Mining coins suddenly becomes really fast and far more energy efficient. All 21M BTC would be mined before we hit all 5 halvings.

This doesn’t happen, because Bitcoin has difficulty adjustments. When computing power rises enough, the difficulty adjusts up to maintain an average block time of 10 minutes. If quantum computing scaled it up so drastically, then the difficulty would rise just as drastically until it was back to an average of 10 minutes.

I don’t thing the blockchain cryptography is quantum resistant, is it?

Not really, no, but that’s more of an issue with the public-private key systems we use to verify ownership of wallets than it is about mining, per se. It would make sense for there to be a hard fork to a quantum-resistant algorithm to make sure the actual state of blocks remain small, but that’s a different issue. The primary change would need to be a switch to quantum-resistant cryptography for public-private key pairs to ensure nobody can steal anyone else’s assets using a quantum computer.

Theoretically, at some point the reward becomes so small, so fractional, that mining itself isn’t cost effective.

Remember fees. People pay to have their transactions included. The goal for Bitcoin is to have these fees pay the miners instead of the block reward, which is effectively just a temporary subsidy.

As of now, fees don’t usually make up more than a few percentage points of the block reward, so it’s looking unlikely that they will ever actually maintain the same, or higher rate than the current subsidy.

If you wanted a blockchain that was closer to being sustainable in terms of fee revenue funding monetary policy, you’d want Ethereum with its burn mechanics.