Learn Quantum Computing: Physics, Math & Theory Basics

[sol66]

I know this is a rather new field of research and that I may seem rather silly for asking, but I would like to know besides upper divison undergrad quantum mechanics ( which I've already studied ), what other subjects should I learn to get the basic background for researching quantum computers.

Physics and especially quantum mechanics is an interesting subject, in which I've felt that I've learn so much yet I cannot see how I would even apply it to creating qubits. My understanding of quantum mechanics goes as far as pertubation and such, but that is about it.

Also, what other types of math should I learn, possibly topology or differential geometry? I'm guessing Quantum Field Theory, Atomic Physics, and Quantum Electro Dynamics would be the next theories I might want to learn. But then again I don't want to waste my time picking up on things that are useless.

I am ofcourse infinnetly ignorant so please educate me. Oh, and telling me I'm crazy isn't going to keep me from learning.

 

[krilvyn]

It depends whether you are more interested in the computation side of quantum computing (e.g., quantum algorithms, quantum information theory, etc.) or more interested in the physics side (figuring out how to actually build quantum computers). On either side, I think having a really strong knowledge of linear algebra is the most important thing from a math point of view. As far as I know diff. geom. doesn't have direct application to quantum computing, but I could be wrong. Topology, information theory, more advanced algebra would certainly be useful. For the computation side, you'd want to take mostly CS theory courses in algorithms, theory of computing, computational complexity, etc. On the physics side, I think anything you mentioned would be useful but it really depends on the specific area you want to work in, as there are many different methods of building quantum computers that are currently being researched.

Your best bet is probably to pick up the Nielsen+Chuang book, or to read the online books/notes by John Preskill, Scott Aronson, etc. to get the foundations of quantum computing down, and then you'll see what areas you are weak in, or what areas you are particularly interested in and figure out your future studies based on that.