[Jump to code hierarchy]

Union-Jack color code[1]

Description

2D 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].

Cousin

Member of code lists

Primary Hierarchy

Quantum Domain
Qubit Kingdom
Qubit codeQECC Quantum
Union stabilizer (USt) codeQECC Quantum
Qubit stabilizer codeStabilizer Hamiltonian-based Qubit QECC Quantum
Coherent-parity-check (CPC) code
Qubit CSS codeCSS Stabilizer Qubit Hamiltonian-based QECC Quantum
Generalized homological-product qubit CSS codeGeneralized homological-product QLDPC CSS Stabilizer Hamiltonian-based QECC Quantum
Quantum rainbow code
Quantum pin codeStabilizer Hamiltonian-based Qubit QECC Quantum
Color code
2D color codeGeneralized homological-product Twist-defect color Lattice stabilizer QLDPC CSS Stabilizer Qubit Abelian topological Topological Hamiltonian-based QECC Quantum
Parents
2D color code
Union-Jack color code

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

Your contribution is welcome!

on github.com (edit & pull request)— see instructions

edit on this site

Zoo Code ID: union_jack_color

Cite as:
“Union-Jack color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/union_jack_color
BibTeX:
@incollection{eczoo_union_jack_color, title={Union-Jack color code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/union_jack_color} }
Share via:
Twitter | Mastodon |  | E-mail
Permanent link:
https://errorcorrectionzoo.org/c/union_jack_color

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.