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.
An extensive article explaining the future of Bitcoin mining using fossil fuels.
The future of Bitcoin mining forces us to consider what tradeoffs we are willing to make for the continued growth of the network. Mining blocks in a world with mass Bitcoin adoption will require orders of magnitude more energy than present. There is nothing inherently immoral about that, but it does present a challenge in the pursuit of a multi-trillion dollar market capitalization.
Most of us know the Lightning Network, a possible layer 2 solution for the scaling problem. But did you hear about Statechains? No? Here is a good introduction:
The basic idea behind Statechains is that you lock up money between two parties in a 2-of-2 multisig: the Statechain entity and the user. When the user wants to transfer the money (the entire UTXO), they simply hand over their private key, which we call the transitory key, to the intended recipient.