People have already said here most of what I want to say in this comment, but just to make it as explicit as possible:

Essentially the only reason anyone thinks that useful quantum computation is possible is because of things called threshold theorems, which state that as long as the noise in each qubit is less than some small but non-zero error rate you can add more qubits and use quantum error correction to make your computation arbitrarily precise. In other words as long as you're below the threshold rate quantum computers scale well.

Of course those threshold rates are very very small, and creating significiant numbers of qubits which are below the threshold rates is incredibly difficult, but theoretically it works.