Quantum interference with time-frequency modes and multiple-photons generated by a silicon nitride microresonator

We demonstrate bipartite gaussian boson sampling with squeezed light in 6 mixed time-frequency modes. Non-degenerate two-mode squeezing is generated in two time-bins from a silicon nitride microresonator with simultaneous high spectral purity (>0.86(3)) and indistinguishability (0.985(2)). An unbalanced interferometer embedding electro-optic modulators, which is stabilized by exploiting the continuous energy-time entanglement of the generated photon pairs, controls time and frequency-bin modes. We measure 144 collision-free events with 4 photons at the output, achieving a fidelity >0.98 with the theoretical probability distribution. We use this result to identify the similarity between families of isomorphic graphs with 6 vertices, and present an approach for the realization of universal operations on time-frequency modes.