Optimal control of two-level dissipative quantum systems

Dominique Sugny

Dominique Sugny, Bernard Bonnard A

The objective of this article is to present techniques of geometric time-optimal control developed to analyze the control of two-level dissipative quantum systems. Combined with numerical simulations they allow to compute the time-minimal control using a shooting method. The robustness with respect to initial conditions and dissipative parameters is also analyzed using a continuation method.

Bernard Bonnard A, Dominique Sugny

The objective of this article is to apply recent developments in geometric optimal control to analyze the time minimum control problem of dissipative two-level quantum systems whose dynamics is governed by the Lindblad equation. We focus our analysis on the case where the extremal Hamiltonian is integrable.

Cyrill Kontz, Dominique Sugny, Hans Rudolf Jauslin

M. A. Jafarizadeh, Fahimeh Naghdi, M. R. Bazrafkan

L. C. Wang, X. L. Huang, X. X. Yi

We show that it is possible to modify the stationary state by a feedback control in a two-level dissipative quantum system. Based on the geometric control theory, we also analyze the effect of the feedback on the time-optimal control in the dissipative system governed by the Lindblad master equation. These effects are reflected in the functions ${\ensuremath{\Delta}}_{A}(\stackrel{P\vec}{x})$ and ${\ensuremath{\Delta}}_{B}(\stackrel{P\vec}{x})$, which characterize the optimal trajectories, as well as the switching functions $\ensuremath{\Phi}(t)$ and $\ensuremath{\theta}(t)$, which characterize the switching point in time for the time-optimal trajectory.