  Graph representations are a powerful concept for solving complex problems
across natural science, as patterns of connectivity can give rise to a
multitude of emergent phenomena. Graph-based approaches have proven
particularly fruitful in quantum communication and quantum search algorithms in
highly branched quantum networks. Here we introduce a new paradigm for the
direct experimental realization of excitation dynamics associated with
three-dimensional networks by exploiting the hybrid action of spatial and
polarization degrees of freedom of photon pairs in complex waveguide circuits
with tailored birefringence. This novel testbed for the experimental
exploration of multi-particle quantum walks on complex, highly connected graphs
paves the way towards exploiting the applicative potential of fermionic
dynamics in integrated quantum photonics.
