Kitaev's Z_d-Codes Threshold Estimates

Authors Guillaume Duclos-Cianci, David Poulin

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Guillaume Duclos-Cianci
David Poulin

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Guillaume Duclos-Cianci and David Poulin. Kitaev's Z_d-Codes Threshold Estimates. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 285-293, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)


We study the quantum error correction threshold of Kitaev's toric code over the group Z_d subject to a generalized bit-flip noise. This problem requires novel decoding techniques, and for this purpose we generalize the renormalization group method we previously introduced in [Duclos-Cianci/Poulin,arXiv:0911.0581,2009; Duclos-Cianci/Poulin,ITW'10,2010] for Z_2 topological codes.
  • Quantum error-correction threshold
  • Topological stabilizer codes
  • Qudit stabilizer codes


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