Computers are machines that do math really fast. We program them to solve calculation problems that are useful to us, like predicting tomorrow's weather or telling you how to avoid all of the construction on your way to work so that you get there fast. You can think of using a computer as giving it some information as an input (a list of construction sites), running the computer, and then getting some information back out (the best route to work). Computers are good at solving a lot of useful calculation problems, but there are other important problems that computers seem really bad at solving.
Quantum computers are a hypothetical kind of computer based on the laws of quantum mechanics. They can solve some of the problems that seem hard for regular computers by using a different kind of information: "quantum information." Quantum information is stored in tiny particles like electrons and photons; you can't write it down on paper. So far, we've studied what quantum computers are good for when we ask them to answer questions written in normal information. We haven't studied what quantum computers are good for when we ask them to solve problems written in quantum information. My goal is to find out which "quantum information problems" quantum computers are good at solving. To do that, I'll figure out how to use quantum computers to solve some of those problems, and figure out how "quantum information problems" are related to the well-understood "normal information problems."