Lie Algebraic Analysis and Control of Quantum Dynamics
Abstract
Description
In this paper, we show how to use the analysis of the Lie algebra associated with a quantum mechanical system to study its dynamics and facilitate the design of controls. We give algorithms to decompose the dynamics and describe their application to the control of two coupled spin 1/2's.
New version. It does not contain the application to quantum walks. This part in the previous version contained an error. It has been corrected and expanded in a new paper called `Analysis of quantum walks with time varying coin on d-dimensional lattices' to be posted on the archives. Also a proof in the previous version was incomplete and it has been corrected
New version. It does not contain the application to quantum walks. This part in the previous version contained an error. It has been corrected and expanded in a new paper called `Analysis of quantum walks with time varying coin on d-dimensional lattices' to be posted on the archives. Also a proof in the previous version was incomplete and it has been corrected