To add to what you have said.
Cryptocurrencies right now use the blockchain as the distributed ledger on which all transactions are recorded. Traditional computers find it very difficult to break crypto security, but quantum computers (for the reason explained above) would be able to crack the encryption used for private keys. This makes them vulnerable to quantum computer attacks. This is why blockchains will eventually become obsolete and will be replaced by The Tangle, a new platform for cryptocurrency, that eliminates mining. It is also quantum-resistant. The first example of this is IOTA.