Selected References for Students
This page collects books, lecture notes, videos, 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
The book was co-authored by Leonard Susskind and Art Friedman, who was a student in Susskind's lectures at Stanford to professionals in the area that had an interest in learning some real physics (these lectures are online for free). The book and the lectures are absolute gold. They present the conceptual underpinnings of quantum mechanics in the clearest manner I have seen at this level. This book is a great supplement to a core introductory quantum course.
David Tong is a world-renowned theoretical physicist and a prolific writer of excellent lecture notes. I think these notes are the perfect follow-up to Susskind's theoretical minimum and an essential reference for upper-undergraduate QM courses.
This book was developed through many years of Barton's 8.05 course at MIT. The lecture videos and courseware are freely available, making this an even better resource to learn from. The book is expensive, so unless you want/need a hardcopy, I recommend using the freely available lecture notes from MIT open courseware.
Legendary lecture notes by UC Berkeley professor Robert Littlejohn. They are the perfect supplement to the standard graduate quantum textbook in the United States (Modern Quantum Mechanics by J.J. Sakurai).
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.
Group theory, even just as it applies in physics, is an enormous field. So, group theory in a nutshell is still quite a lot of material! That said, I think this book strikes an excellent balance between conversational tone and mathematical rigor.
High-dimensional Probability
Essential reference on the topic.
Quantum Information Theory
Also known as "Mike and Ike" or "The Bible." This is the classic text in the field. It is pedagogical, rigorous, and thorough. If want to get into quantum computation and quantum information, this is a great place to start.
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.