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

Exact solutions for time-optimal control of spin I=1 by NMR