Unsupervised Deep Neural Network Approach To Solve Bosonic Systems

TL;DR

This paper introduces an unsupervised deep neural network method combined with Monte Carlo techniques to efficiently simulate bosonic quantum systems, overcoming traditional computational limitations.

Contribution

It presents a novel neural network architecture tailored for bosonic states and demonstrates its effectiveness on the Bose-Hubbard model, enabling larger and more complex system simulations.

Findings

Successfully finds ground states of the Bose-Hubbard model

Demonstrates improved convergence with adaptive momentum optimizer

Flexible in simulating various lattice geometries

Abstract

The simulation of quantum many-body systems poses a significant challenge in physics due to the exponential scaling of Hilbert space with the number of particles. Traditional methods often struggle with large system sizes and frustrated lattices. In this research article, we present a novel algorithm that leverages the power of deep neural networks combined with Markov Chain Monte Carlo simulation to address these limitations. Our method introduces a neural network architecture specifically designed to represent bosonic quantum states on a 1D lattice chain. We successfully achieve the ground state of the Bose-Hubbard model, demonstrating the superiority of the adaptive momentum optimizer for convergence speed and stability. Notably, our approach offers flexibility in simulating various lattice geometries and potentially larger system sizes, making it a valuable tool for exploring complex quantum phenomena. This work represents a substantial advancement in the field of quantum simulation, opening new possibilities for investigating previously challenging systems.