Combining the generation and manipulation of complex quantum states of light on a single chip is a crucial step toward practical quantum information technologies. In this internship/PhD project, we will address this challenge by merging two fundamental concepts —nonlinear optics and quantum walks— to realize a compact and versatile source of spatially entangled states of light, and harness them for quantum simulation and quantum state engineering tasks. For this we will tune the coupling between waveguides to implement various lattice geometries, allowing to implement the quantum Fourier transforms of entangled states, Anderson localization in a quasi-periodic potential, or the topological protection of quantum states of light in the Su-Schrieffer-Heeger model. This opens up the stimulating perspective to simulate with photons physical problems that are otherwise difficult to access in condensed matter systems.