Subsystem Galois-qudit stabilizer code

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

Subsystem Galois-qudit code

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

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/quantum/qudits_galois/subsystem/galois_subsystem_stabilizer.yml.