Discussion

Other point to be considered is the training stage. Basically, the rule given by equation (13) updates the parameters of the system. This is much more closer to a (classical) neural network approach than the expression (4).

Despite of these advantages, a doubt about this QNN is that its neural
network approach is *virtual* in the sense that it is just a biased
interpretation of an approximated quantum model of the system.

Although this argument may be consistent, it does not discard the model
because a neural network should have three basic elements: (1) An *operator*
to process the input signal(s) (equation (7)
in the above model); (2) A *test* to decide if the results is the
desired one (expression (11));
(3) A rule to adapt parameters if need (equation (12)).
In the above model, these relations are not virtual ones in the sense that
the final result is a system that reproduce a desired behavior (a gate,
for example).