An important computation model is circuits. The basic component of circuits are gates. With different gates sets we can build different kinds of circuits, or, in other words, different computations. Classification of computations we can do with different gate sets is what we want to know. In the classical setting, we have Post’s lattice. However little is known in the quantum setting. The aim of this project is to make steps towards a better understanding of the structure of the lattice of quantum gate sets. I will first work on the structure of classical reversible gates over non-binary alphabets, in hopes of getting a theory parallel to the classical (non-reversible) clone theory over non-binary alphabets.

I worked with Yibo Gao, Adrian Vladu, and Dr. Richard Peng on semidefinite programming in summer 2014. I have been working with Dr. Emanuele Dotto on equivariant cohomology theory since spring 2015. I did internship at Google Inc. in summer 2015.