Great resource! Thanks for sharing that. So I take it that if post-quantum cryptography is already being worked on in order to be prepared then that extra layer of security can be written into the Bitcoin code, even that far down the road?
Bitcoin is inherently resistant to quantum computing as it does not disclose the public key, instead it hashes it twice! So the attacker literally has no chance to 'derive' the private key even armed to a super quantum computer like in a science fiction.
So far so good, BUT when one 'spends' his wallet, eventually has to disclose his/her public key and if s/he accidentally tries to use the same address again, well, from here on the alarming flags should be raised if there are powerful enough QCs commercially available.
Note:
In the limited interval between the time of the spend Tx even for the brand new addresses, until they get confirmed, there is a window for the QC attack to compromise the private key and generate another transaction with higher fee and priority and steal funds, taking advantage of this window needs very huge QCs to break the code very fast, not like few days, but few seconds. Such QCs not likely to be built ever.
Anyway, when it comes to upgrade, there will be a soft fork, implementing new address types and thus new cryptographic algorithms. After the fork, all new transactions will be safe in heaven, the only weakness will be the elder UTXOs with used addresses, though it will be the holders' responsibility to renew their wallets asap.
Panic over I guess