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Journal of Control Theory and Applications

State transfer based on decoherence-free target state by Lyapunov-based control

Jie Jie, Yang, Shuang, Cong Cong

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

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。

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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。
这份报纸探索由联系量与 decoherence 作斗争的潜力有 decoherence 免费的 subspaces (DFS ) 的概括测量。联系量概括了 subspace 投影机测量(QGSPM ) ，量与操作员条件概括了盒子投影机测量(QGCPM ) 因为 DFS 将提高压制 decoherence 的能力因为 Markovian 和 non-Markovian 打开量系统，这被表明。量测量能被认为是一个工具操作量状态，这被强调。因为协调控制哈密尔顿能积极地被设计，这个方法是有益的。
The problem of quantum state control in open quantum systems based on the Lyapunov method is studied. The control laws are designed to drive the system to a pure target state in decoherence-free subspace (DFS) in the interaction picture, where the average of an observable operator P is chosen as a Lyapunov function. By analyzing the positive limit set via Barbalat’s lemma, we propose a sufficient condition on the observable operator such that the positive limit set only contains the target state. Under this condition, it is proved that the control laws can drive the open system to any pure target state in DFS in the interaction picture. Also, we provide a method to construct the observable operator via Schmidt orthogonalization. Numerical simulations on a three-level system validate the effectiveness of the proposed control strategy.
We present a scheme to drive a finite-dimensional quantum system into the decoherence-free subspaces (DFS) by Lyapunov control. Control fields are established by Lyapunov function. This proposal works well for both closed and open quantum systems, with replacing the DFS by desired subspaces for closed systems. An example which consists of a four-level system with three degenerate states driven by three lasers is presented to gain further insight on the scheme. Numerical simulations for the dynamics of the system are performed and the results are good.
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。