探索随机量子演化稳定控制的鲁棒性
Exploring the Robustness of stabilizing controls for stochastic quantum evolutions
AI总结：
本文分析了建模误差对量子随机演化中纯态或子空间稳定性的影响，针对开环和反馈控制协议分别证明了均值有界性及扰动效应的期望与概率界限，揭示了目标动力学不变性的关键作用。
摘要：
在本研究中，我们分析并界定了建模误差对纯态或子空间稳定性的影响，针对量子随机演化展开讨论。针对开环和反馈控制协议采用了不同的方法。对于两者，我们强调了目标动力学不变性的关键作用：如果扰动保持不变性，则在一些额外假设下，可以证明它也保持其吸引性。此外，我们证明了在开环协议下受扰动系统解的均值有界性。对于反馈策略，在不假设不变性的一般情形下，我们给出了扰动效应在期望和概率上的界限，以及针对非破坏性标称系统的特定界限。
英文摘要：
In this work we analyze and bound the effect of modeling errors on the stabilization of pure states or subspaces for quantum stochastic evolutions. Different approaches are used for open-loop and feedback control protocols. For both, we highlight the key role of dynamical invariance of the target: if the perturbation preserves invariance, it is possible to prove that it also preserves its attractivity, under some additional assumptions. In addition, we prove boundedness in mean of the solutions of perturbed systems under open-loop protocols. For the feedback strategies, in the general case without assumptions on invariance, we provide bounds on the perturbation effect in expectation and in probability, as well as specific bounds for non-demolition nominal systems.
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