Low-depth, compact, and error-tolerant photonic matrix-vector multiplication beyond the unitary group

Large-scale programmable photonic circuits are opening up new possibilities for information processing providing fast and energy-efficient means for matrix-vector multiplication. Here, we introduce what we believe to be a novel architecture of photonic circuits capable of implementing non-unitary transfer matrices, usually required by photonic neural networks, iterative equation solvers, or quantum samplers. Our architecture exploits compact low-depth beam-splitter meshes rather than bulky fully connected mixing blocks used in previous designs, making it more compatible with planar integrated photonics technology. We have shown that photonic circuits designed with our architecture have lower depth than their standard counterparts and are extremely tolerant of hardware errors.