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Bellman equations for optimal feedback control of qubit states

Luc Bouten·Simon Edwards·V P Belavkin
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Abstract

Using results from quantum filtering theory and methods from classical control theory, we derive an optimal control strategy for an open two-level system (a qubit in interaction with the electromagnetic field) controlled by a laser. The aim is to optimally choose the laser's amplitude and phase in order to drive the system into a desired state. The Bellman equations are obtained for the case of diffusive and counting measurements for vacuum field states. A full exact solution of the optimal control problem is given for a system with simpler, linear, dynamics. These linear dynamics can be obtained physically by considering a two-level atom in a strongly driven, heavily damped, optical cavity.

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Luc Bouten, Simon Edwards, V P Belavkin. 2005-03-21. Bellman equations for optimal feedback control of qubit states. https://doi.org/10.1088/0953-4075/38/3/002

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