  We apply an extension of the Pontryagin Maximum Principle to derive
time-optimal controls of two-level quantum systems by means of piecewise
constant pulses. Global optimal solutions are obtained for state-to-state
transfer in the cases with one and two controls. Exact quantum speed limits are
established as a function of the sampling period. We observe numerically an
exponential convergence towards the minimum time in the continuous limit when
this period goes to zero. We show that this convergence is only polynomial for
a linearized quantum system. We discuss the experimental impact of this result.
