But as far as I know, quantum computers are just an abstract theoretical concept, right? I don't think there's any working ones outside of very limited laboratory tests. Certainly nothing practical in the sense of being able to do ordinary everyday computing tasks. So I'm not overly worried about that for the time being.
I admit it is a concern in the long-term. Probably the entire field of cryptography (and by extension cryptocurrencies) will have to change in some fundamental way if / when the quantum revolution finally comes.
There are some baby quantum computers with very small processing power, that they have constructed in labs, but nothing that is better than a classical supercomputer.
Yes the internet will be affected, and many online services but Bitcoin will not be if you follow the advices in this artcile and the next one:
https://steemit.com/bitcoin/@profitgenerator/bitcoin-security-overview-and-quantum-computers