  It is recently shown that discrete $N\times N$ linear unitary operators can
be represented by interlacing $N+1$ phase shift layers with a fixed intervening
operator such as Discrete Fractional Fourier Transform (DFrFT). Here, we show
that introducing perturbations to the intervening operations does not
compromise the universality of this architecture. Furthermore, we show that
this architecture is resilient to defects in the phase shifters as long as no
more than one faulty phase shifter is present in each layer. These properties
enable post-fabrication auto-calibration of such universal photonic circuits,
effectively compensating for fabrication errors and defects in phase
components.
