Title: Universal quantum computation with qutrits

Abstract:

It was shown by R. Brylinski and J.-L. Brylinski that a universal set of single qudit gates together with any 2-qudit entangling gate is sufficient for universal quantum computation. In this talk we focus on the qutrit and a specific anyonic system, namely the Kauffman-Jones version of Chern-Simons theory SU(2)4. We deal with two sets of four anyons of topological charge 2 forming a qutrit and present a way to make a 2-qutrit entangling gate. The operations we use consist of ancilla pair creation, braids, interferometric measurements, fusions and unfusions of anyons.

Depending on time and interest, we will also outline how to prepare an ancilla for the same qutrit, which can be successfully used to make an infinite order phase gate, thus leading to a universal set of single qutrit gates by a result of M. Freedman and Z. Wang.