[grungegun]

There's one big issue with QC currently. There is no mathematical demonstration that QC is scalable. All the speed-ups need some form of error correction to scale the way digital computation has. All hardware advances are just increases in computational fidelity so far to allow more useful qubits. Shor has an error correction algorithm for a single qubit, and there have been improvements to that, but nothing general enough to show that QC can even scale like digital computers can.

[throw149102]

From my understanding, the quantum threshold theorem states that if you have a low base error rate (1-3%) you can apply multiple levels of a single quantum error correcting code to get arbitrarily low levels of errors on a logical qubit ("remove errors faster than you introduce them"). Right now that means that you need approximately 1000x physical qubits for 1 logical qubit, but to me that's a solid mathematical/theoretical demonstration that you can scale QC.

[grungegun]

You're right. I've looked at quantum codes before, but apparently my understanding was lacking - thanks for the info.