My research focuses on mathematical aspects of quantum information and computation. One goal is to make theoretical advances towards the realization of a fault-tolerant quantum computer. Another is to gain a better understanding of the physical nature of information, computation and complexity.
One direction of my research aims to characterize the optimal asymptotic rates for performing tasks like error correction, communication and entanglement manipulation in quantum systems. Another direction uses number theory and geometry to explore arithmetic aspects of gates, codes, algorithms and measurements for quantum systems. I am particularly interested in algebraic measures of complexity that exist in this setting, especially in ways they may relate to notions of complexity considered in high energy physics. I am also interested in various aspects of topological phases in 2+1D, from explicit realization in physical systems to the arithmetic of modular categories.