Dynamic programming and viscosity solutions for the optimal control of quantum spin systems

DOI10.1016/J.SYSCONLE.2011.05.010zbMATH Open1229.49027arXiv1002.3067OpenAlexW1581750055MaRDI QIDQ645578

Matthew R. James, Srinivas Sridharan

Publication date: 10 November 2011

Published in: Systems \& Control Letters (Search for Journal in Brave)

Abstract: The purpose of this paper is to describe the numerical solution of the Hamilton-Jacobi-Bellman (HJB) for an optimal control problem for quantum spin systems. This HJB equation is a first order nonlinear partial differential equation defined on a Lie group. We employ recent extensions of the theory of viscosity solutions from Euclidean space to Riemannian manifolds to interpret possibly non-differentiable solutions to this equation. Results from differential topology on the triangulation of manifolds are then used to develop a finite difference approximation method, which is shown to converge using viscosity solution techniques. An example is provided to illustrate the method.

Full work available at URL: https://arxiv.org/abs/1002.3067

zbMATH Keywords

optimal controlnumerical methoddynamic programmingviscosity solutionquantum spin systems

Mathematics Subject Classification ID

Dynamic programming in optimal control and differential games (49L20) Dynamic programming (90C39) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) Quantum coherence, entanglement, quantum correlations (81P40)

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Related Items (2)

Solution to the HJB equation for LQR-type problems on compact connected Lie groups ⋮ A reduced complexity MIN-plus solution method to the optimal control of closed quantum systems

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