Course description: This course covers quantum information theory, quantum algorithms, quantum error correction, topological quantum computing, quantum Shannon theory, and some special topics.
Class meetings: Monday and Wednesday 2:30-3:55 in 103 Downs.
Lectures and references:
The primary reference for most of the lectures will be these lecture notes (JP). Other useful books are Quantum Computation and Quantum Information by Nielsen and Chuang (NC), Classical and Quantum Computation by Kitaev, Shen, and Vyalyi (KSV), Quantum Computing Since Democritus by Aaronson, and Quantum Information Theory by Wilde.
The fall term focused on quantum algorithms, and was taught by Professor Kitaev.
Course outline for winter term:
The main topics will be quantum error correction (JP Chapter 7), fault-tolerant quantum computing, and topological quantum computing (JP Chapter 9).
Other good references on quantum error correction are this review by Gottesman, and this review by Terhal.
See also these Handwritten
lecture notes on toric code recovery,
fault-tolerant recovery, and fault-tolerant gates
Lecture 1 (Jan 3): The Knill-Laflamme quantum error correction conditions
Lecture 2 (Jan 8): More about the error correction conditions
Lecture 3 (Jan 10): Classical linear codes and CSS quantum codes
Lecture 4 (Jan 17): Quantum stabilizer codes
Lecture 5 (Jan 22): Examples of stabilizer codes
Lecture 6 (Jan 24): Cleaning lemma for stabilizer codes, quantum Gilbert-Varshamov bound
Lecture 7 (Jan 29): Concatenated quantum codes, toric code
Lecture 8 (Jan 31): Toric code recovery
Lecture 9 (Feb 5): Existence of string operators in 2D stabilizer codes, self-correcting codes
Lecture 10 (Feb 7): Bounds on [[n,k,d]] for local stabilizer codes
Lecture 11 (Feb 12): Fault-tolerant quantum error correction
Lecture 12 (Feb 14): Fault-tolerant quantum gates, Eastin-Knill theorem
Lecture 13 (Feb 21): Universal fault-tolerant gates, quantum accuracy threshold theorem
Lecture 14 (Feb 26): Measurement-based fault-tolerant gates
Lecture 15 (Feb 28): Measurement-based quantum computing with cluster states
Notes on cluster states
Course outline for spring term:
Professor Kitaev taught the first half of this term. The main topic was connections between quantum information and black holes.
For the second half of the term, the main topic is topological quantum computing (JP Chapter 9).
Lecture 1 (May 7). Abelian anyons, braid group.
Lecture 2 (May 9). Anyons in quantum double models.
Lecture 3 (May 14). Computing with quantum double anyons.
Lecture 4 (May 21). General anyon models, F and R matrices.
Lecture 5 (May 23). Simulating anyons with a quantum computer.
Lecture 6 (May 30). Universal computation with Fibonacci anyons.
Lecture 7 (Jun 5). S-Matrix and Verlinde formula.
Lecture 8 (Jun 7). Ising anyons and Majorana modes.
Notes for Lectures 7 and 8
All students taking the course for credit are required to do the homework. Unless otherwise announced, homework will be due on Thursday at 5pm.
Problem Set 1. CSS quantum codes. Due Thursday 25 January 2018
Problem Set 2. Code properties. Due Thursday 8 February 2018
Problem Set 3. Topological codes. Due Thursday 22 February 2018
Problem Set 4. Fault-tolerant quantum computing. Due Thursday 8 March 2018
Problem Set 5. Anyons. Due Thursday 7 June 2018