  Recent discoveries in topological physics hold a promise for disorder-robust
quantum systems and technologies. Topological states provide the crucial
ingredient of such systems featuring 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.
