Anyway, also, here's another piece from today:
IBM makes significant breakthrough towards scalable quantum computers
This might come closer to answering your question than anything I said:
Quote:
Information is measured in ‘bits’, and a bit may have two positions (described typically as 0 or 1). Quantum computers however don’t use these bits, and instead they use quantum bits, or ‘qubits’. But while a bit must be a 0 or a 1, a qubit can be both 0, 1, or a superposition of both. This difference might seem small and subtle, but in fact, it is absolutely humongous: a mere hundred qubits can store more classical ‘bit’ information than there are atoms in the Universe.

As to the how? Still no idea.
Actually, wait. Now that I think about it, I have a vague idea. Stand by.
So you have these qubits and they are "entangled" with each other. The presentation I saw was on the CS theory of it, not the physics, so I don't know how exactly it relates to quantum entanglement, but I imagine they used the same word because the one has something to do with the other. Anyway, these qubits are represented as nodes on a graph (hypercube, IIRC), and they are entangled if they share an edge. And the state of one qubit depends on the states of all the others it's adjacent to. And then there's a lot of math, like what happens to the whole graph if this one node changes state? So I guess you can represent a whole lot of information that way, a lot more than just 2^n (or 3^n if you're counting superposition as a state).