Certain Crypto Currencies are claiming to have them already. When Bitcoin?
In fact, there are clear proposals for this, namely P2MR or pay-to-merk root addresses from BIP-360.
These addresses (bc1z) are expected to be Bitcoin's first step as a measure to protect against quantum computing.
This new type of address eliminates the disclosure of public-key spending, forcing all transactions to be carried out through a script. This is based on hash functions, which are much more resistant to quantum attacks, and never exposes the public key directly on the blockchain, although at the moment there is no imminent threat related to quantum computing.
And it's important to note BIP 360 itself isn't enough.
P2MR does not, by itself, protect against short exposure quantum attacks, but these attacks can be mitigated by future activation of post-quantum signatures.
Combined with P2MR, post-quantum signature schemes can provide comprehensive quantum resistance to P2MR outputs, including protection from short exposure attacks.
Who knows how long before developer choose suitable QC-resistant cryptography, partly because such cryptography are relative new and not really "battle tested".
