Senior Honors Thesis

Senior Honors Thesis - Samuel Greydanus

Wednesday, May 24, 2017 4:00 pm Wilder 104

Title: Approximating Matrix Product States with Machine Learning

Abstract: Obtaining compressed representations of slightly entangled systems is an important open problem in quantum mechanics. The Density Matrix Renormalization Group (DMRG) algorithm introduced by S. R. White in 1992 has been successful at solving one-dimensional cases but does not generalize well to arbitrary dimensions. We explore the possibility of using neural network models to solve ground state problems. In experiments on a system of four spin-½ particles interacting by the Heisenberg Hamiltonian, we show that this approach can approximate ground state energies and Matrix Product State coefficients to a mean percent error of less than 7%. Our findings suggest that neural networks, which generalize well to arbitrary dimensions, could be useful tools for solving 2D and 3D systems where DMRG fails.