  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.
