  Analytic solutions are developed for two-state systems (e.g. qubits) strongly
perturbed by a series of rapidly changing pulses, called `kicks'. The evolution
matrix may be expressed as a time ordered product of evolution matrices for
single kicks. Single, double, and triple kicks are explicitly considered, and
the onset of observability of time ordering is examined. The effects of
different order of kicks on the dynamics of the system are studied and compared
with effects of time ordering in general. To determine the range of validity of
this approach, the effect of using pulses of finite widths for 2s-2p
transitions in atomic hydrogen is examined numerically.
