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arXiv · 1210.7127

Modeling and Control of Quantum Systems: An Introduction

Claudio Altafini·Francesco Ticozzi
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Abstract

The scope of this work is to provide a self-contained introduction to a selection of basic theoretical aspects in the modeling and control of quantum mechanical systems, as well as a brief survey on the main approaches to control synthesis. While part of the existing theory, especially in the open-loop setting, stems directly from classical control theory (most notably geometric control and optimal control), a number of tools specifically tailored for quantum systems have been developed since the 1980s, in order to take into account their distinctive features: the probabilistic nature of atomic-scale physical systems, the effect of dissipation and the irreversible character of the measurements have all proved to be critical in feedback-design problems. The relevant dynamical models for both closed and open quantum systems are presented, along with the main results on their controllability and stability. A brief review of several currently available control design methods is meant to provide the interested reader with a roadmap for further studies.

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Claudio Altafini, Francesco Ticozzi. 2012-10-26. Modeling and Control of Quantum Systems: An Introduction. https://doi.org/10.1109/tac.2012.2195830

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