I work on quantum algorithms and quantum cryptography, two broad applications of quantum computing. I try to figure out what types of problems we can do faster with a quantum computer than we can with a classical computer, what those algorithms look like, and how we can do those computations securely. There are some kinds of classical algorithms that can always be sped up with a quantum computer. For example, if you want to find a mathematical object that has a particular property, you might start to look at a whole bunch of objects and test each one for the property you want. That search process of continually sampling will be much faster on a quantum computer than on a classical one, so any time you have a classical algorithm that relies on that technique, you know right away that the quantum version will be an improvement. In other cases, there is no classical analog to a quantum algorithm, but instead we look at the techniques we have available to us and try to imagine what other problems they might be able to help us solve. By proving that a new algorithm would find the answer to a given question in a certain number of steps — hopefully a smaller number than it would take on a classical computer — we hope to optimize these quantum processes, which will be useful for all kinds of future applications in quantum computing.