On the controllability of bilinear quantum systems

Dong Ning

Bilinear systems, matrix systems and right-invariant systems are distinguished first. Then controllability theorems of such three different systems are summarized, the key points focus on the necessary and sufficient controllability conditions for right-invariant systems, and the relation with bilinear systems. Controllability theorems of these three different systems are especially emphasized by using Lie groups and Lie algebra. Different controllability theorems of quantum systems using similar method are analyzed in detail. Corresponding relations of controllability between quantum systems with bilinear systems are pointed out by means of comparison, and each type of controllability applied to different situations are also given. Relationships among different notions of controllability of quantum systems are established.

Sonia G. Schirmer, I. C. H. Pullen, A. I. Solomon

Gabriel Turinici, HERSCHEL A. RABITZ

Qixing Zheng

By means of the achievement of bilinear systems theory research in the macroscopic fields, associated with the characteristic that the mathematical model of quantum mechanical system is bilinear, an iterative optimal controller for a quantum mechanical system is designed through the derivation of the optimal controller with two points boundary values problem. Also by the simulation experiment of states transfer control of the designed quantum system, the effects to control results with different control parameters are detailly analyzed.

Gabriel Turinici, HERSCHEL A. RABITZ

We present controllability results for quantum systems interacting with lasers. Exact controllability for the wavefunction in these bilinear systems is proved in the finite-dimensional case under very natural hypotheses.

TZYH JONG TARN, John W. Clark, Garng M. Huang