Numerical Solution of the Dynamic Programming Equation for the Optimal Control of Quantum Spin Systems
Quantum Physics
2011-10-05 v2 Optimization and Control
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.
Cite
@article{arxiv.1002.3067,
title = {Numerical Solution of the Dynamic Programming Equation for the Optimal Control of Quantum Spin Systems},
author = {Srinivas Sridharan and Matthew R. James},
journal= {arXiv preprint arXiv:1002.3067},
year = {2011}
}
Comments
11 pages, 5 figures