CPSC 648: Quantum Codes and Applications to Complexity
- Lecturer: Gaurav Mahajan (gaurav.mahajan@yale.edu)
- Office Hours: Tuesday 1-2 PM. Kline Tower, KT 1319
- Location: Thursday 1:30-3:20PM. Kline Tower, KT 1327
- Canvas: https://yale.instructure.com/courses/100565
- Scribe List: link to google sheet
- Project List: link to google sheet
- Lecture Notes: link to overleaf for scribe
Course Description
The course will cover the theory of quantum error correction and its applications to quantum complexity theory.
We will start with basic quantum codes and then progress towards more advanced code constructions,
particularly focusing on good quantum low-density parity-check codes.
In the latter half of the course, we will discuss various applications of quantum codes in quantum
complexity.
Deadlines
- Sep 21st: Project selection due
- Oct 21st: Rough draft due
- Nov 21st: Project presentations
- Dec 06th: Final report due
Lectures
- Chapter 1 (Week 1): Basics of Quantum Computation
- Quantum bits, multiple qubits, gates, and measurement
- Chapter 2 (Week 2): Introduction to Quantum Codes
- Repetition code, quantum noise, fixing bit flip and phase errors, 9-qubit Shor code
- Chapter 3 (Week 3): Knill-Laflamme Conditions
- Quantum noise model, error-correcting codes, Knill-Laflamme conditions, distance of a code
- Chapter 4 (Week 4): Stabilizer Codes
- Pauli group, stabilizer codes, dimension and distance of stabilizer codes, logical operators
- Chapter 5 (Week 5): Calderbank-Shor-Steane Codes
- Classical linear codes, distance of classical linear codes, CSS code, distance of CSS code
- Chapter 6 (Week 6): Toric Code
- Stars and plaquettes, closed loop and boundary, distance of toric code
- Chapter 7 (Week 7): Chain Complexes
- Chain complexes, homology, dual chain
- Chapter 8 (Week 8): Hypergraph Product Codes
- Classical codes as chain complexes, hypergraph product code
- Chapter 9 (Week 8): Tanner Codes
- Distance of Tanner codes, expander graphs
- Chapter 10 (Week 9): Quantum Tanner Codes
- Left-right Cayley complex, quantum Tanner code, dimension of the code
- Chapter 11 (Week 10): Distance of Quantum Tanner Code
- Product expansion, minimal representation, minimum distance