  We develop a new quantum neural network layer designed to run efficiently on
a quantum computer but that can be simulated on a classical computer when
restricted in the way it entangles input states. We first ask how a classical
neural network architecture, both fully connected or convolutional, can be
executed on a quantum computer using quantum phase estimation. We then deform
the classical layer into a quantum design which entangles activations and
weights into quantum superpositions. While the full model would need the
exponential speedups delivered by a quantum computer, a restricted class of
designs represent interesting new classical network layers that still use
quantum features. We show that these quantum deformed neural networks can be
trained and executed on normal data such as images, and even classically
deliver modest improvements over standard architectures.
