Quantum Simulation
Using one controllable quantum system to imitate another. The field's most credible near-term payoff, and where hardware is closest to useful.
Quantum simulation is the original use case, Feynman's 1982 pitch: nature is quantum mechanical, so simulate it with something quantum mechanical. Classical computers choke on many-body quantum systems because the description grows exponentially with particle count. A quantum simulator sidesteps this by being a many-body quantum system, engineered so its natural dynamics mirror the material or molecule you care about.
It comes in two styles: analog (build a physical mimic, atoms in an optical lattice standing in for electrons in a crystal) and digital (compile the dynamics into gates). Analog simulation is arguably where quantum hardware is closest to telling physicists something they didn't already know; JILA and NIST Boulder have been running world-class versions for years without calling it quantum computing.