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 and for various backgrounds.

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, and Sankar Das Sarma. This is the paper that most others cite, but it is difficult to read if you are a beginner. If you have a solid understanding of one of the following approaches, this paper will help you see the bigger picture.
2. Topological Quantum Computing: Plenty of Room in the Middle, a talk by Jason Alicea.
   A physical overview of topological quantum computation, including a description of state-of-the-art experiments.
3. Topological Quantum Computing: Part 1 & 2, a talk by Steve Simon.
   If you want to learn about the Kauffman bracket or the Kitaev model, watch these! No one gets bored during Steve Simon’s lectures—they’re always interesting!
4. Topological Quantum Computation: Part 1, 2 & 3 by Nick Bonesteel.
5. For more talks, check out this YouTube playlist. It is ordered by level of difficulty based on an undergraduate knowledge of physics and mathematics.

Holistic and Comprehensive View

1. Topological Quantum Matter by Steve Simon.
   I recommend starting with this book if you do not have prior knowledge of topological matter and quantum computation. It walks you through complex subjects while building intuition with humor—you won’t even realize when you’ve learned some of the most difficult topics! It also includes numerous exercises. (Don’t panic when you reach the Surgery and Quantum Gravity chapters—keep going!)
2. TQC ZOO https://errorcorrectionzoo.org/

Physical Approach

1. Topological Quantum Matter, an online course described as “a joint effort of Delft University of Technology, QuTech, NanoFront, University of Maryland, and Joint Quantum Institute.”
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 Alexei Kitaev.
   This paper does not explicitly discuss topological quantum computation but provides a comprehensive account of the mathematical structure behind the model. It does not directly use categorical jargon, but knowing a bit of category theory—at least the definition of a monoidal category—helps in recognizing categorical correspondences. This is one of those papers you might want to keep handy!

Open Problems

1. Classifying Fusion Categories, edited by Scott Morrison and David Penneys.
   A list tracking problems in this area.

Topological Quantum 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.