  Parameterized quantum circuits (PQC, aka, variational quantum circuits) are
among the proposals for a computational advantage over classical computation of
near-term (not fault tolerant) digital quantum computers. PQCs have to be
"trained" -- i.e., the expectation value function has to be maximized over the
space of parameters.
  This paper deals with the number of samples (or "runs" of the quantum
computer) which are required to train the PQC, and approaches it from an
information theoretic viewpoint. The main take-away is a disparity in the large
amount of information contained in a single exact evaluation of the expectation
value, vs the exponentially small amount contained in the random sample
obtained from a single run of the quantum circuit.
