Quantum physics is opening new pathways for processing and transmitting information, enabling powerful applications in quantum computing, simulation, and communication. Photons lie at the core of this revolution, acting as versatile carriers of quantum information. A major challenge is to miniaturize these operations onto a single chip and exploit high-dimensional quantum states for greater scalability. This internship/PhD project aims to address these challenges using arrays of nonlinear waveguides. Besides serving as efficient sources of entangled states, waveguide arrays also provide a powerful platform for quantum simulation. We recently demonstrated how such systems can implement 1D topological Hamiltonians and protect photon-pair generation from disorder. The project aims to extend this approach to higher dimensions by exploiting synthetic dimensions, where internal photonic modes emulate additional spatial coordinates to realize complex Hamiltonians. This framework will be used to simulate Floquet topological insulators, implement a topological pump for the robust transfer of entangled states, and explore how decoherence can enhance quantum transport. Together, these studies will establish waveguide arrays with synthetic dimensions as a powerful platform for simulating condensed matter problems in a well-controlled environment and probing new regimes of light–matter interaction tailored at the microscale.