Figure 3

Haar-random with losses and noise. Noise and losses affect the implementation of Haar-random unitaries in different ways in the C- and R-designs. (a,c) Average fidelity F for different levels of loss η per beam splitter and size m of the interferometer in the C (a) and R (c) designs. Note the difference in vertical scale, due to the more balanced structure of C where the dependency on η arises from the slight path asymmetry of the outer waveguides. (b,d) Average fidelity F for different levels of noise σ in the optical elements and size m, averaged over 500 noisy unitaries. Here noise is treated equally on both beam splitters and phase shifters, namely σ = σ _BS  = σ _PS . Note that the scaling is identical in (b,d) since, averaging over the unitaries, the deterioration of F is due to the number of noisy elements, which is the same in the two schemes. Surfaces: heuristic non-linear fits of the data (see Supplementary Note 1).