Optimal control equation for quantum stochastic differential equations

Abstract

interaction of open quantum systems with fundamental noncommutative quantum noises can be described by quantum stochastic differential equations (QSDE). These equations have a key role in quantum network analysis and design, especially for quantum information processing. Hence, in this paper, we derive a Hamilton-JacobiBellman equation for quantum stochastic differential equations. The Bellman optimality principle is developed for open quantum systems. The cost functional of quantum observable to be minimized is considered to be general noncommutative polynomial of quantum operator. Since the method directly deals with QSDE, then it is a useful tool for optimal control of quantum optical networks. In addition, we will exhibit some electro-optical and all-optical feedback control schematics for implementation of quantum control based on QSDEs.

Hydrochemical characteristics and geothermometry applications of thermal groundwater in northern Jinan, Shandong, China

“…where {X s : s ∈ [t 0 , T ]} is the solution to (1.7) with the initial condition X 0 , u denotes a continuous control function, taking values in R n . James [26], Sharifi and Momeni [41] investigated the optimal control problems of the following quantum systems…”