There are many digital signature schemes (such as SIDH, New Hope, Lamport+Merkle, SPHINCS, etc) which are not vulnerable to any important quantum attacks.
Further, it is known that BQP (bounded error quantum polynomial time. The quantum computer equivalent of P) is contained in PSPACE. However P=PSPACE is still an open question. This means that we still do not have any theoretical proof that quantum computers are more powerful that classical computers.
What the paper seems to target is quantum-proof account management, a problem which atleast on the Ethereum blockchain is trivial to solve at the moment with some inconvenience and with later Hardforks implementing the account abstraction, will be part of how the chain works. Everyone can then just use a Lamport/Merkle signature, SIDH, New Hope, whatever, as long as it can be implemented on the EVM.
I'm not certain why we need to throw quantum-computing at the blockchain until some arbitrary amount sticks that can be declared "secure".