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