https://github.com/wyldelarue/thesis

My undergraduate thesis in quantum computing with advisor Jamie Pommersheim. I used representation theoretic tools to analyze lower bounds of certain classes of quantum algorithms.
https://github.com/wyldelarue/thesis

quantum-computing representation-theory

Last synced: 4 months ago
JSON representation

My undergraduate thesis in quantum computing with advisor Jamie Pommersheim. I used representation theoretic tools to analyze lower bounds of certain classes of quantum algorithms.

• Host: GitHub
• URL: https://github.com/wyldelarue/thesis
• Owner: WyldeLaRue
• Created: 2018-10-04T18:48:59.000Z (over 7 years ago)
• Default Branch: master
• Last Pushed: 2019-06-08T01:13:35.000Z (about 7 years ago)
• Last Synced: 2025-02-28T10:55:09.966Z (over 1 year ago)
• Topics: quantum-computing, representation-theory
• Language: TeX
• Homepage:
• Size: 1.69 MB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

Awesome Lists containing this project

README

          
## Thesis Outline

Chapter 1:

   - Learning Problems

        * Motivating Example

        * sorting

   - Classical Computing

        * Logic Gates

        * Circuits

        * Learning Problems in Classical Circuits

   - Quantum Computing

        - Qubits

        - Dirac Notation

        - Quantum Gates

        - Quantum Circuits

   - Quantum Learning Problems

        - Solution to Motivating Example

        - Bernstein-Vazirani

Chapter 2: 

   - Representations  

   - Schur's Lemma

   - Maschke's Theorem

   - Relationship to Quantum Computing

   - Characters 

        - Definition

        - Burnside-Brauer

        - Orthogonality

        - Examples

Chapter 3: 

   - Base Size

   - Quantum Base Size

   - Introduce results from Copeland-Pommersheim

   - Overview of methods

Chapter 4:

   - Representation Theory of GL(2, q)

        - Character Table

   - Query Complexity

   - Lower Bounds