

Problems of Mathematical Control Theory
March 4, 2016 15:00, Moscow, Steklov Mathematical Institute, Room 430 (8 Gubkina)






Some topics in control of twolevel quantum systems
N. B. Il'in^{} 
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Abstract:
This talk is devoted to some topics in control of twolevel quantum systems.
In the first part we will consider coherent control of quantum systems. The goal of control is to maximize the objective functional. A physical example of this problem is control of spin 1/2 system by laser pulse. An important problem is the analysis of traps — local but not global maxima of the objective functional. We will present some theorems about traps for twolevel quantum systems.
In the second part we will consider incoherent control of twolevel quantum systems using nonselective measurements as control. In addition to the unitary evolution, the system state is transformed under backaction of nonselective measurements of some observables $Q_i$, $1\le i\le n$, at times $t_i$. The control goal is to maximize an objective functional on the set of sequences $Q_1,...,Q_n$. This problem can be used to approximate the quantum Zeno effect. The theorem which gives explicit expressions for the optimal observables will be presented.

