  We numerically investigate the implementation of Haar-random unitarity
transformations and Fourier transformations in photonic devices consisting of
beam splitters and phase shifters, which are used for integrated photonics
implementations of boson sampling. The distribution of reflectivities required
to implement an arbitrary unitary transformation is skewed towards low values,
and this skew becomes stronger the larger the number of modes. A realistic
implementation using Mach-Zehnder interferometers is incapable of doing this
perfectly and thus has limited fidelity. We show that numerical optimisation
and adding extra beam splitters to the network can help to restore fidelity.
