[gjm11]

Here's Scott Aaronson's answer to a similar question on his blog a couple of weeks ago:

Yes, Nielsen and Chuang is the standard textbook for quantum computing; it’s excellent (even though 16 years old by now). If you wanted to start with something shorter and more introductory, you could try David Mermin’s “Introduction to Quantum Computer Science.”

[dmmckay]

Lipton wrote a pretty decent and short intro to QC that builds the theory a little differently from usual. It is aimed more towards Mathematicians and Computer Scientists than Physicists, I believe, but I think it is pretty understandable in general.

I think Sipser is probably the best introduction to Computation if you do not have a background in Computability and Complexity. Arora and Barak's text has a much larger breadth and is much more detailed as far as Complexity goes. It is the more appropriate of the two if you are just interested in Computational Complexity.

[anukulrm]

Great, thanks! I'll check those out.