Bellman equations for optimal feedback control of qubit states
TLDR
In this article, an optimal control strategy for an open two-level system (a qubit in interaction with the electromagnetic field) controlled by a laser is derived using results from quantum filtering theory and methods from classical control theory.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.read more
Citations
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Journal ArticleDOI
An Introduction to Quantum Filtering
TL;DR: In this paper, an introduction to quantum probability theory is given, focusing on the spectral theorem and the conditional expectation as a least squares estimate, and culminating in the construction of Wiener and Poisson processes on the Fock space.
Journal ArticleDOI
A Discrete Invitation to Quantum Filtering and Feedback Control
TL;DR: This expository paper demonstrates estimation and feedback control of quantum mechanical systems in what is essentially a noncommutative version of the binomial model that is popular in mathematical finance and allows a full development of the theory while remaining completely within the setting of finite-dimensional Hilbert spaces.
Proceedings ArticleDOI
On the Separation Principle in Quantum Control
Luc Bouten,Ramon van Handel +1 more
Posted Content
Optimal Quantum Filtering and Quantum Feedback Control
TL;DR: In this article, a quantum Bellman equation is applied to the explicitly solvable quantum linear-quadratic-Gaussian (LQG) problem, which emphasizes many similarities with the corresponding classical control problem.
Journal ArticleDOI
Quantum games: a review of the history, current state, and interpretation
TL;DR: This work reviews both theoretical and experimental developments in the area of quantum games since the inception of the subject circa 1999 and offers a narrative on the controversy that surrounded the subject in its early days.
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