  The universal quantum computation is obtained when there exists asymmetric
anisotropic exchange between electron spins in coupled semiconductor quantum
dots. The asymmetric Heisenberg model can be transformed into the isotropic
model through the control of two local unitary rotations for the realization of
essential quantum gates. The rotations on each qubit are symmetrical and depend
on the strength and orientation of asymmetric exchange. The implementation of
the axially symmetric local magnetic fields can assist the construction of
quantum logic gates in anisotropic coupled quantum dots. This proposal can
efficiently use each physical electron spin as a logical qubit in the universal
quantum computation.
