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
Code Capacity Threshold
\(50\%\) threshold for noise infinitely biased towards \(X\) or \(Y\) or \(Z\) errors using cellular-automaton decoder [1].Independent \(X,Y\) noise: threshold value of the sum of both noise probabilities is between \(9\%\) and \(14\%\), depending on the noise bias [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.
- Fracton stabilizer code — The XYZ color code resembles a Type-II fracton code in the limit of infinite noise bias [1].
- 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
Page edit log
- Victor V. Albert (2024-03-29) — most recent
Cite as:
“XYZ color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/xyz_color