  We introduce an extended Dicke model with controllable long-range atom-atom
interaction to simulate topologically ordered states and achieve
decoherence-protected qubits. We illustrate our idea in an experimentally
feasible circuit quantum electrodynamics scenario. Due to the intrinsic
competition with the atom-field coupling strength, we first demonstrate that
this atom-atom interaction can exhibit a novel topological quantum interference
effect arising from the instanton and anti-instanton tunneling paths. As a
consequence, this proposed model only with a few odd-number of atoms has a
two-fold absolute degenerate ground-subspace with a large energy gap, which can
become larger with the increasing of the system-size. It may also support the
excitation of anyonic statistics, and thus can be regarded as a possible
candidate for processing topological quantum memory.
