A Review of Geometric Optimal Control for Quantum Systems in Nuclear Magnetic Resonance | Zendy

Bernard Bonnard | Zendy; Steffen J. Glaser | Zendy; Dominique Sugny | Zendy

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A Review of Geometric Optimal Control for Quantum Systems in Nuclear Magnetic Resonance

Author(s) -

Bernard Bonnard,

Steffen J. Glaser,

Dominique Sugny

Publication year - 2012

Publication title -

advances in mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.283

H-Index - 23

eISSN - 1687-9139

pISSN - 1687-9120

DOI - 10.1155/2012/857493

Subject(s) - optimal control , gravitational singularity , computation , hamiltonian (control theory) , pontryagin's minimum principle , maximum principle , mathematics , point (geometry) , mathematical optimization , physics , computer science , mathematical analysis , algorithm , geometry

International audienceWe present a geometric framework to analyze optimal control problems of uncoupled spin 1/2 particles occurring in nuclear magnetic resonance. According to the Pontryagin's maximum principle, the optimal trajectories are solutions of a pseudo-Hamiltonian system. This computation is completed by sufficient optimality conditions based on the concept of conjugate points related to Lagrangian singularities. This approach is applied to analyze two relevant optimal control issues in NMR: the saturation control problem, that is, the problem of steering in minimum time a single spin 1/2 particle from the equilibrium point to the zero magnetization vector, and the contrast imaging problem. The analysis is completed by numerical computations and experimental results

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