  Multilayer perceptron is the most common used class of feed-forward
artificial neural network. It contains many applications in diverse fields such
as speech recognition, image recognition, and machine translation software. To
cater for the fast development of quantum machine learning, in this paper, we
propose a new model to study multilayer perceptron in quantum computer. This
contains the tasks to prepare the quantum state of the output signal in each
layer and to establish the quantum version of learning algorithm about the
weights in each layer. We will show that the corresponding quantum versions can
achieve at least quadratic speedup or even exponential speedup over the
classical algorithms. This provide us an efficient method to study multilayer
perceptron and its applications in machine learning in quantum computer.
Finally, as an inspiration, an exponential fast learning algorithm (based on
Hebb's learning rule) of Hopfield network will be proposed.
