  Correct swap action can be realized via the control of the anisotropic
Heisenberg interaction in solid-state quantum systems. The conditions of
performing a swap are derived by the dynamics of arbitrary bipartite pure
state. It is found that swap errors can be eliminated in the presence of
symmetric anisotropy. In realistic quantum computers with unavoidable
fluctuations, the gate fidelity of swap action is estimated. The scheme of
quantum computation via the anisotropic Heisenberg interaction is implemented
in a one dimensional quantum dots. The slanting and static magnetic field can
be used to adjust the anisotropy.
