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A variety of topological Hamiltonians have been demonstrated in photonicplatforms, leading to fundamental discoveries and enhanced robustness inapplications such as lasing, sensing, and quantum technologies. To date, eachtopological photonic platform implements a specific type of Hamiltonian withinexistent or limited reconfigurability. Here, we propose and demonstratedifferent topological models by using the same reprogrammable integratedphotonics platform, consisting of a hexagonal mesh of silicon Mach-Zehnderinterferometers with phase-shifters. We specifically demonstrate aone-dimensional Su-Schrieffer-Heeger Hamiltonian supporting a localizedtopological edge mode and a higher-order topological insulator based on atwo-dimensional breathing Kagome Hamiltonian with three corner states. Theseresults highlight a nearly universal platform for topological models that mayfast-track research progress toward applications of topological photonics andother coupled systems.

Programmable Integrated Photonics for Topological Hamiltonians