  The parameters of the quantum circuit in a variational quantum algorithm
induce a landscape that contains the relevant information regarding its
optimization hardness. In this work we investigate such landscapes through the
lens of information content, a measure of the variability between points in
parameter space. Our major contribution connects the information content to the
average norm of the gradient, for which we provide robust analytical bounds on
its estimators. This result holds for any (classical or quantum) variational
landscape. We validate the analytical understating by numerically studying the
scaling of the gradient in an instance of the barren plateau problem. In such
instance we are able to estimate the scaling pre-factors in the gradient. Our
work provides a new way to analyze variational quantum algorithms in a
data-driven fashion well-suited for near-term quantum computers.
