Selected References for Students
This page collects books, lecture notes, and articles that I have found useful and/or enjoyable over the years. The list is far from comprehensive but contains many of the resources I most frequently recommend to students that are interested in conducting research in theoretical aspects of quantum information science. Each resource is tagged by difficulty and intended audience so you can find an entry point that matches your background. In addition to technical references, I also list articles and popular books that supplement content with the history, philosophy, or nature of science/math. I have found the history, philosophy, and nature of math/science both interesting and useful to myself and my students, so I encourage you to develop a working knowledge of the these areas alongside your technical study of the topics.
Difficulty: Introductory Intermediate Advanced | Audience: Physics Mathematics Computer Science General
Linear Algebra
For a second course in linear algebra, I agree with the title whole-heartedly.
Quantum Mechanics
This book was developed through many years of Barton's 8.01 sequence at MIT. The lecture videos and courseware are freely available, making this an even better resource to learn from.
Group and Representation Theory
An excellent and succinct first introduction to group and representation theory for a cross-listed math/physics course at the University of Alberta.
High-dimensional Probability
Essential reference on the topic.
Quantum Information Theory
A classic set of lecture notes that develops quantum information and basic quantum computing from a physics point of view. Good for students who are comfortable with linear algebra and Dirac notation and want a more conceptual, calculation-oriented introduction.
Quantum Learning Theory
Scribe notes from John's course at UC Berkeley.
Quantum Metrology
Classic paper in the field.
Advice for Mathematicians and Scientists
Useful advice from a well-known MIT mathematician and philosopher.
If you are a student interested in a reading or research project, feel free to reach out — I’m happy to suggest a tailored sequence of resources based on your background and goals.