same highly favourable landscape features exist in many other domains of science. The implications of this broader evidence are discussed. Specifically, control landscape examples from quantum mechanics, chemistry and evolutionary biology are presented. Despite the obvious differences, commonalities between these areas are highlighted within a unified mathematical framework. This mathematical framework is driven by the wide-ranging experimental evidence on the ease of finding optimal controls (in terms of the required algorithmic search effort beyond the laboratory set-up overhead). The full scope and implications of this observed common control behaviour pose an open question for assessment in further work.This article is part of the themed issue 'Horizons of cybernetical physics'.
科学领域的一个共同目标是通过选择控制变量来优化目标函数，从而实现期望的结果。这种情况可以用作为控制变量函数的目标的控制景观来表示。在最基本的层面上，已知绝大多数量子控制景观不存在陷阱，因为陷阱的存在会阻碍目标的实现。本文回顾并扩展了量子控制景观评估，提出证据表明许多其他科学领域也存在同样高度有利的景观特征。讨论了这一更广泛证据的含义。具体而言，给出了量子力学、化学和进化生物学的控制景观示例。尽管存在明显差异，但在统一的数学框架内突出了这些领域之间的共性。这个数学框架是由关于寻找最优控制的难易程度的广泛实验证据驱动的（就超出实验室设置开销所需的算法搜索工作量而言）。这种观察到的共同控制行为的全部范围和含义构成了一个有待进一步工作评估的开放性问题。本文是主题为“控制论物理学的视野”的特刊的一部分。
