Realization of higher winding number topological states of the long-range magnonic SSH model using superconducting circuits*

Superconducting circuits are emerging as a promising platform to probe topological phenomena that are difficult to observe in real materials. The Su-Schrieffer-Heeger (SSH) model is the paradigmatic example of a Hamiltonian exhibiting nontrivial topological invariants and topological insulator states. While the topological states of the magnonic SSH model have been realized in superconducting platforms, the topological phases of the extended SSH model with long-range interactions have not been reported on any experimental platform. Here, we report the realization of topological states of the extended magnonic SSH model using an analog superconducting circuit quantum simulator with all-to-all connections. We measure the winding number of the topological phases and probe the topological edge states by introducing single-qubit excitations. Our results paves the way to realize other exotic topological phases using superconducting circuits.