Quantum computation is very powerful. If you have quantum computer, none of the current cryptography works and everything, including bitcoin, is compromised.
Like that researcher, I too have scanned blockchain for compromised public address and have been able to find some. This is unrelated to quantum cryptography but pertaining to the weak methods of encryption used such as brain wallets with common keywords. People don't use it anymore.
Currently, there is no method to extract private key. Nor will it ever be, because that is maths for you. But yes, you can guess someone's private key, by trying all possible keys that can be. Quantum computers would be much faster so just make that brute force guess faster.
Great explanation! Thanks!