  The ultimate accuracy as regards controlling a qubit with a coherent field is
studied in terms of degradation of the fidelity by employing a fully quantum
mechanical treatment. While the fidelity error accompanied by pi/2 pulse
control is shown to be inversely proportional to the average photon number in a
way similar to that revealed by the Gea-Banacloche's results. Our results show
that the error depends strongly on the initial state of the qubit. When the
initial state of the qubit is in the ground state, the error is about 20 times
smaller than that of the control started from the exited state, no matter how
large N is. This dependency is explained in the context of an exact quantum
mechanical description of the pulse area theorem. By using the result, the
error accumulation tendency of successive pulse controls is found to be both
non-linear and initial state-dependent.
