Non-Abelian Geometric Manipulation of a Crystal of Molecular NanomagnetMn12

Based on the strong magnetic anisotropy along the symmetry of the crystal, we construct a U(2) non-Abelian gauge potential for the molecular nanomagnet Mn₁₂ by varying the external magnetic field adiabatically. Moreover, the non-Abelian geometric phase and the unitary matrix operation, which are the key steps to realize the universal holonomic quantum computing in the degenerate subspace, are also obtained by means of choosing an evolution path properly.