  We introduce a machine learning model, the q-CNN model, sharing key features
with convolutional neural networks and admitting a tensor network description.
As examples, we apply q-CNN to the MNIST and Fashion MNIST classification
tasks. We explain how the network associates a quantum state to each
classification label, and study the entanglement structure of these network
states. In both our experiments on the MNIST and Fashion-MNIST datasets, we
observe a distinct increase in both the left/right as well as the up/down
bipartition entanglement entropy during training as the network learns the fine
features of the data. More generally, we observe a universal negative
correlation between the value of the entanglement entropy and the value of the
cost function, suggesting that the network needs to learn the entanglement
structure in order the perform the task accurately. This supports the
possibility of exploiting the entanglement structure as a guide to design the
machine learning algorithm suitable for given tasks.
