  We present a new technique for computing Hilbert series of N=1 supersymmetric
QCD in four dimensions with unitary and special unitary gauge groups. We show
that the Hilbert series of this theory can be written in terms of determinants
of Toeplitz matrices. Applying related theorems from random matrix theory, we
compute a number of exact Hilbert series as well as asymptotic formulae for
large numbers of colours and flavours -- many of which have not been derived
before.
