  Photonic circuits, optical platforms that connect input and output modes
according to a specific map, serve as effective optical processors for both
classical and quantum states of light. The number of optical elements typically
scales with that of processed modes, leading to a direct correlation between
system size, circuit complexity, and optical losses. Here we present a photonic
circuit technology implementing large-scale unitary maps, linking a single
input to hundreds of output modes in a two-dimensional compact layout. The map
corresponds to the outcome of a quantum walk of structured photons, realized
experimentally through light propagation in three liquid-crystal metasurfaces,
having the local orientation of optic axes artificially engineered in a complex
pattern. Theoretically, the walk length and the number of connected modes can
be arbitrary, keeping optical losses constant. The patterns can be designed to
accurately replicate multiple unitary maps. We also discuss limited
reconfigurability by adjusting the overall birefringence and the relative
displacement of the three optical elements. These results lay the basis for the
design of low-loss photonic circuits that target a broader range of unitary
maps, primarily for manipulating multi-photon states in genuinely quantum
regimes.
