发表机构
Xi’an Jiaotong University; CentraleSupélec, Université Paris-Saclay; University of Technology Sydney（西安交通大学; 巴黎萨克雷大学中央理工-高等学院; 悉尼科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文从控制论角度综述开放量子系统的测量反馈，提出递推-收缩框架，以不变性、估计和收缩为核心，连接量子滤波与非线性随机控制，并讨论实施挑战与开放问题。
AI 中文摘要
本综述从控制论视角探讨连续监测的开放量子系统的测量反馈，主要分析集中于由扩散型随机主方程描述的有限维系统。我们引入相关的状态空间、不变子空间和量子非破坏结构，将量子滤波解释为非线性观测器动力学，并回顾开环渐近性、滤波器稳定性、状态反馈镇定、鲁棒性以及基于降阶观测器的控制。特别强调递推-收缩框架，其中哈密顿反馈消除非目标不变阻碍，而测量诱导动力学提供局部指数收缩。尽管详细分析针对有限维扩散模型展开，但潜在的测量-估计-反馈架构广泛适用于各类量子平台。我们进一步讨论实施挑战和开放问题，涉及可扩展估计、采样与延迟、自适应、混合及非马尔可夫动力学、实际稳定性、最优控制以及基于学习的设计。通过围绕不变性、估计、递推和收缩组织这些进展，本综述为测量量子反馈与非线性随机控制之间提供了教程式桥梁。
英文摘要
This review develops a control-theoretic perspective on measurement-based feedback for continuously monitored open quantum systems, with the main analysis focused on finite-dimensional systems governed by diffusive stochastic master equations. We introduce the relevant state-space, invariant-subspace, and quantum non-demolition structures, interpret quantum filtering as nonlinear observer dynamics, and review open-loop asymptotics, filter stability, state-feedback stabilization, robustness, and reduced-order observer-based control. Particular emphasis is placed on a recurrence--contraction framework, in which Hamiltonian feedback removes non-target invariant obstructions while measurement-induced dynamics provide local exponential contraction. Although the detailed analysis is developed for finite-dimensional diffusive models, the underlying measurement--estimation--feedback architecture is relevant across a broad range of quantum platforms. We further discuss implementation challenges and open problems involving scalable estimation, sampling and delay, adaptation, hybrid and non-Markovian dynamics, practical stability, optimal control, and learning-based design. By organizing these developments around invariance, estimation, recurrence, and contraction, the review provides a tutorial bridge between measurement-based quantum feedback and nonlinear stochastic control.
