The Mathematics of Topological Quantum Computation -

The Mathematics of Topological Quantum Computation

Time: 2018-06-05 Published By: Xiaoni Tan

Speaker(s): Eric Rowell (Texas A&M University)

Time: 14:00-15:30 July 30, 2018

Venue: Room 77201, Jingchunyuan 78, BICMR

Time: 14:00 -15:30, July 30, July 31, August 1, August 2,August 3, 2018.

In this mini-course we will learn the fundamental mathematics of topological quantum computation. Taking representations of the braid group as an entry point, we will discuss the following topics:

1. Topological Quantum Field Theory as a model for topological phases of matter.

2. The computational equivalence of the quantum circuit and topological models for quantum computation, and the universality of (certain) topological systems.

3. Jones polynomial evaluations and the efficient quantum algorithm for approximating their values.

4. Temperley-Lieb-Jones categories and the diagrammatic calculus of ribbon categories--the "programming language" of topological quantum computation.

5. Local braid group representations and direct simulation of topological operations on quantum circuits.

Time permitting we will explore some future directions including fermionic and 3D systems as well as symmetry enriched topological phases.

The prerequisites for this course are minimal--we will use some elementary notions from linear algebra, group theory and low-dimensional topology.

The course will be accessible to graduate students and advanced undergraduate students from mathematics and physics.