  Quantum Monte-Carlo simulations of hybrid quantum-classical models such as
the double exchange Hamiltonian require calculating the density of states of
the quantum degrees of freedom at every step. Unfortunately, the computational
complexity of exact diagonalization grows $ \mathcal{O} (N^3)$ as a function of
the system's size $ N $, making it prohibitively expensive for any realistic
system. We consider leveraging data-driven methods, namely neural networks, to
replace the exact diagonalization step in order to speed up sample generation.
We explore a model that learns the free energy for each spin configuration and
a second one that learns the Hamiltonian's eigenvalues. We implement data
augmentation by taking advantage of the Hamiltonian's symmetries to
artificially enlarge our training set and benchmark the different models by
evaluating several thermodynamic quantities. While all models considered here
perform exceedingly well in the one-dimensional case, only the neural network
that outputs the eigenvalues is able to capture the right behavior in two
dimensions. The simplicity of the architecture we use in conjunction with the
model agnostic form of the neural networks can enable fast sample generation
without the need of a researcher's intervention.
