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

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• 作者：Claire Levaillant
• 关键词：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
• 刊名：Quantum Information Processing
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：15
• 期：3
• 页码：1135-1188
• 全文大小：3,800 KB
• 参考文献：1.Bauer, B., Bonderson, P., Freedman, M.H., Hastings, M., Levaillant, C., Wang, Z., Yard, J.: Anyonic gates beyond braiding, unpublished
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  14.Levaillant, C.: The Freedman group: a physical interpretation for the \(SU(3)\) -subgroup \(D(18,1,1;2,1,1)\) of order 648. J. Phys. A Math. Theor. 47, 285203 (2014)MathSciNet CrossRef MATH
  15.Levaillant, C.: On some projective unitary qutrit gates. arXiv:​1401.​0506
  16.Levaillant, C.: Making a circulant 2-qubit entangling gate. arXiv:​1501.​01013
  17.Levaillant, C.: Protocol for making a 2-qutrit entangling gate in the Kauffman–Jones version of \(SU(2)_4\) . arXiv:​1501.​01019
  18.Levaillant, C., Bauer, B., Freedman, M., Wang, Z., Bonderson, P.: Universal gates via fusion and measurement operations on \(SU(2)_4\) anyons. Phys. Rev. A 92, 012301 (2015)ADS CrossRef
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• 作者单位：Claire Levaillant (1)
  
  1. Paris, France
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Physics
  Mathematics
  Engineering, general
  Computer Science, general
  Characterization and Evaluation Materials
  
• 出版者：Springer Netherlands
• ISSN：1573-1332

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.