  Although we are currently in the era of noisy intermediate scale quantum
devices, several studies are being conducted with the aim of bringing machine
learning to the quantum domain. Currently, quantum variational circuits are one
of the main strategies used to build such models. However, despite its
widespread use, we still do not know what are the minimum resources needed to
create a quantum machine learning model. In this article, we analyze how the
expressiveness of the parametrization affects the cost function. We
analytically show that the more expressive the parametrization is, the more the
cost function will tend to concentrate around a value that depends both on the
chosen observable and on the number of qubits used. For this, we initially
obtain a relationship between the expressiveness of the parametrization and the
mean value of the cost function. Afterwards, we relate the expressivity of the
parametrization with the variance of the cost function. Finally, we show some
numerical simulation results that confirm our theoretical-analytical
predictions. To the best of our knowledge, this is the first time that these
two important aspects of quantum neural networks are explicitly connected.
