  Optical unitary converter (OUC) that can convert a set of N mutually
orthogonal optical modes into another set of arbitrary N orthogonal modes is
expected to be the key device in diverse applications, including the optical
communication, deep learning, and quantum computing. While various types of OUC
have been demonstrated on photonic integration platforms, its sensitivity
against a slight deviation in the waveguide dimension has been the crucial
issue in scaling N. Here, we demonstrate that an OUC based on the concept of
multi-plane light conversion (MPLC) shows outstanding robustness against
waveguide deviations. Moreover, it becomes more and more insensitive to
fabrication errors as we increase N, which is in clear contrast to the
conventional OUC architecture, composed of 2 $\times$ 2 Mach-Zehnder
interferometers. The physical origin behind this unique robustness and
scalability is studied by considering a generalized OUC configuration. As a
result, we reveal that the number of coupled modes in each stage plays an
essential role in determining the sensitivity of the entire OUC. The maximal
robustness is attained when all-to-all-coupled interferometers are employed,
which are naturally implemented in MPLC-OUC.
