Programmable nonlinear quantum photonic circuits.

The lack of interactions between single photons prohibits direct nonlinear operations in quantum optical circuits, representing a central obstacle in photonic quantum technologies. Here, we demonstrate multi-mode nonlinear photonic circuits where both linear and direct nonlinear operations can be programmed with high precision at the single-photon level. Nonlinear interaction is realised with a tunable quantum dot embedded in a nanophotonic waveguide mediating interactions between individual photons within a temporal linear optical interferometer. We demonstrate the capability to reprogramme the nonlinear photonic circuits and implement protocols where strong nonlinearities are required, in particular for quantum simulation of anharmonic molecular dynamics, thereby showcasing the new key functionalities enabled by our technology.