Quantum Information Processing

, Volume 15, Issue 3, pp 1135–1188 | Cite as

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



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.


Quantum computation with anyons Braids Fusion measurements Interferometric measurements Ancilla preparation Irrational qubit and qutrit phase gates Computational universality for n-qubit gates Computational universality for 1-qutrit gates Controlled NOT gate 



The author is delighted to heartedly thank Michael Freedman for kind, exciting and generous guidance and for many inspiring discussions. Working with him and Station Q on these topics is a great chance and a fabulous experience. She thanks Matthew Hastings for enlightening discussions. She is also quite pleased to thank Bela Bauer, Stephen Bigelow, Parsa Bonderson, Meng Cheng, Spiros Michalakis, Chetan Nayak and Zhenghan Wang for helpful discussions.


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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.ParisFrance

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