  We theoretically analyze the dynamical evolution of photonic quantum walks on
M\"obius strips and other exotic structures in 3D integrated photonics. Our
flexible design allows discrete observations of continuous time quantum walks
of photons in a variety of waveguide arrays. Furthermore, our design allows one
to inject photons during the evolution, allowing the possibility of interacting
with the photons as they are 'walking'. We find that non-trivial array
topologies introduce novel time-dependent symmetries of the two-photon
correlations. These properties allow a large degree of control for quantum
state engineering of multimode entangled states in these devices.
