Experimental loopback boson sampling

We report an experimental implementation of single-photon boson sampling with optical feedback. A 25-mode femtosecond-laser-written interferometer is configured so that five output modes are connected back to five input modes, enabling photons from consecutive injection cycles to interfere. This feedback converts repeated use of a fixed spatial interferometer into a structured spatio-temporal sampler described by a block lower-triangular Toeplitz transfer matrix, rather than by independent block-diagonal repetitions of a conventional boson sampler. We reconstruct the interferometer transfer matrix, include measured source and loss parameters in a numerical model, and validate the experiment using Bayesian hypothesis tests. The data distinguish indistinguishable-photon sampling from distinguishable-particle and uniform alternatives, and distinguish the open-feedback configuration from the corresponding blocked-feedback/no-feedback configuration. The experiment demonstrates a controllable mechanism for increasing the spatio-temporal sampling space of a discrete-variable photonic sampler and provides an experimentally calibrated platform for scaling feedback-assisted architectures toward regimes relevant for quantum advantage with single photons.