Traditional sampling methods such as the Monte Carlo method are computationally expensive and not feasible for studying large and complex systems. These methods are essential for developing new materials, optimizing chemical reactions, and understanding biological processes. However, simulating thermodynamic systems for physically relevant system sizes is computationally challenging. This is partly due to the exponential growth of the configuration space with the system size. With the current Monte Carlo methods, studying the same system for different investigation of its properties means repeating the expensive computation multiple times. In this article, I showed that thermodynamic systems can be sampled using a surrogate neural network model thereby avoiding the computationally expensive proposal Monte Carlo methods for subsequent investigations. To demonstrate the method, I trained a feed-forward neural network surrogate for the Boltzmann distribution of the Ising model. This approach would potentially help accelerate Monte Carlo simulations towards understanding the physics of novel materials and some biological processes.

I have studied the role of lattice connectivity and coupling weights distribution on the entanglement of  quantum spin-glasses. It's found in this work that the connectivity of the lattice weakly influence the degree of entanglement in the spin-glass compared to the distribution of the coupling constants between the spins. This suggest important implications for machine learning models such as Boltzmann machines and the study of complex quantum systems.