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