Most cryptocurrencies rest on cryptography that a large enough quantum computer can break. There is more than one way to build something that holds up. Designs built on hash functions have the longest track record; newer lattice-based schemes have now been standardised, though they have had far less time under public scrutiny. What is striking is how few chains use any of it to protect ordinary funds today.
There is now a page on this site that sets out where each one actually stands: Which cryptocurrencies survive a quantum computer? It grades well-known chains on what is actually deployed and usable on mainnet. A roadmap, a testnet or a target date is not protection, however credible it is, though it does separate a chain that is working on the problem from one where no public plan could be found. Every claim carries a source.
This site is run by the Neptune community, so read the grading sceptically and check the sources; they are all linked. If a grade is wrong, say so on the forum; corrections are genuinely welcome.