  The physical scalar product between spin-networks has been shown to be a
fundamental tool in the theory of topological quantum neural networks (TQNN),
which are quantum neural networks previously introduced by the authors in the
context of quantum machine learning. However, the effective evaluation of the
scalar product remains a bottleneck for the applicability of the theory. We
introduce an algorithm for the evaluation of the physical scalar product
defined by Noui and Perez between spin-network with hexagonal shape. By means
of recoupling theory and the properties of the Haar integration we obtain an
efficient algorithm, and provide several proofs regarding the main steps. We
investigate the behavior of the TQNN evaluations on certain classes of
spin-networks with the classical and quantum recoupling. All results can be
independently reproduced through the "idea.deploy"
framework~\href{https://github.com/lullimat/idea.deploy}{\nolinkurl{https://github.com/lullimat/idea.deploy}}
