文摘
By braiding and measuring anyons, we realize irrational qubit and qutrit phase gates within the anyonic system the Kauffman-Jones version of SU(2) Chern-Simons theory at level 4. We obtain universality on 1-qubit and 1-qutrit gates. In the qubit case, we also provide a protocol for realizing the controlled NOT gate, thus leading to universality on n-qubit gates.