  Non-reciprocity is an important topic in fundamental physics and
quantum-device design, as much effort has been devoted to its engineering and
manipulation. Here we experimentally demonstrate non-reciprocal transport in a
two-dimensional quantum walk of photons, where the directional propagation is
highly tunable through dissipation and synthetic magnetic flux. The
non-reciprocal dynamics hereof is a manifestation of the non-Hermitian skin
effect, with its direction continuously adjustable through the photon-loss
parameters. By contrast, the synthetic flux originates from an engineered
geometric phase, which competes with the non-Hermitian skin effect through
magnetic confinement. We further demonstrate how the non-reciprocity and
synthetic flux impact the dynamics of the Floquet topological edge modes along
an engineered boundary. Our results exemplify an intriguing strategy for
achieving tunable non-reciprocal transport, highlighting the interplay of
non-Hermiticity and gauge fields in quantum systems of higher dimensions.
