Topological quantum computation within the anyonic system the Kauffman-Jones version of SU(2) Chern-Simons theory at level 4

TL;DR

This paper develops methods for implementing phase and permutation gates in topological quantum computation using the Kauffman-Jones SU(2) Chern-Simons theory at level 4, advancing the control of anyonic systems.

Contribution

It introduces techniques to convert ancillas into phase gates, realizes irrational phase gates, and implements all 2-qubit permutation gates within this topological framework.

Findings

Methods to turn ancillas into phase gates

Realization of irrational phase gates

Implementation of all 2-qubit permutation gates

Abstract

We provide ways to turn ancillas into phase gates (chapter 1), leading to irrational phase gates (chapter 2). We realize all the 2-qubit permutation gates (chapter 3).