  Fermions are fundamental particles which obey seemingly bizarre
quantum-mechanical principles, yet constitute all the ordinary matter that we
inhabit. As such, their study is heavily motivated from both fundamental and
practical incentives. In this dissertation, we will explore how the tools of
quantum information and computation can assist us on both of these fronts. We
primarily do so through the task of partial state learning: tomographic
protocols for acquiring a reduced, but sufficient, classical description of a
quantum system. Developing fast methods for partial tomography addresses a
critical bottleneck in quantum simulation algorithms, which is a particularly
pressing issue for currently available, imperfect quantum machines. At the same
time, in the search for such protocols, we also refine our notion of what it
means to learn quantum states. One important example is the ability to
articulate, from a computational perspective, how the learning of fermions
contrasts with other types of particles.
