Quantum Computation

2018

**Go to home page for
Ph219/CS219 in past years.**

**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.

**Instructor:
**John Preskill, 206 Annenberg, X-6691, email: preskill(at)caltech(dot)edu

Teaching assistant:

Eric Morgan, 233 Annenberg, email: eric(at)caltech(dot)edu

Office hours: 11am Wednesdays.

**Lectures and references:
**The primary reference for most of the lectures will be these lecture
notes (JP). Other useful books are

Other recommended lecture notes: John Watrous, Umesh Vazirani, Andrew Childs, Scott Aaronson

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

**Homework assignments:**

All students taking the course for credit are required to do the homework. Unless otherwise announced, homework will be
due on Thursday at 5pm.

Winter term

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

Spring term.

Problem
Set 5. Anyons. Due Thursday 7 June 2018