  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 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 to hardware
errors.
