Pierre Rouchon - Quantum systems and control 1

arima:1904 - Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, September 22, 2008, Volume 9, 2007 Conference in Honor of Claude Lobry, 2008 - https://doi.org/10.46298/arima.1904
Quantum systems and control 1

Authors: Pierre Rouchon

This paper describes several methods used by physicists for manipulations of quantum states. For each method, we explain the model, the various time-scales, the performed approximations and we propose an interpretation in terms of control theory. These various interpretations underlie open questions on controllability, feedback and estimations. For 2-level systems we consider: the Rabi oscillations in connection with averaging; the Bloch-Siegert corrections associated to the second order terms; controllability versus parametric robustness of open-loop control and an interesting controllability problem in infinite dimension with continuous spectra. For 3-level systems we consider: Raman pulses and the second order terms. For spin/spring systems we consider: composite systems made of 2-level sub-systems coupled to quantized harmonic oscillators; multi-frequency averaging in infinite dimension; controllability of 1D partial differential equation of Shrödinger type and affine versus the control; motion planning for quantum gates. For open quantum systems subject to decoherence with continuous measures we consider: quantum trajectories and jump processes for a 2-level system; Lindblad-Kossakovsky equation and their controllability.

Volume: Volume 9, 2007 Conference in Honor of Claude Lobry, 2008
Published on: September 22, 2008
Submitted on: March 23, 2008
Keywords: Quantum systems, Schrödinger equations, decoherence and open quantum systems, controllability, averaging and second order approximation,Systèmes quantiques,équation de Schrödinger,dé-cohérence et systèmes quantiques ouverts,contrôlabilité,moyennisation et approximation du second order,[INFO] Computer Science [cs],[MATH] Mathematics [math]


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