alt Hacker News> The assumption is that the SNR of logical (error-corrected) qubits is near infinite, and that such logical qubits can be constructed from noisey physical qubits.
This is an argument I've heard before and I don't really understand it[1]. I get that you can make a logical qubit out of physical qubits and build in error correction so the logical qubit has perfect SNR, but surely if (say the number of physical qubits you need to get the nth logical qubit is O(n^2) for example, then the SNR (of the whole system) isn't near infinite it's really bad.
[1] Which may well be because I don't understand quantum mechanics ...
The really important thing is that logical qbit error decreases exponentially with error correction amount. As such, for the ~1000 qbit regime needed for factoring, the amount of error correction ends up being essentially a constant factor (~1000x physical to logical). As long as you can build enough "decent" quality physical qbits and connect them, you can get near perfect logical qbits.