Papers › The XYZ² hexagonal stabilizer code
The XYZ² hexagonal stabilizer code
Basudha Srivastava, Anton Frisk Kockum, Mats Granath
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
We consider a topological stabilizer code on a honeycomb grid, the "XYZ²" code. The code is inspired by the Kitaev honeycomb model and is a simple realization of a "matching code" discussed by Wootton [J. Phys. A: Math. Theor. 48, 215302 (2015)], with a specific implementation of the boundary. It utilizes weight-six (XYZXYZ) plaquette stabilizers and weight-two (XX) link stabilizers on a planar hexagonal grid composed of 2d² qubits for code distance d, with weight-three stabilizers at the boundary, stabilizing one logical qubit. We study the properties of the code using maximum-likelihood decoding, assuming perfect stabilizer measurements. For pure X, Y, or Z noise, we can solve for the logical failure rate analytically, giving a threshold of 50%. In contrast to the rotated surface code and the XZZX code, which have code distance d² only for pure Y noise, here the code distance is 2d² for both pure Z and pure Y noise. Thresholds for noise with finite Z bias are similar to the XZZX code, but with markedly lower sub-threshold logical failure rates. The code possesses distinctive syndrome properties with unidirectional pairs of plaquette defects along the three directions of the triangular lattice for isolated errors, which may be useful for efficient matching-based or other approximate decoding.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections