Could you elaborate? I'm not sure I follow. It's been a while since my CS Theory classes.

Basically, you can do 64 bit calculations on a 16 bit traditional computer, it just takes more steps and some RAM. However, to do 64 bit quantum calculations you need a 64 quibit quantum computer. Now, we may be able to build a 64 QC, bout even that is useless for real world encryption. Further, it while it does not take more time to run a 64vs 4096 quibit QC, it does become exponentially harder to build.

Sort of like trying to measure a building to the nearest inch is harder than nearest foot, and every added digit of accuracy is even harder.

Good analogy; and quite accurate.

It's not just the number of bits that affects signal to noise ratio, though... It's also the complexity of the calculation; more gate operations and longer storage in memory leads to more quantum decoherence. And AFAIK, each type of calculation must be implemented in hardware, because reversible quantum gates must be used. This means you would need a specialized chip for each algorithm. I haven't confirmed this understanding with someone that specializes in QC, but I don't see a way around it, other than to combine many algos onto a single chip, sharing as many gates as possible, but degrading S/N further.

Re: need custom hardware for each algorithm

Something tells me, for an intelligence agency, building a quantum computer only for the purpose of breaking cryptographic keys would be a worthwhile investment.

An investment they have already made:

The effort to build “a cryptologically useful quantum computer” -- a machine exponentially faster than classical computers-- is part of a $79.7 million research program called “Penetrating Hard Targets.”

article

https://www.washingtonpost.com/world/national-security/nsa-s...

leaked document

http://apps.washingtonpost.com/g/page/world/a-description-of...

Yes, that's one of the big questions in QC. If people manage to build good error correction for QC some day, scaling will be less of an issue.

Scott Aaronson's blog has some good background information for the layman.