X-cube model code[1] 

Description

A Type-I fracton code supporting a subextensive number of logical qubits.

Decoding

Parallelized matching decoder [2].

Code Capacity Threshold

Independent \(X,Z\) noise: \(\sim 7.5\%\), higher than 3D surface code and color code [3].

Parents

References

[1]
S. Vijay, J. Haah, and L. Fu, “Fracton topological order, generalized lattice gauge theory, and duality”, Physical Review B 94, (2016) arXiv:1603.04442 DOI
[2]
B. J. Brown and D. J. Williamson, “Parallelized quantum error correction with fracton topological codes”, Physical Review Research 2, (2020) arXiv:1901.08061 DOI
[3]
H. Song et al., “Optimal Thresholds for Fracton Codes and Random Spin Models with Subsystem Symmetry”, Physical Review Letters 129, (2022) arXiv:2112.05122 DOI
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Zoo Code ID: xcube

Cite as:
“X-cube model code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/xcube
BibTeX:
@incollection{eczoo_xcube, title={X-cube model code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/xcube} }
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Permanent link:
https://errorcorrectionzoo.org/c/xcube

Cite as:

“X-cube model code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/xcube

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/quantum/qubits/stabilizer/topological/fracton/xcube.yml.