  Universal unitary photonic devices can apply arbitrary unitary
transformations to a vector of input modes and provide a promising hardware
platform for fast and energy-efficient machine learning using light. We
simulate the gradient-based optimization of random unitary matrices on
universal photonic devices composed of imperfect tunable interferometers. If
device components are initialized uniform-randomly, the locally-interacting
nature of the mesh components biases the optimization search space towards
banded unitary matrices, limiting convergence to random unitary matrices. We
detail a procedure for initializing the device by sampling from the
distribution of random unitary matrices and show that this greatly improves
convergence speed. We also explore mesh architecture improvements such as
adding extra tunable beamsplitters or permuting waveguide layers to further
improve the training speed and scalability of these devices.
