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We theoretically analyze the dynamical evolution of photonic quantum walks onM\"obius strips and other exotic structures in 3D integrated photonics. Ourflexible design allows discrete observations of continuous time quantum walksof photons in a variety of waveguide arrays. Furthermore, our design allows oneto inject photons during the evolution, allowing the possibility of interactingwith the photons as they are 'walking'. We find that non-trivial arraytopologies introduce novel time-dependent symmetries of the two-photoncorrelations. These properties allow a large degree of control for quantumstate engineering of multimode entangled states in these devices.

Discretely-observable continuous time quantum walks on M\"obius strips and other exotic structures in 3D integrated photonics