# How much can we compute with one single qubit?

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?

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.