There are more than 1,000,000 'shalecoins' with a 10+ billion US$ value. So we can expect that there are private groups - not institutions like the link below - who want/try to build a supercomputer.
If the potential cost outweighs the potential profit, then I think this will only be written in diagrams and blueprints and will never materialize. We are still not close into designing a viable quantum computer that would be able to decode SHA-256, ECDSA and other involved algorithms contained within the bitcoin protocol. Even if it does, well, it will still take a huge amount of time, and by then we
may have moved into other algorithms that are quantum-resistant.
Truly so, though honestly I don't see why many are crazy about it being applied to bitcoin, and if in case it was successful, it will only damage the value of the said crypto as everyone holding bitcoins and their mothers would rush into selling it immediately to the highest bidder at that time.