The market price of Bitcoin may be completely detached from the global mining effort from a mathematical point of view but it will still be dependent on it – the amount of energy put towards securing the network is still a fundamental key parameter of Bitcoin.
Using a quantum computer can perform the hashcash PoW by performing quadratically fewer hashes than is needed by a classical computer.
However, the extreme speed of current specialized ASIC hardware for performing the hashcash PoW, coupled with much slower projected gate speeds for current quantum architectures, essentially negates this quadratic speedup, at the current difficulty level, giving quantum computers no advantage.
Rory Highside has written a fantastic article diving deeper into proof of work with the following topics:
Consensus & The Byzantine Generals Problem.
Proof-of-Work and Competition.
Proof-of-Work economically incentivizes Bitcoin to become the ultimate arbiter of truth.
The symbiotic relationship miners have with Bitcoin.
World Kilowatt Dollars.
Bitcoin Time-Energy Accounting and Thermodynamics.
The Bitcoin Metabolism.
Read his monumental article here:
Due to the network effect on multiple other reasons, the one and only King will be Bitcoin:
Tamas Blummer dives deeper:
Proof of Work
Scarcity through POW