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Synthetic dimensions have generated great interest for studying many types oftopological, quantum, and many-body physics, and they offer a flexible platformfor simulation of interesting physical systems, especially in high dimensions.In this Letter, we describe a programmable photonic device capable of emulatingthe dynamics of a broad class of Hamiltonians in lattices with arbitrarytopologies and dimensions. We derive a correspondence between the physics ofthe device and the Hamiltonians of interest, and we simulate the physics of thedevice to observe a wide variety of physical phenomena, including chiral statesin a Hall ladder, effective gauge potentials, and oscillations inhigh-dimensional lattices. Our proposed device opens new possibilities forstudying topological and many-body physics in near-term experimental platforms.

Programmable photonic system for quantum simulation in arbitrary topologies