Analysis of Graph-based Decoders for Quantum Low Density Parity Check Codes

Authors

Kirsten Morris, University of Nebraska-LincolnFollow

First Advisor

Christine A. Kelley

Degree Name

Doctor of Philosophy (Ph.D.)

Committee Members

Jack Jeffries, Jamie Radcliffe, Khalid Sayood, Tefjol Pllaha, Xavier Pérez-Giménez

Department

Mathematics

Date of this Version

8-2025

Document Type

Dissertation

Citation

A dissertation presented to the Graduate College of the University of Nebraska in partial fulfillment of requirements for the degree of Doctor of Philosophy

Major: Mathematics

Under the supervision of Christine A. Kelley

Lincoln, Nebraska, August 2025

Comments

Copyright 2025, Kirsten Morris. Used by permission

Abstract

Quantum computing has the potential for radically increased computational ability. However, the physical realization of quantum states are fragile and susceptible to noise and decoherence. For this reason, robust quantum error correction is imperative to achieve quantum computation at scale.

Of particular interest in realizing effective quantum error correction are quantum low density parity check (QLDPC) codes. Classical LDPC codes were invented by Robert Gallager in the 1960s and came in to prominence in the 1990s. Due to Daniel Gottesman’s stabilizer formalism and the invention of Calderbank-Shor-Steane (CSS) codes, we can apply LDPC codes to the quantum setting.

As in classical decoding, the decoding of QLDPC codes suffers from the presence of structures in the code’s Tanner graph representation. The contribution of this dissertation is threefold. First, we analyze absorbing sets, combinatorial structures known to cause decoding failures in classical decoding, and see that they remain problematic within the QLDPC decoding framework. Secondly, we extend our understanding of problematic structures to partitions of absorbing sets and situate symmetric stabilizers, a purely quantum harmful structure, within this framework. Finally, we explore the benefits of adding redundancy to CSS codes and see improved decoding performance for CSS codes constructed from Hamming codes.

Advisor: Christine A. Kelley

Recommended Citation

Morris, Kirsten, "Analysis of Graph-based Decoders for Quantum Low Density Parity Check Codes" (2025). Dissertations and Doctoral Documents from University of Nebraska-Lincoln, 2023–. 339.
https://digitalcommons.unl.edu/dissunl/339