Protected ground states in short chains of coupled spins in circuit quantum electrodynamics

The two degenerate ground states of the anisotropic Heisenberg (XY) spin model of a chain of qubits (pseudospins) can encode quantum information, but their degree of protection against local perturbations is known to be only partial. We examine the properties of the system in the presence of nonlocal spin-spin interactions, possibly emerging from the quantum electrodynamics of the device. We find a phase distinct from the XY phase admitting two ground states which are highly protected against all local field perturbations, persisting across a range of parameters. In the context of the XY chain we discuss how the coupling between two ground states can be used to observe signatures of topological edge states in a small controlled chain of superconducting transmon qubits.