Optimal Quantum Feedback Control for Canonical Observables

John E. Gough

Optimal Quantum Feedback Control for Canonical Observables

Department of Physics

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Abstract

We consider the problem of optimal feedback control of a quantum system with linear dynamics undergoing continual non-demolition measurement of position and/or momentum, or both together. Specically, we show that a stable domain of solutions for the ltered state of the system will be given by a class of randomized squeezed states and we exercise the control problem amonst these states. Bellman's principle is then applied directly to optimal feedback control of such dynamical systems and the Hamilton Jacobi Bellman equation for the minimum cost is derived. The situation of quadratic performance criteria is treated as the important special case and solved exactly for the class of relaxed states.

Original language	English
Title of host publication	Quantum Stochastics and Information: Statistics, Filtering and Control
Publisher	World Scientific
Pages	262-279
Number of pages	18
ISBN (Print)	9789812832955
Publication status	Published - 12 Nov 2008

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N2 - We consider the problem of optimal feedback control of a quantum system with linear dynamics undergoing continual non-demolition measurement of position and/or momentum, or both together. Specically, we show that a stable domain of solutions for the ltered state of the system will be given by a class of randomized squeezed states and we exercise the control problem amonst these states. Bellman's principle is then applied directly to optimal feedback control of such dynamical systems and the Hamilton Jacobi Bellman equation for the minimum cost is derived. The situation of quadratic performance criteria is treated as the important special case and solved exactly for the class of relaxed states.

AB - We consider the problem of optimal feedback control of a quantum system with linear dynamics undergoing continual non-demolition measurement of position and/or momentum, or both together. Specically, we show that a stable domain of solutions for the ltered state of the system will be given by a class of randomized squeezed states and we exercise the control problem amonst these states. Bellman's principle is then applied directly to optimal feedback control of such dynamical systems and the Hamilton Jacobi Bellman equation for the minimum cost is derived. The situation of quadratic performance criteria is treated as the important special case and solved exactly for the class of relaxed states.

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SP - 262

EP - 279

BT - Quantum Stochastics and Information: Statistics, Filtering and Control

PB - World Scientific

ER -

Optimal Quantum Feedback Control for Canonical Observables

Abstract

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