Quantum Science Seminar, Shawn Cui


Title: Mathematics of topological quantum computing.

Topological quantum computing (TQC) is among the best approaches to building a large-scale
fault-tolerant quantum computer. The quantum media for TQC are topological phases of
matter that harbor non-Abelian anyons and quantum gates are implemented by braiding of
anyons. The mathematics of topological phases of matter is described by modular tensor
categories or equivalently by topological quantum field theories. We give a review on the rich
interactions between TQC and the subjects mentioned above. We illustrate the concept of TQC
with an important class of anyons, namely, metaplectic anyons, and show that braidings of
anyons assisted by certain topologically protected measurements is universal for quantum
computing. The interest in metaplectic anyons arises from the potential physical realization in
fractional quantum Hall systems. Time permitting, we also talk about the application of
topological quantum field theories in topology and give a new invariant of smooth 4-manifolds
of state-sum type.

The audio recording and speaker slides are below