\([[6k+2,3k,2]]\) Campbell-Howard code[1]
Description
Family of \([[6k+2,3k,2]]\) qubit stabilizer codes with quasi-transversal \(CZZ^{\otimes k}\) gates that are relevant to magic-state distillation.
Magic
A total of \(r\) rounds of magic-state distillation yields a magic-state yield parameter \(\gamma\to 1^{+}\) as \(k,r\rightarrow \infty\). This matches a conjectured bound for \(\gamma\) [2].
Transversal Gates
Quasi-transversal \(CZZ^{\otimes k}\) gates [1].
Parents
Child
References
- [1]
- E. T. Campbell and M. Howard, “Unified framework for magic state distillation and multiqubit gate synthesis with reduced resource cost”, Physical Review A 95, (2017) arXiv:1606.01904 DOI
- [2]
- S. Bravyi and J. Haah, “Magic-state distillation with low overhead”, Physical Review A 86, (2012) arXiv:1209.2426 DOI
Page edit log
- Victor V. Albert (2024-07-23) — most recent
- Earl T. Campbell (2024-07-23)
Cite as:
“\([[6k+2,3k,2]]\) Campbell-Howard code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/campbell_howard