  We consider the problem of time-optimal control of quadrupole nucleus with
the spin I=1 by NMR. In contrast to the conventional methods based on selective
pulses, the control is implemented using nonselective pulses separated by free
evolution intervals. Using the Cartan decomposition, the system of equations is
obtained for finding parameters of a control field. Partial time-optimal
solutions for the important single-qutrit gates (selective rotations and
quantum Fourier transform) are found. The strong dependence of minimum gate
implementation times on global phase of the gate is observed. The analytical
values of minimum times are consistent with the numerical data.
