Since Google only has a 72 qubit Q-computer, and it has taken a decade to reach this point, then a 2,500 qubit quantum processor appears to be approximately 7 years away.
With that said, this will still likely be a super specific system, so I doubt it would actually be used to identify the links between public and private keys.
There is no connection between the problem of finding a private key knowing the public key (and knowing the ciphertext, the problem of asymmetric encryption systems) and the problem of finding the law of obtaining hash from input information.
These are fundamentally different problems. Mathematically, the first task is cryptanalysis.
The second one is solved by brute force attack.
That's why we need so many kubits to solve the SHA256 task.
But protection against this danger is also very simple; SHA256 can be easily made into SHA512 or 1024.
But you can't do that with a pair of public key + private key. This cryptography breaks down with any length of key, including mathematical.
For this reason they are looking for new post quantum systems to replace asymmetric encryption systems.
It is for this reason that symmetric encryption systems do not need to be upgraded to withstand quantum computers.
There is one more option, you can see the details here:https://bitcointalk.org/index.php?topic=5204368.0
As far as I'm aware, current attempts at making Bitcoin and other cryptocurrencies quantum-computer proof actually rely on using a complete different solution, rather than simply moving one step ahead by using more robust encryption.
See the following: https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.180410
It outlines a slow defence against quantum attacks, and a novel solution IMO;
"We then propose a simple but slow commit–delay–reveal protocol, which allows users to securely move their funds from old (non-quantumresistant) outputs to those adhering to a quantum-resistant digital signature scheme."