Section: New Results

Optimal control for quantum systems and applications to MRI

Participants : Bernard Bonnard, Thierry Combot [Université de Bourgogne, IMB] , Alain Jacquemard [Université de Bourgogne, IMB] , Dominique Sugny [Université de Bourgogne, LIC] .

Important results have been obtained in this aera that we detail next :

• A complete solution to the time minimal control of a chain of three spins with Ising coupling which is a toy example applicable to quantum computing [42] , [3] .

• Optimal control of an ensemble of spins systems with application to MRI : this work is performed in the framework of the ANR project Explosys , based on our previous results in the contrast problem in Nuclear Magnetic Imaging. In relation with the laboratory Creatis (Insa Lyon) and TUM (S. Glaser) the objective is to design robust pulses control, with respect to the relaxation parameters and the B0 and B1 inhomogneities. The computations are intricated from both the numerical point of view and exact computaions. From this second point a systematic study of the controlled Bloch equation has been initiated using exact computer algebraic method in relation with the Inria project-team POLSYS .