It is true that I am not being mathematically precise in my statements. The precise way to say what I said is: In order to represent completely an arbitrary state in the space of one billion qubits, you will need a number of bytes exponential in that number of qubits. If we have, as mathematical entities, one billion additional qubits, this will be equivalent to increasing the dimension of our existing system by 2^(1 billion) times.

Of course, I am saying "mathematical entities", and almost all practitioners of quantum computing are aware of the challenge to actually build them.

> there are very few problem for which quantum computers are known to perform better than standard computers.

http://math.nist.gov/quantum/zoo/

That is a great list! (But I don't think it contradicts what I wrote)