Université Paul Sabatier - Bat. 3R1b4 - 118 route de Narbonne 31062 Toulouse Cedex 09, France

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Optimal control of quantum systems with applications in Quantum Technologies

Salle de séminaire de FeRMI, bât 3R1b4 3e étage portes N325 et 327

Abstract :
Optimal control can be viewed as a generalization of the classical calculus of variations for problems with dynamical constraints. Optimal control is born in its modern version with the Pontryagin Maximum Principle in the late 1950’s. Its development was originally inspired by problems of space mechanics, but it is now a key tool to study a large spectrum of applications extending from robotics and electronics to quantum mechanics. Solving an optimal control problem means finding a particular control law (i.e. a particular pulse sequence), the optimal control, such that the corresponding trajectory satisfies given boundary conditions and minimizes a cost criterion. Although its implementation looks straightforward, the practical use of optimal control techniques is far from being trivial and each control problem has to be investigated using geometric and numerical methods.
This talk is aimed at giving an introduction and a general overview of the current
development of optimal control theory and of its application in the design of control pulses for Quantum Technologies. Both geometric and numerical approaches will be described and applied to control quantum dynamics. Different examples (with experimental results) will be treated such as the control of spin systems in Magnetic Resonance, the control of molecular rotation or the control of Bose Einstein Condensates. Short and long-term perspectives will be discussed.

Quantum optimal control in quantum technologies. Strategic report on current status, visions ans goals for research in Europe C. P. Koch, U. Boscain, T. Calarco, G. Dirr, S. Filipp, S. Glaser, R. Kosloff, S. Montangero, T. Schulte-Herbruggen, D. Sugny and F. K. Wilhelm submitted to Eur. J. Phys. (2022)

Introduction to the Pontryagin Maximum Principle for Quantum Optimal Control
U. Boscain, M. Sigalotti and D. Sugny
PRX Quantum 2, 030203 (2021)

Quantum control of molecular rotation
C. P. Koch, M. Lemeshko and and D. Sugny
Rev. Mod. Phys. 91, 035005 (2019)