Subsystem Galois-qudit stabilizer code[1]
Description
Galois-qudit generalization of a subsystem qubit stabilizer code. Can be obtained by taking a Galois-qudit stabilizer code and assigning some of its logical qubits to be gauge qubits.
Protection
Bounds on code parameters are formulated in Ref. [2].
Parent
Children
- Subsystem qubit stabilizer code — Subsystem Galois-qudit stabilizer codes reduce to subsystem qubit stabilizer codes for qudit dimension \(q=2\).
- Subsystem Galois-qudit CSS code
Cousins
- Galois-qudit stabilizer code — Subsystem Galois-qudit stabilizer codes reduce to Galois-qudit stabilizer codes when there are no gauge qudits.
- Hermitian-construction code — The Hermitian construction has been extended to subsystem Galois-qudit stabilizer codes [2].
References
- [1]
- A. Klappenecker and P. K. Sarvepalli, “Clifford Code Constructions of Operator Quantum Error Correcting Codes”, (2006) arXiv:quant-ph/0604161
- [2]
- S. A. Aly, A. Klappenecker, and P. K. Sarvepalli, “Subsystem Codes”, (2006) arXiv:quant-ph/0610153
Page edit log
- Victor V. Albert (2022-11-09) — most recent
Cite as:
“Subsystem Galois-qudit stabilizer code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/galois_subsystem_stabilizer