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
- 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.
Member of code lists
- 2D stabilizer codes
- Color code and friends
- Hamiltonian-based codes
- Quantum codes
- Quantum codes based on homological products
- Quantum codes with code capacity thresholds
- Quantum codes with transversal gates
- Quantum CSS codes
- Quantum LDPC codes
- Stabilizer codes
- Surface code and friends
- Topological codes
Primary Hierarchy
Generalized homological-product qubit CSS codeGeneralized homological-product QLDPC CSS Stabilizer Hamiltonian-based QECC Quantum
2D color codeGeneralized homological-product Twist-defect color Lattice stabilizer QLDPC CSS Stabilizer Qubit Abelian topological Topological Hamiltonian-based QECC Quantum
Parents
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
- 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