Galois-qudit color code[1]
Also known as \(\mathbb{F}_q\)-qudit color code.
Description
Extension of the color code to 2D lattices of Galois qudits.
Parents
- Galois-qudit CSS code
- 2D lattice stabilizer code
- Generalized homological-product CSS code
- Quantum-double code — A Galois qudit for \(q=p^m\) can be decomposed into a Kronecker product of \(m\) modular qudits [2,4][3; Sec. 5.3]. Galois-qudit color codes yield Abelian quantum-double codes with Abelian-group topological order via this decomposition.
Child
- 2D color code — Galois-qudit 2D color codes reduce to 2D color codes for \(q=2\).
Cousin
- Abelian quantum-double stabilizer code — A Galois qudit for \(q=p^m\) can be decomposed into a Kronecker product of \(m\) modular qudits [2,4][3; Sec. 5.3]. Galois-qudit color codes yield Abelian quantum-double codes with Abelian-group topological order via this decomposition.
References
- [1]
- P. Sarvepalli, “Topological color codes over higher alphabet”, 2010 IEEE Information Theory Workshop (2010) DOI
- [2]
- A. Ashikhmin and E. Knill, “Nonbinary quantum stabilizer codes”, IEEE Transactions on Information Theory 47, 3065 (2001) DOI
- [3]
- A. Niehage, “Quantum Goppa Codes over Hyperelliptic Curves”, (2005) arXiv:quant-ph/0501074
- [4]
- D. Gottesman. Surviving as a quantum computer in a classical world (2024) URL
Page edit log
- Victor V. Albert (2022-07-27) — most recent
Cite as:
“Galois-qudit color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/galois_color