Doubled color code[1]
Description
Family of \([[2t^3+8t^2+6t-1,1,2t+1]]\) subsystem color codes (with \(t\geq 1\)), constructed using a generalization of the doubling transformation [2], that admit a Clifford + \(T\) transversal gate set using gauge fixing.
Transversal Gates
Doubled color codes are triply-even, so they yield a transversal \(T\) gate [1]. Using gauge fixing, the codes admit a Clifford + \(T\) transversal gate set.
Parent
Child
- \([[15,1,3]]\) quantum Reed-Muller code — The \([[15,1,3]]\) code, when extended to a gauge color code, is the smallest doubled color code.
Cousin
- Divisible code — Doubled color codes are constructed using a generalization of the doubling transformation [2] that combine doubly-even codes to make triply-even codes.
References
- [1]
- S. Bravyi and A. Cross, “Doubled Color Codes”, (2015) arXiv:1509.03239
- [2]
- K. Betsumiya and A. Munemasa, “On triply even binary codes”, Journal of the London Mathematical Society 86, 1 (2012) arXiv:1012.4134 DOI
Page edit log
- Victor V. Albert (2023-01-24) — most recent
Cite as:
“Doubled color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/doubled_color