  Programmable unitary photonic devices are emerging as promising tools to
implement unitary transformation for quantum information processing, machine
learning, and optical communication. These devices typically use a rectangular
mesh of Mach-Zehnder interferometers (MZIs), which has a clear mathematical
structure and can be configured deterministically. However, this mesh
architecture is sensitive to fabrication errors, and the correction techniques
are still under investigation. In contrast, the multi-plane light conversion
(MPLC) architecture is more robust against fabrication errors, but a
deterministic method for configuring the converter has not yet been developed
due to its complex mathematical structure. In this work, we propose a fast
iterative configuration method for MPLC, following the mathematical review of
the matrix distance and proposal of a new norm. We show through numerical
simulations that adding a few redundant layers significantly improves the
convergence of the MPLC architecture, making it a practical and attractive
option. We also consider the effects of finite resolution and crosstalk in
phase shifters in our simulations. In addition, we propose a phase-insensitive
distance suited for applications using only intensity detections. Our method
demonstrates orders of magnitude better accuracy and a 20-fold speed-up
compared to previous approaches.
