\([[8,2,2]]\) hyperbolic color code[1]
Description
An \([[8,2,2]]\) hyperbolic color code defined on the projective plane.
Transversal Gates
Applying transversal \(S\) and \(S^{\dagger}\), \(\sqrt{X}\), and Hadamard gates yields various logical gates [2].
Parents
- Hyperbolic color code — The \([[8,2,2]]\) hyperbolic color code is defined on the projective plane.
- Small-distance block quantum code
Cousin
- \([[9,1,3]]\) Shor code — The Shor code (\([[8,2,2]]\) color code) is a small surface (color) code defined on the projective plane.
References
- [1]
- C. Vuillot and N. P. Breuckmann, “Quantum Pin Codes”, IEEE Transactions on Information Theory 68, 5955 (2022) arXiv:1906.11394 DOI
- [2]
- H. Chen et al., “Automated discovery of logical gates for quantum error correction (with Supplementary (153 pages))”, Quantum Information and Computation 22, 947 (2022) arXiv:1912.10063 DOI
Page edit log
- Victor V. Albert (2024-02-13) — most recent
Cite as:
“\([[8,2,2]]\) hyperbolic color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/stab_8_2_2