The canonical reference for learning quantum computing is the textbook Quantum computation and quantum information by Nielsen and Chuang. Another good book (with more of a "little yellow book" experience) is Classical and Quantum Computation by Kitaev, Shen and Vyalyi.

There are also great free resources online.

- David Mermin's lecture notes are elementary and have a CS focus
- John Preskill's lecture notes are slightly more advanced and use a physics perspective.

If you want to get a flavor of what research is currently hot, then one place to look is at the program of the last few QIP workshops. A less curated list of interesting papers can be found at scirate.com, where looking at the most scited papers in the last year should bring up some interesting work.

Some more specialized books/lecture notes are:

- Quantum Algorithms lecture notes by Andrew Childs
- From Classical to Quantum Shannon Theory by Mark Wilde. Thorough and detailed with plenty of exercises.
- The Functional Analysis of Quantum Information Theory written by Gupta, Mandayam and Sunder based on lectures by Effros, Paulsen, Pisier and Winter. Denser and focused on the math side more than applications.
- Alice and Bob meet Banach by Aubrun and Szarek. Incomplete textbook draft, but it looks like it'll be the definitive treatment of the probabilistic method in quantum information.
- The Mathematics of Entanglement by Brandao, Christandl, Walter and myself. Idiosyncratic and incomplete lecture notes on some of our pet topics.

If you have more resources to suggest or any comments on this page, then please email me at aram@mit.edu.