  Topological qubits based on $SU(N)$-symmetric valence-bond solid models are
constructed. A logical topological qubit is the ground subspace with two-fold
degeneracy, which is due to the spontaneous breaking of a global parity
symmetry. A logical $Z$-rotation by angle $\frac{2\pi}{N}$, for any integer $N
> 2$, is provided by a global twist operation, which is of topological nature
and protected by the energy gap. A general concatenation scheme with standard
quantum error-correction codes is also proposed, which can lead to better
codes. Generic error-correction properties of symmetry-protected topological
order are also demonstrated.

Quantum Physics;Strongly Correlated Electrons