  Topological phases of matter is a natural place for encoding robust qubits
for quantum computation. In this work we extend the newly introduced class of
qubits based on valence-bond solid models with SPT (symmetry-protected
topological) order to more general cases. Furthermore, we define and compare
various classes of topological qubits encoded in the bulk ground states of
topological systems, including SSB (spontaneous symmetry-breaking), TOP
(topological), SET (symmetry-enriched topological), SPT, and subsystem SPT
classes. We focus on several features for qubits to be robust, including error
sets, logical support, code distance and shape of logical gates. In particular,
when a global U(1) symmetry is present and preserved, we find a twist operator
that extracts the SPT order plays the role of a topological logical operator,
which is suitable for global implementation.
