Universal topological quantum computing via double-braiding in SU(2) Witten–Chern–Simons theory
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Abstract
We study the problem of universality in the anyon model described by the SU(2) Witten–Chern–Simons theory at level k. A classic theorem of Freedman–Larsen–Wang states that for k≥3,k≠4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k \ge 3, \ k \ne 4$$\end{document}, braiding of the anyons of topological charge 1/2 is universal for topological quantum computing. For the case of one qubit, we prove a stronger result that double-braiding of such anyons alone is already universal.