Fig. 1: Schematics of the programmable nonlinear quantum photonic circuit.

a The programmable nonlinear photonic circuit comprises tunable QD nonlinear transformations interleaved between two controllable linear optical circuits implemented via time-bin Mach-Zehnder interferometers that couple a pair of temporal optical modes. The photons are injected into the circuit in the first spatial mode and subsequently interfere and interact via linear and nonlinear operations, respectively. The transmitted photons are finally recorded with pseudo-photon-number-resolution (pPNR) using SNSPDs. b SEM image of the GaAs nanophotonic device, which is used to implement the nonlinear interaction by scattering the photons off an InAs QD embedded in a photonic crystal waveguide. Grating couplers are used for in- and out-coupling of photons from the device to interconnect it with the linear parts of the circuit. The electric field across the QD is controlled with electrodes (highlighted in yellow) that allow tuning of the nonlinear interaction by controlling the detuning Δ between the QD resonance and the incoming photons via the DC Stark effect. c Schematic of the linear optical setup. The pair of optical modes represented in a) are here encoded in the temporal degree of freedom of the photons, where the first optical mode corresponds to an early (E) time-bin and the second to a late (L) time-bin. The linear operations are implemented in a self-stabilising time-bin interferometer that couples the E and L modes and applies a relative linear phase ϕ between them. Photons are injected and retrieved from the GaAs device hosted in a 1.6K cryostat, where nonlinearities are implemented by scattering off the QD at the two different times E and L. The two temporal modes are recombined in the time-bin interferometer, where the output interference is affected by both linear and nonlinear phases. The nonlinear interaction significantly changes the properties of the photons, as illustrated by the theoretical joint temporal intensity (JTI) shown with (right inset) and without (left inset) nonlinear interactions for different settings of ϕ.