Sudden switching in qubits

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.