\([[6k+2,3k,2]]\) 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
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Zoo Code ID: campbell_howard

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
BibTeX:
@incollection{eczoo_campbell_howard, title={\([[6k+2,3k,2]]\) Campbell-Howard code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/campbell_howard} }
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Permanent link:
https://errorcorrectionzoo.org/c/campbell_howard

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

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/stabilizer/magic/k-divisible/campbell_howard.yml.