Ethereum is not slow (tps) because it has to make difficult computations. Ethereum is slow because it needs to be fair to all participants considering the following issues:
1) latency. All data needs to be distributed to all nodes
2) coherency. All participants need to agree on the data and it's ordering (consensus)
3) distributed nature. No centralized authority doing the heavy lifting.
Essentially the slowness is due to the consensus protocol.
At this point I assume you are familiar with the basic concepts of mining.
If one node gained an unfair advantage in the mining (quantum computing?) the network would become less decentralized as the one node would complete more and more of the mining. But that would not increase the speed in any way. It only means that the one node solves the mining puzzle faster than other nodes and gets more rewards.
I can't think of a way how faster computing could make the network any faster - or slower. There is no difficult computing to be made except the mining part which is difficult on purpose.
A different consensus mechanism could change the speed but would also mean a radically different network. I'm not fully up to speed with the different consensus mechanisms but they all have their pros and cons - there is a reason Ethereum chose a "slow" mechanism.