  The aim of this thesis is to compare the capacity of different models of
neural networks. We start by analysing the problem solving capacity of a single
perceptron using a simple combinatorial argument. After some observations on
the storage capacity of a basic network, known as an associative memory, we
introduce a powerful statistical mechanical approach to calculate its capacity
in the training rule-dependent Hopfield model. With the aim of finding a more
general definition that can be applied even to quantum neural nets, we then
follow Gardner's work, which let us get rid of the dependency on the training
rule, and comment the results obtained by Lewenstein et al. by applying
Gardner's methods on a recently proposed quantum perceptron model.
