Restricted Boltzmann Machines and their Information Geometry in Quantum Many-Body Problems

Abstract

Quantum many-body problems face a scalability challenge, since the wave function scales exponentially with the number of bodies in the system. Fortunately, several machine learning approaches have been recently proposed to overcome this challenge. Specially promising are the Restricted Boltzmann Machines (RBMs), to turn the problem into a manageable computational form. Moreover, information geometry has been studied in RBMs, and the Fisher Matrix has shown to reveal relevant information about the system. Here, we create from scratch a RBM representation of the ground state for the transverse Ising model (short and long-range), and analyze the corresponding Fisher Matrix across different quantum phases, and its potential to signal the phase transition