  We simulate the control of the spin states in a two-electron double quantum
dot when an external detuning potential is used for passing the system through
an anticrossing. The hyperfine coupling of the electron spins with the
surrounding nuclei causes the anticrossing of the spin states but also the
decoherence of the spin states. We calculate numerically the singlet-triplet
decoherence for different detuning values and find a good agreement with
experimental measurement results of the same setup. We predict an interference
effect due to the coupling of T0 and T+ states.
