  Quantum walks are powerful tools for quantum applications and for designing
topological systems. Although they are simulated in a variety of platforms,
genuine two-dimensional realizations are still challenging. Here we present an
innovative approach to the photonic simulation of a quantum walk in two
dimensions, where walker positions are encoded in the transverse wavevector
components of a single light beam. The desired dynamics is obtained by means of
a sequence of liquid-crystal devices, which apply polarization-dependent
transverse "kicks" to the photons in the beam. We engineer our quantum walk so
that it realizes a periodically-driven Chern insulator, and we probe its
topological features by detecting the anomalous displacement of the photonic
wavepacket under the effect of a constant force. Our compact, versatile
platform offers exciting prospects for the photonic simulation of
two-dimensional quantum dynamics and topological systems.
