XY surface code[1]
Alternative Names: Tailored surface code (TSC).
Description
A variant of the surface code whose generators are \(XXXX\) and \(YYYY\), obtained by mapping \(Z \to Y\) in the surface code. While this code is equivalent to a CSS surface code with the same distance, other properties like noise-bias performance can differ significantly.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 depolarizing noise with maximum-likelihood decoder [2].Threshold
\(6.32(3)\%\) for infinite \(Z\) bias, and thresholds of \(\approx 5\%\) for \(Z\) bias around \(\eta = 100\) using a variant of the minimum-weight perfect matching decoder [3].Cousins
- Heavy-hexagon code— XY surface code can be adapted for a heavy-hexagonal point set [4].
- Asymmetric quantum code (AQC)— XY surface codes perform well against biased noise [1].
Member of code lists
Primary Hierarchy
Generalized homological-product qubit CSS codeQLDPC Qubit Generalized homological-product CSS Stabilizer Hamiltonian-based QECC Quantum
Kitaev surface codeCDSC Twist-defect surface QLDPC Qubit CSS Generalized homological-product Lattice stabilizer Stabilizer Abelian topological Topological Hamiltonian-based QECC Quantum
Parents
The XY surface code is obtained from the surface code by applying \(H\sqrt{Z}H\) to all qubits, thereby exchanging \(Z\leftrightarrow Y\). While it is equivalent to a CSS surface code with the same distance, but other properties like noise-bias performance can differ significantly.
XY surface code
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) arXiv:1708.08474 DOI
- [2]
- D. K. Tuckett, A. S. Darmawan, C. T. Chubb, S. Bravyi, S. D. Bartlett, and S. T. Flammia, “Tailoring Surface Codes for Highly Biased Noise”, Physical Review X 9, (2019) arXiv:1812.08186 DOI
- [3]
- D. K. Tuckett, S. D. Bartlett, S. T. Flammia, and B. J. Brown, “Fault-Tolerant Thresholds for the Surface Code in Excess of 5% Under Biased Noise”, Physical Review Letters 124, (2020) arXiv:1907.02554 DOI
- [4]
- Y. Kim, J. Kang, and Y. Kwon, “Design of Quantum error correcting code for biased error on heavy-hexagon structure”, (2022) arXiv:2211.14038
Page edit log
- Victor V. Albert (2026-06-08) — most recent
- Victor V. Albert (2022-01-20)
- Arpit Dua (2022-01-19)
Cite as:
“XY surface code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/xysurface, arXiv:2606.11484