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

The quasi-degenerate ground state manifold of the anisotropic Ising spin model can encode quantum information, but its degree of protection against local perturbations is known to be only partial. We explain how the coupling between the two ground states can be used to observe signatures of Majorana zero modes in a small controlled chain of qubits. We argue that the protection against certain local perturbations persists across a range of parameters even away from the ideal point. Remarkably, when additional non-local interactions are considered the system enters a phase where the ground states are fully protected against all local field perturbations.