严格约束条件下的量子最优控制
Searching for quantum optimal controls under severe constraints
摘要：
量子最优控制在实验和理论上的成功都与相应的控制景观的拓扑结构有关，如果满足以下三个条件，这些控制景观就不会有局部陷阱：（1）量子系统是可控的，（2）从控制场到演化算子的映射的雅可比矩阵是满秩的，（3）控制场上没有约束。本文研究了假设（3）的违反如何影响全局最优控制域的梯度搜索。假设（1）和（2）的满足确保了控制景观没有基本陷阱，但某些控制约束仍然可以引入人为陷阱。这些约束的适当管理是数值模拟以及在实验室中的优化具有重要实际意义的问题。使用最优控制模拟，我们表明，数量的限制，如控制变量的数量，控制持续时间，和磁场强度可能是严重的，足以防止成功的目标优化。对于每个这样的约束，我们表明，超过量化的限制，可以防止梯度搜索达到全局最优解。这些结果表明，仔细选择相关的控制参数有助于消除人为陷阱，并促进成功的优化。
英文摘要：
The success of quantum optimal control for both experimental and theoretical objectives is connected to the topology of the corresponding control landscapes, which are free from local traps if three conditions are met: (1) the quantum system is controllable, (2) the Jacobian of the map from the control field to the evolution operator is of full rank, and (3) there are no constraints on the control field. This paper investigates how the violation of assumption (3) affects gradient searches for globally optimal control fields. The satisfaction of assumptions (1) and (2) ensures that the control landscape lacks fundamental traps, but certain control constraints can still introduce artificial traps. Proper management of these constraints is an issue of great practical importance for numerical simulations as well as optimization in the laboratory. Using optimal control simulations, we show that constraints on quantities such as the number of control variables, the control duration, and the field strength are potentially severe enough to prevent successful optimization of the objective. For each such constraint, we show that exceeding quantifiable limits can prevent gradient searches from reaching a globally optimal solution. These results demonstrate that careful choice of relevant control parameters helps to eliminate artificial traps and facilitate successful optimization.
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。
