increased robustness to disorder and imperfections. Here, we use an array of superconducting qubits to engineer a one-dimensional topologically nontrivial quantum metamaterial. By performing microwave spectroscopy of the fabricated array, we experimentally observe the spectrum of elementary excitations. We find not only the single-photon topological states but also the bands of exotic bound photon pairs arising due to the inherent anharmonicity of qubits. Furthermore, we detect the signatures of the two-photon bound edge-localized state which hints towards interaction-induced localization in our system. Our work demonstrates an experimental implementation of the topological model with attractive photon-photon interaction in a quantum metamaterial.