Bipartite Gaussian boson sampling in the time-frequency-bin domain with squeezed light generated by a silicon nitride microresonator

We demonstrate high-dimensional bipartite Gaussian boson sampling with squeezed light across 6 mixed time-frequency modes. Non-degenerate two-mode squeezing is generated in two time-bins from a silicon nitride microresonator. An unbalanced interferometer embedding electro-optic modulators and stabilized by exploiting the continuous energy-time entanglement of the generated photon pairs, couples time and frequency-bin modes arranged in a two-dimensional 3 by 2 rectangular lattice, thus enabling both local and non-local interactions. We measure 144 collision-free events with 4 photons at the output, achieving a fidelity greater than 0.98 with the theoretical probability distribution. We use this result to identify the similarity between families of isomorphic graphs with 6 vertices.