XY surface code[1]

Description

Non-CSS derivative of the surface code whose generators are \(XXXX\) and \(YYYY\), obtained by mapping \(Z \to Y\) in the surface code.

Protection

As a stabilizer code, \([[n=O(d^2), k=O(1), d]]\).

Code Capacity Threshold

\(50\%\) at infinite \(Z\) bias with maximum-likelihood decoder [2].\(18.7\%\) for standard depolarising noise with maximum-likelihood decoder [2].

Threshold

\(6.32(3)\%\) for infinite \(Z\) bias, and thresholds of \(\sim 5\%\) for \(Z\) bias around \(\eta = 100\) using a variant of the minimum-weight perfect matching decoder [3].

Parent

Zoo code information

Internal code ID: xysurface

Your contribution is welcome!

on github.com (edit & pull request)

edit on this site

Zoo Code ID: xysurface

Cite as:
“XY surface code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/xysurface
BibTeX:
@incollection{eczoo_xysurface, title={XY surface code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/xysurface} }
Permanent link:
https://errorcorrectionzoo.org/c/xysurface

References

[1]
D. K. Tuckett, S. D. Bartlett, and S. T. Flammia, “Ultrahigh Error Threshold for Surface Codes with Biased Noise”, Physical Review Letters 120, (2018). DOI; 1708.08474
[2]
D. K. Tuckett et al., “Tailoring Surface Codes for Highly Biased Noise”, Physical Review X 9, (2019). DOI; 1812.08186
[3]
D. K. Tuckett et al., “Fault-Tolerant Thresholds for the Surface Code in Excess of 5% Under Biased Noise”, Physical Review Letters 124, (2020). DOI; 1907.02554

Cite as:

“XY surface code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/xysurface

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/quantum/qubits/surface/xysurface.yml.