A Collection of Resources for Learning Topological Quantum Computation

A Collection of Resources for Learning Topological Quantum Computation

Here is a list of resources for learning topological quantum computation from different perspectives for different backgrounds. Please contribute to the list. The recommendation and description of materials are the personal views of a graduate student and have no claim of being an expert’s view on the topic. So please feel free to extend/alter them!

History

A concise history of the field is tweeted by Maissam Barkeshli on his personal twitter account, here

Introductory Materials or General Reviews

1. Non-Abelian anyons and topological quantum computation by Chetan Nayak, Steven H. Simon, Ady Stern, Michael Freedman, Sankar Das Sarma </br> It is The paper that most papers cite it, but it is hard to read if you are a beginner. If you have a good handle of one of the following approaches, this paper sheds light on the whole picture.
2. Topological Quantum Computing: Plenty of Room in the Middle a talk by Jason Alicia </br> A physical overview of topological quantum computation with a description of the state-of-the-art experiments.
3. Topological Quantum Computing: Part 1 & 2 a talk by Steve Simon </br> If you want to learn about the Kauffman bracket or Kitaev model, watch them! No one gets bored from Steve Simon’s lectures, always interesting!
4. Topological Quantum Computation: Part 1, 2 & 3 by Nick Bonesteel
5. For more talks check this youtube playlist, it is ordered by level of difficulty based on an undergraduate knowledge of physics/mathematics.

Holistic and Comprehensive View

1. Topological Quantum Matter by Steve Simon </br> I would suggest starting with this book if you do not have any prior knowledge of topological matter and quantum computation. This book walks you through all difficult subjects and builds your intuition with jokes and humor that you do not realize when you have learned a lot of difficult topics! It includes quite a few exercises. (Do not panic by Surgery and Quantum Gravity chapters keep going! )

2. TQC ZOO https://errorcorrectionzoo.org/

Physical Approach

1. Topological Quantum Matter an online course which is “a joint effort of Delft University of Technology, QuTech, NanoFront, University of Maryland, and Joint Quantum Institute.”(site description)
2. Introduction to Topological Quantum Matter & Quantum Computation by Jiannis K. Pachos
3. Parsa Hassan Bonderson’s thesis

Axiomatic Approach without Invoking Category Theory

1. Lecture Notes for Physics 219: Quantum Computation: Chapter 9 by John Preskill
2. An Invitation to the Mathematics of Topological Quantum Computation by Eric C. Rowell

Categorical Approach

1. Topological Quantum Computation by Zhenghan Wang
2. MATHEMATICS OF TOPOLOGICAL QUANTUM COMPUTING by ERIC C. ROWELL AND ZHENGHAN WANG
3. Appendix of Anyons in an exactly solved model and beyond by Alexie Kitave </br> This paper does not explicitly discuss topological quantum computation, but it gives a comprehensive account of the mathematical structure behind the model. It also does not explicitly mention the categorical jargon, but knowing a bit of category theory at least the definition of monoidal category helps to spot categorical correspondence. One of the papers you might want to keep handy!

Open Problems

1. Classifying fusion categories Edited by Scott Morrison and David Penneys A list to track problems in this area.

Topological Qauntum Field Theory(not an exhaustive list)

1. Frobenius Algebras and 2-D Topological Quantum Field Theories By Joachim Kock
2. Undergraduate Lecture Notes in Topological Quantum Field Theory
3. Lectures on Field Theory and Topology