  We consider the problem of controlling in minimum time a two-level quantum
system which can be subject to a drift. The control is assumed to be bounded in
magnitude, and to affect two or three independent generators of the dynamics.
We describe the time optimal trajectories in $SU(2)$, the Lie group of possible
evolutions for the system, by means of a particularly simple parametrization of
the group. A key ingredient of our analysis is the introduction of the optimal
front line. This tool allows us to fully characterize the time-evolution of the
reachable sets, and to derive the worst-case operators and the corresponding
times. The analysis is performed in any regime: controlled dynamics stronger,
of the same magnitude or weaker than the drift term, and gives a method to
synthesize quantum logic operations on a two-level system in minimum time.
