Q:

How much I should know in Computer Science to work with Quantum Computing

I browsed some books about quantum computers and there is some concepts from computer science (for example, Turing machine) except quantum physics and mathematics.  So, if I want to study quantum computing what I should know from computer science?  Is it useful to read SICP, for example? 

A:

Chapters 2 and 3 of Nielsen and Chuang should give you the background you need.  
The Feynman Lectures on Computation provides an easy to understand introduction to CS for physicists. 
Beyond that, you can read some of Kitaev's Arxiv papers to see whether you're a genius. 
SICP may not be directly applicable, but it may very well be the best programming book ever written, so it's always useful!