  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.
