Instead, they rely on the underpinnings of quantum mechanics, a branch of physics that's defied conventional understanding for about 100 years, to manipulate individual particles and solve previously unsolvable problems.
If you wanted to say that a quantum computer runs on magic, you wouldn't be too far off. Science fiction daydreams like time travel and teleportation are run of the mill when we're dealing with objects this tiny (think: smaller than an individual atom). The "rules" don't apply.
This opens up some exciting possibilities, especially in a branch of mathematics known as optimization, which is pretty much what it sounds like: finding the best answer from a large set of potential answers. For such a specific slice of math, this field addresses some of the most tangible problems in the real world. What's the best route for a UPS truck to make its deliveries? How do you schedule flights at an airport to keep things running smoothly?