Given that observing the state of a qubit changes it, and (I guess) that changes all entangled qubits, what methodology is used to read out the result of a quantum computer's calculation?
When the quantum computation is finished, you suck it up and you measure. The entire point of the quantum algorithm was to set things up in such a way that, even as the measurement destroys the superposition state, the right answer is observed with a high probability (since you used constructive and destructive interference to boost its amplitude, while suppressing the amplitudes of the wrong answers).