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Reprogrammable linear optical circuits are essential elements of photonicquantum technology implementations. Integrated optics provides a naturalplatform for tunable photonic circuits, but faces challenges when highdimensions and high connectivity are involved. Here, we implementhigh-dimensional linear transformations on spatial modes of photons usingwavefront shaping together with mode mixing in a multimode fiber, and measurephoton correlations using a time-tagging single-photon avalanche diode (SPAD)array. In order to prove the suitability of our approach for quantumtechnologies we demonstrate two-photon interferences in a tunable complexlinear network -- a generalization of a Hong-Ou-Mandel interference to 22output ports. We study the scalability of our approach by quantifying thesimilarity between the ideal photon correlations and the correlations obtainedexperimentally for various linear transformations. Our results demonstrate thepotential of wavefront shaping in complex media in conjunction with SPAD arraysfor implementing high-dimensional reconfigurable quantum circuits.Specifically, we achieved $(80.5 \pm 6.8)\%$ similarity for indistinguishablephoton pairs and $(84.9 \pm 7.0)\%$ similarity for distinguishable photon pairsusing 22 detectors and random circuits. These results emphasize the scalabilityand reprogrammable nature of our approach.

Large Reconfigurable Quantum Circuits with SPAD Arrays and Multimode Fibers