Date of Award
Spring 6-14-2025
Document Type
Undergraduate Honors Thesis
Degree Name
B.S. in Mathematics
Organizational Unit
College of Natural Science and Mathematics, Mathematics
First Advisor
Petr Vojtechovsky
Copyright Statement / License for Reuse
This work is licensed under a Creative Commons Attribution 4.0 International License.
Keywords
Quantum error correction (QEC), Shor’s Factoring Algorithm, 9-qubit CSS code, Surface code, Toric code, Threshold theorem, Fault-tolerant quantum computation
Abstract
The introduction of quantum computing has presented algorithmic solutions to computationally difficult challenges that are far more efficient than those of classical computers. These algorithms leverage the properties of quantum mechanics to manipulate the quantum properties of subatomic particles, requiring immense precision and stability. Current quantum hardware, however, is too noisy and introduces too many errors for these algorithms to be useful in practice, necessitating the use of error correction algorithms. This field survey seeks to introduce various principles of quantum mechanics relevant to quantum computing and quantum error correction (QEC), detail the implementation and motivations of a basic QEC algorithm, and provide insight into the current research direction.
Copyright Date
6-11-2025
Publication Statement
Copyright is held by the author. User is responsible for all copyright compliance.
Rights Holder
Derek Rodriguez
Provenance
Received from author
File Format
application/pdf
Language
English (eng)
Extent
13 pgs
File Size
269 KB
Recommended Citation
Rodriguez, Derek, "Basic Theory and Implementations of Quantum Error Correction" (2025). Undergraduate Theses, Capstones, and Recitals. 54.
https://digitalcommons.du.edu/undergraduate_theses/54