Time optimal simultaneous control of two level quantum systems

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.