- Principles of Effective Research by Michael Nielsen. I consulted this many times during my PhD, and it has been extremely influential in shaping my own research philosophy.
- Advice for beginning graduate students by Achim Kempf. Although written for students at the University of Waterloo, most of the document contains very good general advice.
- Advice to a young mathematician — great research advice that is useful as well for young theoretical physicists!
- For graduate students in quantum information, here is a list of essential research papers compiled by Felix Leditzky.
Listed below are books that I have found useful over the years.
Quantum Physics and Quantum Theory
The following two texts are standard ones used in undergraduate physics programs.
- Introduction to Quantum Mechanics, 2nd Ed. by David Griffiths.
- Modern Quantum Mechanics by J. J. Sakurai.
- Quantum Mechanics: A Modern Development by Leslie Ballentine. Out of the three books listed here, I recommend this one the most.
The following books are more suitable for graduate students, though not completely out of reach for senior undergraduates.
- Quantum Theory: Concepts and Methods by Asher Peres.
- Quantum Theory for Mathematicians by Brian Hall.
- Probabilistic and Statistical Aspects of Quantum Theory by Alexander Holevo.
Quantum Information Theory
- Quantum Information Theory by Mark Wilde. (Also freely available at arXiv:1106.1445.) An excellent book covering all important aspects of both classical and quantum information theory. It is mathematically rigorous, and is continuously being updated with the latest results in the field!
- Theory of Quantum Information by John Watrous. Also an excellent book on the basics of quantum information. Suitable for more mathematically-inclined readers.
- Lecture Notes by John Preskill. Yet another solid introduction to quantum information. Unlike the two books above, it also covers quantum computing. (See below for other books on quantum computing.)
Quantum Systems, Channels, Information: A Mathematical Introduction by Alexander Holevo. By a pioneer in the field, this book is notable for its coverage of quantum systems modelled by infinite-dimensional Hilbert spaces.
For a very quick and non-technical introduction to quantum computing, check out this page from the Institute for Quantum Computing.
With small-scale quantum computers from IBM available to use via the cloud (see the IBM Quantum Experience), you can now take a more hands-on approach to quantum computing! The qiskit textbook, as well as this paper, provide an introduction to quantum computing as well as sample programs/algorithms that you can run on IBM’s quantum computers.
Below are some of the standard texts used on courses on quantum computing.
- Quantum Computation and Quantum Information by Michael Nielsen and Issac Chuang. Probably the most well-known and highly-used book in the field by both students and researchers. It is comprehensive in its coverage of both quantum computation and quantum information. (Suitable for senior undergraduates.)
- Quantum Processes, Systems, and Information by Benjamin Schumacher and Michael Westmoreland. By two pioneers of quantum information theory, this is both a good introduction to quantum theory as a whole and to quantum information and computation. It contains a good treatment of entanglement and Bell’s theorem.
- Quantum Computer Science: An Introduction by David Mermin.
- Introduction to Optical Quantum Information Processing by Pieter Kok and Brendon Lovett. How to use optical systems for quantum computing.
Before mentioning some standard textbooks commonly used in undergraduate classrooms, here are some other ones that are perhaps less well-known but are equally good for getting a feel for physics before being bombarded with mathematics.
- Motion Mountain by Christoph Schiller. This is an excellent introduction to physics: it’s elegantly written, full of examples and thought-provoking questions, and explains the physics of many everyday physical phenomena, even some interesting ones you may never have seen before. And best of all, it contains minimal mathematics – just as a physics introduction should be! I highly recommend it.
- The Flying Circus of Physics by Jearl Walker. Geared specifically towards explaining everyday physical phenomena to highlight the ubiquity of physics.
- Conceptual Physics by Paul Hewitt. Formatted like a standard undergraduate physics textbook, but like The Flying Circus of Physics is devoted to conceptual understanding.
Here are some of the standard texts.
- University Physics with Modern Physics by Hugh Young and Roger Freedman.
- Fundamentals of Physics by David Halliday, Robert Resnick, and Jearl Walker.
- The Feynman Lectures on Physics by Richard Feynman.
- Physics: Principles with Applications by Douglas C. Giancoli.
- Essential University Physics by Richard Wolfson.