  Multi-dimensional quantum walks can exhibit highly non-trivial topological
structure, providing a powerful tool for simulating quantum information and
transport systems. We present a flexible implementation of a 2D optical quantum
walk on a lattice, demonstrating a scalable quantum walk on a non-trivial graph
structure. We realized a coherent quantum walk over 12 steps and 169 positions
using an optical fiber network. With our broad spectrum of quantum coins we
were able to simulate the creation of entanglement in bipartite systems with
conditioned interactions. Introducing dynamic control allowed for the
investigation of effects such as strong non-linearities or two-particle
scattering. Our results illustrate the potential of quantum walks as a route
for simulating and understanding complex quantum systems.
