Quantum state processing through controllable synthetic temporal photonic lattices.

Quantum walks on photonic platforms represent a physics-rich framework for quantum measurements, simulations and universal computing. Dynamic reconfigurability of photonic circuitry is key to controlling the walk and retrieving its full operation potential. Universal quantum processing schemes based on time-bin encoding in gated fibre loops have been proposed but not demonstrated yet, mainly due to gate inefficiencies. Here we present a scalable quantum processor based on the discrete-time quantum walk of time-bin-entangled photon pairs on synthetic temporal photonic lattices implemented on a coupled fibre-loop system. We utilize this scheme to path-optimize quantum state operations, including the generation of two- and four-level time-bin entanglement and the respective two-photon interference. The design of the programmable temporal photonic lattice enabled us to control the dynamic of the walk, leading to an increase in the coincidence counts and quantum interference measurements without recurring to post-selection. Our results show how temporal synthetic dimensions can pave the way towards efficient quantum information processing, including quantum phase estimation, Boson sampling and the realization of topological phases of matter for high-dimensional quantum systems in a cost-effective, scalable and robust fibre-based setup.