Year: 2024
Type: dissertation
Abstract: In the 20th century, the research area in coding theory has been progressing rapidly, and the theory is well developed to a sophisticated level.Although classical coding theory has reached a satisfying level since quantum coding theory has difficulty in copying quantum information states [1], people were not clear on how to apply the classical ideas on quantum information until 1996 when Shor [2] and Steane[3] pointed out that quantum error-correcting codes exist.In 1997, a group-theoretical structure and associated subclass of quantum codes, the stabilizer codes, was introduced by A. R. Calderbank et al. [4] and Gottesmann [5].We will look at the concepts of classical error correction theory and how decoding is performed.Then, we will show that the concepts of quantum error correction theory and certain classes of codes similarly follow the characteristics of classical error correction theory.More specifically, we will look at the Quantum Hamming bound, the syndrome-based decoding of the stabilizer code, and the Quantum Gilbert-Varshamov bound.
Author: 김병수
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7066039657