XYZ color code[1] 

Description

Non-CSS variant of the 6.6.6 color code whose generators are \(XZXZXZ\) and \(ZYZYZY\) Pauli strings associated to each hexagonal in the hexagonal (6.6.6) tiling.

Decoding

Cellular-automaton decoder [1].

Code Capacity Threshold

\(50\%\) threshold for noise infinitely biased towards \(X\) or \(Y\) or \(Z\) errors using cellular-automaton decoder [1].

Parent

Cousins

  • Honeycomb (6.6.6) color code — The XYZ color code is obtained from the 6.6.6 color code by applying single-qubit Clifford rotations on a subset of qubits such that the \(X\)- and \(Z\)-type generators are mapped to \(XZXZXZ\) and \(ZYZYZY\), respectively.
  • XZZX surface code — The XZZX surface (XYZ color) is a non-CSS analogue of the rotated surface (6.6.6 color) code such that the two codes are related by single-qubit Clifford rotations.
  • Asymmetric quantum code — XYZ color codes perform well against biased noise [1].

References

[1]
J. F. S. Miguel, D. J. Williamson, and B. J. Brown, “A cellular automaton decoder for a noise-bias tailored color code”, Quantum 7, 940 (2023) arXiv:2203.16534 DOI
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Zoo Code ID: xyz_color

Cite as:
“XYZ color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/xyz_color
BibTeX:
@incollection{eczoo_xyz_color, title={XYZ color code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/xyz_color} }
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Permanent link:
https://errorcorrectionzoo.org/c/xyz_color

Cite as:

“XYZ color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/xyz_color

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/stabilizer/topological/color/non-css/xyz_color.yml.