  The possibility of fine-tuning the couplings between optical modes is a key
requirement in photonic circuits for quantum simulations. In these
architectures, emulating the long-time evolution of particles across large
lattices requires sophisticated setups, that are often intrinsically lossy.
Here we report ultra-long photonic quantum walks across several hundred optical
modes, obtained by propagating a light beam through very few closely-stacked
liquid-crystal metasurfaces. By exploiting spin-orbit effects, these implement
space-dependent polarization transformations that mix circularly polarized
optical modes carrying quantized transverse momentum. As each metasurface
implements long-range couplings between distant modes, by using only a few of
them we simulate quantum walks up to 320 discrete steps without any optical
amplification, far beyond state-of-the-art experiments. To showcase the
potential of this method, we experimentally demonstrate that in the long-time
limit a quantum walk affected by dynamical disorder generates maximal
entanglement between two system partitions. Our platform grants experimental
access to large-scale unitary evolutions while keeping optical losses at a
minimum, thereby paving the way to massive multi-photon multi-mode quantum
simulations.
