Quantum computers ready to leap out of the lab in 2017

is the standard reference. It is well written and light if you have the math background (linear algebra + probability theory)

Even a 32 qbit computer would be a very serious breakthrough.

edit: by a 32 qbit computer, I mean that the device should have 32 qbits of memory in total! I'm not talking about bus size.

That is one of the cool things about quantum computing. You don't need a big device to do interesting computations.