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Simulating quantum mechanics is the big one, frankly.
This could potentially help with designing new drugs and chemical reactions and materials (better solar cells, batteries, high-temperature superconductors...), and even doing simulations of high-energy physics that could help in understanding the origin of the universe.
And it's sort of what quantum computing was "born" to do (it was Richard Feynman's original application from 1981). That quantum computing can EVER help with purely classical problems, like factoring integers, is a sort of miraculous coincidence that didn't need to be true. It's just that, once Peter Shor discovered his quantum factoring algorithm in 1994, the world started demanding/expecting more and more quantum speedups for classical problems, like in the fable of Rumpelstiltskin.
I often say that, for me personally, the #1 application of quantum computing that motivates and excites me, is simply disproving all the people who confidently claimed that scalable quantum computing was impossible! :-D
A lot of bitcoiners are hyper-focused on cryptographically relevant quantum computers deriving private keys from exposed public keys, but we never really talk about what else quantum computers might be useful for. What are the problems people who work on quantum computers are interested in solving?