Fig. 1. High-dimensional GBS from a fully programmable photonic processor.

A periodic pulse train of single-mode squeezed states from a pulsed OPO enters a sequence of three dynamically programmable loop-based interferometers. Each loop contains a VBS, including a programmable phase shifter, and an optical fibre delay line. At the output of the interferometer, the Gaussian state is sent to a 1-to-16 binary switch tree (demux), which partially demultiplexes the output before readout by PNRs. The resulting detected sequence of 216 photon numbers, in approximately 36 μs, comprises one sample. The fibre delays and accompanying beamsplitters and phase shifters implement gates between both temporally adjacent and distant modes, enabling high-dimensional connectivity in the quantum circuit. Above each loop stage is depicted a lattice representation of the multipartite entangled Gaussian state being progressively synthesized. The first stage (τ) effects two-mode programmable gates (green edges) between nearest-neighbour modes in one dimension, whereas the second (6 τ) and third (36 τ) mediate couplings between modes separated by six and 36 time bins in the second and third dimensions (red and blue edges, respectively). Each run of the device involves the specification of 1,296 real parameters, corresponding to the sequence of settings for all VBS units.