  We argue that an excess in entanglement between the visible and hidden units
in a Quantum Neural Network can hinder learning. In particular, we show that
quantum neural networks that satisfy a volume-law in the entanglement entropy
will give rise to models not suitable for learning with high probability. Using
arguments from quantum thermodynamics, we then show that this volume law is
typical and that there exists a barren plateau in the optimization landscape
due to entanglement. More precisely, we show that for any bounded objective
function on the visible layers, the Lipshitz constants of the expectation value
of that objective function will scale inversely with the dimension of the
hidden-subsystem with high probability. We show how this can cause both
gradient descent and gradient-free methods to fail. We note that similar
problems can happen with quantum Boltzmann machines, although stronger
assumptions on the coupling between the hidden/visible subspaces are necessary.
We highlight how pretraining such generative models may provide a way to
navigate these barren plateaus.
