We analyze mathematical aspects related to general quantum Boltzmann
machine models through representations of algebras and functional
analytic techniques. In this context, based on algebraic formulation
we show the existence of a symmetry group for a class of
Hamiltonians based on generators of Clifford algebras and discuss its
implications for the learning scheme. Also, we have developed a rigorous
mathematical analysis that allows us to investigate issues related
to the asymptotic behavior of quantum Boltzmann machines. Particularly,
we obtain a lower bound of fidelity in terms of the upper limit
of quantum relative entropy.