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Acta Automatica Sinica

Quantum Control Strategy Based on State Distance

Cong Cong, Shuang, Kuang Kuang, Sen Sen

Published Jan 1, 2007• 3 citations
OpenAlex

Abstract

把距离基于 Bures，代表在一个需要的状态和一个量系统的实际状态之间的距离的 Lyapunov 功能被选择。就一个起始的状态是并且不分别地对需要的状态直角的盒子而言，我们与保证靠近环的控制系统的稳定性的州的反馈建议控制策略的一个类。特别，控制系统的 asymptotic 稳定性详细被分析，推出并且证明。最后，粒子系统被做的 spin-1/2 的一个模拟实验和在系统之间的关系声明进化时间和控制价值与不同参数被分析。研究结果为量系统的控制有一般理论意思。

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把距离基于 Bures，代表在一个需要的状态和一个量系统的实际状态之间的距离的 Lyapunov 功能被选择。就一个起始的状态是并且不分别地对需要的状态直角的盒子而言，我们与保证靠近环的控制系统的稳定性的州的反馈建议控制策略的一个类。特别，控制系统的 asymptotic 稳定性详细被分析，推出并且证明。最后，粒子系统被做的 spin-1/2 的一个模拟实验和在系统之间的关系声明进化时间和控制价值与不同参数被分析。研究结果为量系统的控制有一般理论意思。
为量状态轨道在量系统的 Liouville 方程追踪密度矩阵，在在量系统控制的概念的帮助下，一个人能两个都把单一的转变用于控制系统和免费进化的目标系统例如把时间变体和非静止的目标系统变成一个静止状态。因此，追踪问题的量状态轨道成为驾驶的。转变的系统的州的驾驶控制法律借助于 Lyapunov 稳定性定理被设计。最后，数字模拟实验为一个五水平的精力量系统被给。原来的系统轨道与另外的方法追踪的比较分析在建议的方法的控制时间说明优点。
我们基于 decoherence 免费的目标状态为州的转移建议一条基于 Lyapunov 的控制途径。期望的目标状态被构造由一块外部激光地是在 decoherence 免费的 subspace (DFS ) 的一个 decoherence 免费的状态我以便系统状态能是从环境，和没有更多的 decoherence 过程的 decoupled 将发生。与 decoherence 免费的目标状态，我们设计基于 Lyapunov 的控制域尽可能完全驾驶给定的起始的状态到开的量系统的 decoherence 免费的状态的 II，和 decouple 从环境的系统状态同时。最后，设计的州的转移控制在一种类型上实现，这被验证没有联合到环境，四水平的原子系统，和系统能在 decoherence 免费的目标状态上留下来。
Abstract Based on Bures distance, a Lyapunov function that represents the distance between a desired state and the actual state of a quantum system is selected. Considering the cases that an initial state is and is not orthogonal to the desired state respectively, we propose a class of control strategies with state feedback that ensures the stability of the closed-loop control system. Especially, the asymptotic stability of the control system is analyzed, deduced and proved in detail. Finally, a simulation experiment on a spin-1/2 particle system is done and the relation between the system state evolution time and control value is analyzed with different parameters. Research results have general theoretical meaning for control of quantum systems.
Based on Bures distance, a Lyapounov function that represents a desired state and an actual state is selected for quantum systems. Considering the problems that the initial state is and isn't orthogonal to the desired state respectively, a class of feedback control strategies is designed that ensures the stability of closed-loop systems. Finally, we make a simulation experiment on a spin-1/2 system with two types of controls and make an effect analysis of system evolution time and control size in the cases with different parameters.