Union-Jack color code

Union-Jack color code[1]

Description

Triangular color code defined on a patch of the Tetrakis square tiling (a.k.a. the Union Jack lattice).

Transversal Gates

Transversal logical Clifford gates [1].

Code Capacity Threshold

Independent \(X,Z\) noise: The threshold under ML decoding corresponds to the value of a critical point of a two-dimensional three-body random-bond Ising model (RBIM) on the Nishimori line [2,3], calculated to be \(10.9\%\) [1].

Parent

2D color code

Cousin

Square-octagon (4.8.8) color code — Adding a vertex to the center of every tile of the 4.8.8 tiling yields a rotated version of the Union-Jack lattice.

References

[1]: H. G. Katzgraber, H. Bombin, R. S. Andrist, and M. A. Martin-Delgado, “Topological color codes on Union Jack lattices: a stable implementation of the whole Clifford group”, Physical Review A 81, (2010) arXiv:0910.0573 DOI
[2]: H. Nishimori, “Geometry-Induced Phase Transition in the ±JIsing Model”, Journal of the Physical Society of Japan 55, 3305 (1986) DOI
[3]: H. G. Katzgraber, H. Bombin, and M. A. Martin-Delgado, “Error Threshold for Color Codes and Random Three-Body Ising Models”, Physical Review Letters 103, (2009) arXiv:0902.4845 DOI

Page edit log

Benjamin J. Brown (2024-07-31) — most recent
Victor V. Albert (2024-07-31)

Cite as:

“Union-Jack color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/union_jack_color

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/stabilizer/topological/color/2d_color/488_color/union_jack_color.yml.