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We consider the problem of time-optimal realization of the quantum Fouriertransform gate for a single qudit with number of levels d from 3 to 8. As aqudit the quadrupole nucleus with spin I > 1/2 controlled by NMR is considered.We calculate the dependencies of the gate error on the duration ofradio-frequency pulse obtained by numerical optimization using Krotov-basedalgorithm. It is shown that the dependences of minimum time of QFT gateimplementation on qudit dimension are different for integer and half-integerspins.

On the time-optimal implementation of quantum Fourier transform for qudits represented by quadrupole nucleus