Quantum circuits with topological two-photon phases induced by interactions

The robustness of topologically protected few-particle states may open new horizons for quantum technologies. We study topological properties of a one-dimensional array of qubits coupled with their nearest neighbors via alternating connecting elements: either an inductance or Josephson junction. By deriving the circuit Hamiltonian, we demonstrate that the presence of coupling Josephson junctions gives rise to the effective photon-photon interactions inducing a non-trivial topological phase of bound photon pair accompanied by an in-gap topological edge state. Studying the effective Su-Schrieffer-Heeger model, we predict the interaction-induced topological transition.