Abelian topological code, such as a surface [1,3] or color  code, constructed on lattices of Galois qudits.
- Kitaev surface code — The surface code has been extended to Galois qudits.
- Abelian quantum double stabilizer code — A Galois qudit for \(q=p^m\) can be decomposed into a Kronecker product of \(m\) modular qudits ; see Sec. 5.3 of Ref. . Galois-qudit topological surface and color codes yield abelian quantum-double codes via this decomposition.
- Color code — The 2D color code has been extended to Galois qudits.
- S. S. Bullock and G. K. Brennen, “Qudit surface codes and gauge theory with finite cyclic groups”, Journal of Physics A: Mathematical and Theoretical 40, 3481 (2007) arXiv:quant-ph/0609070 DOI
- P. Sarvepalli, “Topological color codes over higher alphabet”, 2010 IEEE Information Theory Workshop (2010) DOI
- I. Andriyanova, D. Maurice, and J.-P. Tillich, “New constructions of CSS codes obtained by moving to higher alphabets”, (2012) arXiv:1202.3338
- A. Ashikhmin and E. Knill, “Nonbinary quantum stabilizer codes”, IEEE Transactions on Information Theory 47, 3065 (2001) DOI
- A. Niehage, “Quantum Goppa Codes over Hyperelliptic Curves”, (2005) arXiv:quant-ph/0501074
Page edit log
- Victor V. Albert (2022-07-27) — most recent
“Galois-qudit topological code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/galois_topological