Quantum computing will never replace classical computing. The problems that are tractable by qc are very specialized. The aspects I find bothersome about the learned discussion of qc are that they mainly focus upon the algorithmic manipulation of the entangled qubit state and theoretical advantages of the qc. However, (and this largely reflects my own ignorance) I worry that there are severe bottlenecks in the measurement (read out) of the quantum state, in addition to the problems of stability, etc. You can only read out "part of the state" and you must efficiently, repetitively, make identical copies of the state since read-out is a demolition of the state. You're essentially doing a particle physics scattering experiment with a qc and measuring the distribution of allowed final states.
In the end, if you want to factorize a very large number (eg 500 digits) into two very large prime factors, eg (300 x 200) the qc will give you a probabilistic list of answers (even if the 500 digit number itself is prime). On standby is a companion classical machine that multiplies these "hypothetical answers" together to see which is right
(the multiplication of a 200 digit times a 300 digit number is fast and easy classically; the factorization of the result takes eternity if you don't know the answer). If indeed you had 10^4 possible hypothetical answers, the combined qc and cc could perform the task conveniently quickly, while no cc could ever possibly solve the problem in the lifetime of trillions of universes in series.
However, if at the end you have done the 10^4 multiplications and you have no correct number it only means the original 500 digit number has a high probability of being prime (of course, if your opponent is known to have sent it as an encryption key, then it must be factorizable.)
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