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Quantum walks represent paradigmatic quantum evolutions, enabling powerfulapplications in the context of topological physics and quantum computation.They have been implemented in diverse photonic architectures, but therealization of a two-particle dynamics on a multi-dimensional lattice hashitherto been limited to continuous-time evolutions. To fully exploit thecomputational capabilities of quantum interference it is crucial to developplatforms handling multiple photons that propagate across multi-dimensionallattices. Here, we report a discrete-time quantum walk of two correlatedphotons in a two-dimensional lattice, synthetically engineered by manipulatinga set of optical modes carrying quantized amounts of transverse momentum.Mode-couplings are introduced via the polarization-controlled diffractiveaction of thin geometric-phase optical elements. The entire platform iscompact, efficient, scalable, and represents a versatile tool to simulatequantum evolutions on complex lattices. We expect that it will have a strongimpact on diverse fields such as quantum state engineering, topological quantumphotonics, and Boson Sampling.

Quantum walks of two correlated photons in a 2D synthetic lattice