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The realization of novel phases of matter on quantum simulators is a topic of intense interest.Digital quantum computers offer a route to prepare topological phases with interactions that do not naturally arise in analog quantum simulators. Here, we report the realization of symmetryprotected topological (SPT) phases of a spin-1/2 Hamiltonian with next-nearest-neighbor hopping on up to 11 qubits on a programmable superconducting quantum processor. We observe clear signatures of the two distinct SPT phases, such as excitations localized to specific edges and finite string order parameters. Our work advances ongoing efforts to realize novel states of matter with exotic interactions on digital near-term quantum computers.