Also known as Color code with a twist.
Description
A non-CSS extension of the 2D color code whose non-CSS stabilizer generators are associated with twist defects of the associated lattice.
For lattices with dislocations and rotational disclinations, twist-defect stabilizer generators are placed at the location of the dislocations. Logical dimension is determined by the genus of the underlying surface (for closed surfaces), types of boundaries (for open surfaces), and any twist defects present.
Protection
Code properties depends on the number and size of the twist defects. There are 72 twist defects in the 2D color code [4].
Gates
Clifford gates can be implemented via twist-based lattice surgery [5] or braiding twist defects [6].
Parents
Children
- 2D color code — Twist-defect color codes reduce to 2D color codes when there are no defects. See Ref. [7] for an alternative non-CSS extension of 2D color codes.
- Stellated color code
- XYZ color code
Cousins
- Abelian topological code — Twist-defect color codes realize \(\mathbb{Z}_2 \times \mathbb{Z}_2\) topological order with twist defects.
- Twist-defect surface code
References
- [1]
- H. Bombin, “Topological Order with a Twist: Ising Anyons from an Abelian Model”, Physical Review Letters 105, (2010) arXiv:1004.1838 DOI
- [2]
- H. Bombin, “Clifford gates by code deformation”, New Journal of Physics 13, 043005 (2011) arXiv:1006.5260 DOI
- [3]
- J. C. Y. Teo, A. Roy, and X. Chen, “Unconventional fusion and braiding of topological defects in a lattice model”, Physical Review B 90, (2014) arXiv:1306.1538 DOI
- [4]
- M. S. Kesselring et al., “The boundaries and twist defects of the color code and their applications to topological quantum computation”, Quantum 2, 101 (2018) arXiv:1806.02820 DOI
- [5]
- D. Litinski and F. von Oppen, “Lattice Surgery with a Twist: Simplifying Clifford Gates of Surface Codes”, Quantum 2, 62 (2018) arXiv:1709.02318 DOI
- [6]
- M. G. Gowda and P. K. Sarvepalli, “Color codes with twists: Construction and universal-gate-set implementation”, Physical Review A 104, (2021) arXiv:2104.03669 DOI
- [7]
- P. Padmanabhan et al., “Non-CSS color codes on 2D lattices : Models and Topological Properties”, (2022) arXiv:2112.13617
Page edit log
- Victor V. Albert (2024-03-29) — most recent
Cite as:
“Twist-defect color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/twist_defect_color