Mentored by University of Maryland at College Park Prof. Victor V. Albert and California Institute of Technology Postdoctoral Researcher Dr. Nathanan Tantivasadakarn. Research conducted at the Research Experience for Undergraduates (REU) in Combinatorics, Algorithms, and AI for Real Problems (CAAR) at the University of Maryland, College Park.
Abstract: Using the Laurent polynomial representation of stabilizers to work with topological error correcting codes, we explore the resulting parity check matrices and error syndromes to examine homologies (i.e. torsion) that give rise to logical operators. Extracting the associated string operators and braiding statistics, we apply a symplectic mapping resulting in the creation of CSS codes, and leverage work akin to Wall’s enlargement algorithm to perform a decomposition to classify the transformed topological order. Future work entails generalizing to 3D and higher dimensions.