Time optimal simultaneous control of two level quantum systems

TL;DR

This paper develops a method to determine the minimum time control strategies for multiple two-level quantum systems simultaneously, expanding the understanding of quantum control on Lie groups.

Contribution

It provides an explicit description of the reachable set for multiple quantum systems, generalizing previous single-system results and proposing techniques applicable to broader right-invariant systems.

Findings

Explicit reachable set characterization for N quantum systems

Extension of time optimal control solutions to multiple systems

Potential applicability to larger classes of Lie group systems

Abstract

In this paper, we solve the problem of simultaneously driving in minimum time to arbitrary final conditions, N two level quantum systems subject to independent controls. The solution of this problem is obtained via an explicit description of the reachable set of the associated control system on SU(2). The treatment generalizes previous results on the time optimal control of two level quantum systems and suggests that similar techniques could be used to solve the minimum time control problem for a larger class of right invariant systems on Lie groups.