  Quantum computers herald the arrival of a new era in which previously
intractable computational problems will be solved efficiently. However, quantum
technology is held down by decoherence, a phenomenon that is omnipresent in the
quantum paradigm and that renders quantum information useless when left
unchecked. The science of quantum error correction, a discipline that seeks to
combine and protect quantum information from the effects of decoherence using
structures known as codes, has arisen to meet this challenge. Stabilizer codes,
a particular subclass of quantum codes, have enabled fast progress in the field
of quantum error correction by allowing parallels to be drawn with the widely
studied field of classical error correction. This has resulted in the
construction of the quantum counterparts of well-known capacity-approaching
classical codes like sparse codes and quantum turbo codes. However, quantum
codes obtained in this manner do not entirely evoke the stupendous error
correcting abilities of their classical counterparts. This occurs because
classical strategies ignore important differences between the quantum and
classical paradigms, an issue that needs to be addressed if quantum error
correction is to succeed in its battle with decoherence. In this dissertation
we study a phenomenon exclusive to the quantum paradigm, known as degeneracy,
and its effects on the performance of sparse quantum codes. Furthermore, we
also analyze and present methods to improve the performance of a specific
family of sparse quantum codes in various different scenarios.
