Learning Thermodynamics with Boltzmann Machines

Abstract

The introduction of neural networks with deep architecture has led to a revolution, giving rise to a new wave of technologies empowering our modern society. Although data science has been the main focus, the idea of generic algorithms which automatically extract features and representations from raw data is quite general and applicable in multiple scenarios. Motivated by the effectiveness of deep learning algorithms in revealing complex patterns and structures underlying data, we are interested in exploiting such tool in the context of many-body physics. I will first introduce the Boltzmann Machine, a stochastic neural network that has been extensively used in the layers of deep architectures. I will describe how such network can be used for modelling thermodynamic observables for physical systems in thermal equilibrium, and show that it can faithfully reproduce observables for the 2 dimensional Ising model. Finally, I will discuss how to adapt the same network for implementing the classical computation required to perform quantum error correction in the 2D toric code.