Optimal and Robust Feedback Control of Quantum Systems

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Copyright: Sayed Hassen, S. Z.
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Abstract
Quantum systems have been traditionally subjected to ad hoc control approaches, which although effective, can be restrictive in terms of performance. In an effort to provide for a wider range of potential applications of the next generation of quantum technology, more sophisticated control schemes which can squeeze maximum performance from the closed-loop system are necessary. There is no doubt that the knowledge and use of quantum models in the controller design process, can lead to improved performance. In this thesis, we consider three topics of interest in the broad field of quantum control. The motivation for the first two topics arises out of a need to devise systematic control schemes to optimally control practical quantum systems. We show that for some important problems arising in quantum technology, the application of optimal control schemes can (in theory) achieve performance levels which are limited only by the quantum noises present in the system. The quantum systems we consider are of current interest to experimentalists and physicists working in the field of quantum optics. In the last topic of this thesis, we investigate a robust theoretical approach to the control of quantum systems. Quantum systems are very rarely known to a high degree of accuracy and in particular, they are afflicted by additional sources of uncertainty which are not present in classical systems. Here, we model uncertainty in the “observables” of the quantum systems and using the concept of relative entropy and the framework of Radon-Nikodym derivatives, we formulate and extend a quantum version of the classical risk-sensitive control result. The risk-sensitive control approach is known to possess inherent robust properties and we use a quantum version of this result to determine an upper bound on the cost of a riskneutral problem, obtained using a nominal model of a simple quantum system. Next, we give an overview of each topic.
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Author(s)
Sayed Hassen, S. Z.
Supervisor(s)
Petersen, Ian
James, Matthew
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Publication Year
2010
Resource Type
Thesis
Degree Type
PhD Doctorate
UNSW Faculty
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