Dynamical programming of continuously observed quantum systems
Dynamical programming of continuously observed quantum systems
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连续观测量子系统的动态规划
DOI：
10.1103/physreva.79.022123
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
K. Mølmer
中科院分区：
文献类型：
--
作者：
V. Belavkin;A. Negretti;K. Mølmer
我们发展动态规划方法的目的是最优控制的量子态的凸约束和凹成本和遗赠函数的量子态。我们考虑开环和反馈控制方案，分别对应于确定性和随机主方程动力学。对于具有连续非破坏观测的量子反馈控制方案，我们利用量子随机动力学的滤波和控制分离定理导出了广义Hamilton-Jacobi-Bellman方程.如果控制仅限于汉密尔顿项，则等效于具有额外线性耗散项的汉密尔顿-雅可比方程。在这项工作中，我们特别考虑的情况下，控制仅限于观察。受控量子比特被认为是整个形式主义发展的一个例子。最后，我们讨论了从量子二能级系统的混合态得到纯态的最佳观测策略。
We develop dynamical programming methods for the purpose of optimal control of quantum states with convex constraints and concave cost and bequest functions of the quantum state. We consider both open loop and feedback control schemes, which correspond, respectively, to deterministic and stochastic master equation dynamics. For the quantum feedback control scheme with continuous nondemolition observations, we exploit the separation theorem of filtering and control aspects for quantum stochastic dynamics to derive a generalized Hamilton-Jacobi-Bellman equation. If the control is restricted to only Hamiltonian terms this is equivalent to a Hamilton-Jacobi equation with an extra linear dissipative term. In this work, we consider, in particular, the case when control is restricted only to observation. A controlled qubit is considered as an example throughout the development of the formalism. Finally, we discuss optimum observation strategies to obtain a pure state from a mixed state of a quantum two-level system.