Quantum Money and Scalable 21-cm Cosmology by

This thesis covers two unrelated topics. The first part of my thesis is about quantum money, a cryptographic protocol in which a mint can generate a quantum state that no one can copy. In public-key quantum money, anyone can verify that a given quantum state came from the mint, and in collision-free quantum money, even the mint cannot generate two valid quantum bills with the same serial number. I present quantum state restoration, a new quantum computing technique that can be used to counterfeit several designs for quantum money. I describe a few other approaches to quantum money, one of which is published, that do not work. I then present a technique that seems t