Time-optimal Control of Spin Systems

TL;DR

This paper explores methods for achieving time-optimal control of quantum spin systems by reducing the problem to geometric control on homogeneous spaces, providing explicit solutions in symmetric cases.

Contribution

It introduces a reduction technique to simplify the control problem on Lie groups to homogeneous spaces and explicitly solves for optimal trajectories in symmetric cases.

Findings

Reduction of control problems to homogeneous spaces G/H

Explicit determination of optimal trajectories on symmetric spaces

Application of Lie theory and geometric control methods

Abstract

The paper discusses various aspects of time-optimal control of quantum spin systems, modelled as right-invariant systems on a compact Lie group G. The main results are the reduction of such a system to an equivalent system on a homogeneous space G/H, and the explicit determination of optimal trajectories on G/H in the case where G/H is a Riemannian symmetric space. These results are mainly obtained by using methods from Lie theory and geometric control.