  In this work we study extrema of objective functionals for ultrafast
manipulation by a qubit. Traps are extrema of the objective functionals which
are optimal for manipulation by quantum systems only locally but not globally.
Much effort in prior works was devoted to the analysis of traps for quantum
systems controlled by long enough laser pulses and, for example, manipulation
by a qubit with long control pulses was shown to be trap-free. Ultrafast
femtosecond and attosecond control becomes now widely applicable that motivates
the necessity for the analysis of traps on the ultrafast time scale. We do such
analysis for a qubit and show that ultrafast state transfer in a qubit remains
trap-free for a wide range of the initial and final states of the qubit. We
prove that for this range the probability of transition between the initial and
the final states has a saddle but has no traps.
