  Quantum machine learning techniques have been proposed as a way to
potentially enhance performance in machine learning applications.
  In this paper, we introduce two new quantum methods for neural networks. The
first one is a quantum orthogonal neural network, which is based on a quantum
pyramidal circuit as the building block for implementing orthogonal matrix
multiplication. We provide an efficient way for training such orthogonal neural
networks; novel algorithms are detailed for both classical and quantum
hardware, where both are proven to scale asymptotically better than previously
known training algorithms.
  The second method is quantum-assisted neural networks, where a quantum
computer is used to perform inner product estimation for inference and training
of classical neural networks.
  We then present extensive experiments applied to medical image classification
tasks using current state of the art quantum hardware, where we compare
different quantum methods with classical ones, on both real quantum hardware
and simulators. Our results show that quantum and classical neural networks
generates similar level of accuracy, supporting the promise that quantum
methods can be useful in solving visual tasks, given the advent of better
quantum hardware.
