  There is great interest in designing photonic devices capable of
disorder-resistant transport and information processing. In this work we
propose to exploit 3D integrated photonic circuits in order to realize 2D
discrete-time quantum walks in a background synthetic gauge field. The gauge
fields are generated by introducing the appropriate phase shifts between
waveguides. Polarization-independent phase shifts lead to an Abelian or
magnetic field, a case we describe in detail. We find that, in the disordered
case, the magnetic field enhances transport due to the presence of
topologically protected chiral edge states which do not localize.
Polarization-dependent phase shifts lead to effective non-Abelian gauge fields,
which could be adopted to realize Rashba-like quantum walks with spin-orbit
coupling. Our work introduces a flexible platform for the experimental study of
multi-particle quantum walks in the presence of synthetic gauge fields, which
paves the way towards topologically robust transport of many-body states of
photons.
