Abstract
Topological qubits based on -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 -rotation by angle , 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.