On Exponential Stabilization of Spin-1/2 Systems
Quantum Physics
2019-02-12 v2 Mathematical Physics
math.MP
Optimization and Control
Abstract
In this paper, we study the stabilization problem of quantum spin-1/2 systems under continuous-time measurements. In the case without feedback, we show exponential stabilization around the excited and ground state by providing a lower bound of the convergence rate. Based on stochastic Lyapunov techniques, we propose a parametrized measurement-based feedback which ensures exponential convergence toward the excited state. Moreover, we give a lower bound of the convergence rate for this case. Then, we discuss the effect of each parameter appeared in the control law in the convergence rate. Finally, we illustrate the efficiency of such feedback law through simulations.
Cite
@article{arxiv.1803.10632,
title = {On Exponential Stabilization of Spin-1/2 Systems},
author = {Weichao Liang and Nina H. Amini and Paolo Mason},
journal= {arXiv preprint arXiv:1803.10632},
year = {2019}
}