From my understanding since SegWit got activated exchanging the SHA256 algorithm for a/any quantum resistant algorithm (which already existed in 2017 when the last hard-fork was carried out) is just a matter of another soft-fork... like taproot has been done. And the more nodes are run by single entities from the community the more 'votes' does the community get to decide about such future events.
This also means in a first attempt preventing quantum computers breaking/hacking Bitcoin we can just switch from SHA256 to SHA2048 and everything will be fine for another while...

So, when quantum computers come anywhere near breaking SHA256 (which needs more than 256qBits and especially for Bitcoin it needs way more qBits because: RIPEMD-160(SHA-256(pubkey)) is at work and not just SHA...) miners and pretty much anybody who's got skin in the game will have lots of incentives implementing the best available solution existing on earth that day.
Bitcoin-Qt is the 'consensus' of tested stable software as result of the BIP process (Bitcoin Improvement Proposals) all living and breathing because of open source.

When all of this might happen Bitcoin of course will be downwards compatible (you'll always be able to transfer 'non-quantum-resistant funds') but then we all will be well adviced to redeem our collectibles and transfer funds to quantum resistant addresses.

Don't nail my words to a cross but they are thought to give you a little bit of a relief if you read too much FUD ;-)

Edit4readability'n'correctness

@krogoth: for the exact same reason some days ago I thought about funding a BCmint coin with some honeypot-BTC. But by talking more about BCmint in the collectibles section long-con-scammers might be alarmed...

The silicon transistor is the basic building block of modern CPU, GPU and ASIC. Breakthroughs in P and N doped materials to create semiconductors are the major breakthrough which made post vacuum tube technology possible. There is no quantum equivalent to a silicon transistor. That's the obstacle modern scientists will have to overcome to create a legitimate quantum computer IMO. It is quite a significant technical obstacle to overcome. I don't know if there is anyone in the world today who is seriously working on the problem.

There are no patents being filed for a quantum successor to the silicon transistor. There isn't anyone with a general concept or idea on how it might be possible. If there was they would be able to explain their design in 5 sentences or less. The basic principles which allow for semiconductors to function is very basic and fundamental. And that is what quantum computing technology is lacking at the moment.

I doubt the so called quantum computer will be developed by then. If they succeed, it will be very expensive and unecconomical to attack Bitcoin with it.

Bitcoin could potentially become quantum resistant if you could make it millions of times harder to brute force attack a private keys by using dynamic randomness to hide real keys in millions of empty keys. The nice thing about Bitcoin is it doesn't seem to limit how many address that can be generated.

and by that time, the btc developers should have already come up with a solution. so i don't think they will just be sitting knowing that this currency is at its doom. we can't tell what the future holds but i guess devs will do as much as they can to preserve this currency. but right now, we don't know what quantum technology can really do to the crypto market. all are just speculations as no one knows what will actually happen in such situation.