  In this work, we propose a quantum neural network named quantum perceptron
over a field (QPF). Quantum computers are not yet a reality and the models and
algorithms proposed in this work cannot be simulated in actual (or classical)
computers. QPF is a direct generalization of a classical perceptron and solves
some drawbacks found in previous models of quantum perceptrons. We also present
a learning algorithm named Superposition based Architecture Learning algorithm
(SAL) that optimizes the neural network weights and architectures. SAL searches
for the best architecture in a finite set of neural network architectures with
linear time over the number of patterns in the training set. SAL is the first
learning algorithm to determine neural network architectures in polynomial
time. This speedup is obtained by the use of quantum parallelism and a
non-linear quantum operator.
