A fruitful avenue may be in quantum simulation, i.e. simulating a quantum system and computing its properties. This is why the other commentor mentioned biochemistry and material science, since these are two domains where quantum effects are important to understanding.
To give two concrete examples:
In biochemistry, we could hope to understand how bacteria are able to do nitrogen fixation, possibly leading to a more energy efficient and less GHG-emitting alternative to the Haber process.
In material science, we could hope to better understand the mechanism for current high-temperature superconductivity, possibly leading to the development of superconductive materials at even higher temperatures, lower pressures, and with more convenient other properties (such as toughness, ductility).
Yes, they use superposition of the most "classical" quantum states (coherent states). These are called (Schrödinger) cat states, since his thought experiment was about a quantum superposition of a very classical object (a cat): https://en.wikipedia.org/wiki/Cat_state
It is theorized that CERN is powered by the bodies of dead physicists that turn in their graves every time someone brings up the Schroedinger cat to an audience that doesn't even know complex numbers.
There's also a smaller power section filled with computer scientists that turn when someone says that the quantum computer offers exponential speedups.
The distinction between "big cats" and "small cats" is whether or not they purr. Ocelots and Cheetahs are wild "small cats" which can purr. Lions, tigers, panthers are "big cats" don't purr. There's a taxonomic distinction.
