\([[7,1,3]]\) twist-defect surface code[1] 

Also known as \([[7,1,3]]\) triangle code.

Description

A \([[7,1,3]]\) code (different from the Steane code) that is a small example of a twist-defect surface code.

It is one of sixteen distinct \([[7,1,3]]\) codes [2].

Transversal Gates

Single-qubit Clifford group [1,3].

Parents

References

[1]
T. J. Yoder and I. H. Kim, “The surface code with a twist”, Quantum 1, 2 (2017) arXiv:1612.04795 DOI
[2]
S. Yu, Q. Chen, and C. H. Oh, “Graphical Quantum Error-Correcting Codes”, (2007) arXiv:0709.1780
[3]
H. Chen, M. Vasmer, N. P. Breuckmann, and E. Grant, “Automated discovery of logical gates for quantum error correction (with Supplementary (153 pages))”, Quantum Information and Computation 22, 947 (2022) arXiv:1912.10063 DOI
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Zoo Code ID: twist_defect_7_1_3

Cite as:
“\([[7,1,3]]\) twist-defect surface code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/twist_defect_7_1_3
BibTeX:
@incollection{eczoo_twist_defect_7_1_3, title={\([[7,1,3]]\) twist-defect surface code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/twist_defect_7_1_3} }
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Permanent link:
https://errorcorrectionzoo.org/c/twist_defect_7_1_3

Cite as:

“\([[7,1,3]]\) twist-defect surface code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/twist_defect_7_1_3

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/small_distance/small/7/twist_defect_7_1_3.yml.