%0 Journal Article
%T Variational Methods for Solving High-Dimensional Quantum Systems
%A Daming Li
%J Journal of Modern Physics
%P 686-714
%@ 2153-120X
%D 2025
%I Scientific Research Publishing
%R 10.4236/jmp.2025.165038
%X Variational methods are highly valuable computational tools for solving high-dimensional quantum systems. In this paper, we explore the effectiveness of three variational methods: density matrix renormalization group (DMRG), Boltzmann machine learning, and variational quantum eigensolver (VQE). We apply these methods to solve two different quantum systems: the Fermi-Hubbard model in condensed matter physics and the Schwinger model in high energy physics. To facilitate the computations on quantum computers, we map each model to a spin 1/2 system using the Jordan-Wigner transformation. This transformation allows us to take advantage of the capabilities of quantum computing. We calculate the ground state of both quantum systems and compare the results obtained using three variational methods. Our aim is to demonstrate the power and effectiveness of these variational approaches in tackling complex quantum systems.
%K Density Matrix Renormalization Group
%K Boltzmann Machine Learning
%K Variational Quantum Eigensolver
%K Fermi-Hubbard Model
%K Schwinger Model
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=142804