Quantum Algebraic Geometry Codes

Quantum error correction is an essential aspect of quantum information theory, providing protection for quantum states against noise and decoherence. This thesis investigates the construction of quantum error correction codes derived from classical algebraic geometry (AG) codes. We present two distinct construction techniques, highlighting the flexibility and self-orthogonality of AG codes, and demonstrate their ability to produce asymptotically good quantum codes. Additionally, we explore strategies to fine-tune the parameters of classical AG codes, ensuring they possess the desired properties for quantum code construction. This work serves as a comprehensive guide to the fundamental concepts and common methodologies underlying quantum algebraic geometry codes.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

Masters

Discipline thesis:degree_discipline

Engineering

Grantor

Rice University

Year dc:date.issued

2024

Author dc:creator

• Han, Zhengyi

Advisor dc:contributor.advisor

• Goldman, Ronald

• quantum error correction
• algebraic geometry

Statement dc:rights

• Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1911/118203

OAI identifier oai:identifier

oai:repository.rice.edu:1911/118203