This might be a little stupid question, but I was just talking with some friends who are working in neuroscience and I tried to explain them quantum computing. When I explained them the bloch sphere and the infinite number of points on that sphere, they asked me why we actually do use more than one qubit for computation, since we could store in principle an infinite amount of bits in one qubit (not speaking about reading that out!). So, what I was wondering is the following: Would it be possible in principle by angular manipulation of two qubits - one input and one working qubit to solve any computational problem, like a sat problem, conditioned of course that any operation could be implemented as an angular manipulation?
I think you have answered your own question when you say "not speaking about reading that out!" It doesn't matter if the answer to a problem is encoded in a qubit if that information isn't accessible to us. In fact, it can be shown that measuring a qubit never reveals more than one classical bit of information, the so called "Holevo bound." Exercise for the reader: go look up "superdense coding" and sort through the initial apparent contradiction.
Quantum computers can be simulated by classical computers with a time which is exponentially big in the number of qubits (and linear in the time used by the quantum computer). Thus, if you run a circuit on two qubits which takes time $T$, this can be simulated by a classical computer which uses a time which is $T$ times an exponential function of 2, i.e., a constant: This is, we can do no more with a two-qubit quantum computer efficiently than we can do with a classical computer.
1: quantum calculus is for the moment a theoretical game, there is no existing maching doing it for real.
2: quantum calculus has something very special: you won't get the q-bits back. So you have to think of algorithms and problems with huge combinatory of intermediate calculus based on short data and short output (probably more than 1 bit, still). Not all problems are like that, and algorithms are pretty different.
3: in theory you can have an infinite number of superimposed states in a qbit. But the real world and technologies are about constraints (did you notice that cars not yet roll at the speed of light ? ;-) ) : how long can you keep the states, how precisely can you manage the interactions, how to you inject a data and get a result, etc.