Encoding a 1-D Heisenberg Spin 1/2 Chain in a Simulated Annealing Algorithm for Machine Learning

Pompa, Daniel (2019) Encoding a 1-D Heisenberg Spin 1/2 Chain in a Simulated Annealing Algorithm for Machine Learning. Undergraduate thesis, under the direction of Kevin Beach from Physics and Astronomy, University of Mississippi.

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Abstract

The application areas of machine learning techniques are becoming broader and increasingly ubiquitous in the natural sciences and engineering. One such field of interest within the physics community is the training and implementation of neural networks to aid in quantum many-body computations. Conversely, research exploring the possible computational benefits of using quantum many-body dynamics in the area of artificial intelligence and machine learning has also recently started to gain traction. The marriage of these fields comes naturally with the complementary nature of their mathematical frameworks. The objective of this study was to explore the possibility of encoding a quantum spin ½ system in a binary form in order to train a neural network. Once the spins are transformed into binary form, a bit count is calculated for each state of the system. An exact diagonalization of the XXZ Heisenberg Hamiltonian is then used to compute the energy eigenvectors and eigenvalues. The model is trained to identify the bit counts of the lowest energy state of the system which is found through a stochastic search algorithm known as simulated annealing.

Item Type: Thesis (Undergraduate)
Creators: Pompa, Daniel
Student's Degree Program(s): B.S. in Physics
Thesis Advisor: Kevin Beach
Thesis Advisor's Department: Physics and Astronomy
Institution: University of Mississippi
Subjects: Q Science > QC Physics
Depositing User: Mr. Daniel Pompa
Date Deposited: 08 May 2019 15:12
Last Modified: 08 May 2019 15:12
URI: http://thesis.honors.olemiss.edu/id/eprint/1340

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