Briefly, a fully fault-tolerant quantum computer could give a square-root speedup for Bitcoin's proof-of-work, and could completely break its elliptic-curve-based signature scheme. Both issues could in principle be fixed by migrating Bitcoin to quantumly harder problems, though in practice doing so could open up security holes of its own. This hasn't been done, but I think maybe there are other cryptocurrencies trying to use quantum-secure crypto from the outset? Googling just now, I found something called "Quantum Resistant Ledger" (https://theqrl.org/) -- does anyone here know more about what's out there?
Let me stress that none of this is a concern with the QCs of the near future, which will have at most a few hundred decent qubits and no error correction, and which will not be able to threaten Bitcoin or any other cryptography.