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