alt Hacker News> In the case of quantum algorithms in BQP, though, one of those properties is SNR of analog calculations (which is assumed to be infinite). SNR, as a general principle, is known to scale really poorly.
As far as i understand, that isn't an assumption.
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.
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> 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 ...
There are several properties that separate real quantum computers from the "BQP machine," including decoherence and SNR. Error-correction of qubits is mainly aimed at decoherence, but I'm not sure it really improves SNR of gates on logical qubits. SNR dictates how precisely you can manipulate the signal (these are a sort of weird kind of analog computer), and the QFTs involved in Shor's algorithm need some very precise rotations of qubits. Noise in the operation creates an error in that rotation angle. If your rotation is bad to begin with, I'm not sure the error correction actually helps.