  Random unitaries are an important resource for quantum information
processing. While their universal properties have been thoroughly analyzed, it
is not known what happens to these properties when the unitaries are sampled on
the present-day noisy intermediate-scale quantum (NISQ) computers. We implement
parameterized circuits, which have been proposed as a means to generate random
unitaries, on a transmon platform and model these implementations as quantum
maps. To retrieve the maps, a machine-learning assisted tomography is used. We
find the spectrum of a map to be either an annulus or a disk depending on the
circuit depth and detect an annulus-disk transition. By their spectral
properties, the retrieved maps appear to be very similar to a recently
introduced ensemble of random maps, for which spectral densities can be
analytically evaluated.
