Subsystem Galois-qudit stabilizer code[1] 

Also known as Gauge Galois-qudit stabilizer code.

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]. The Singleton bound has been extended to Galois-qudit subsystem codes [3].

Parent

Children

Cousins

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
[3]
A. Klappenecker and P. K. Sarvepalli, “On subsystem codes beating the quantum Hamming or Singleton bound”, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, 2887 (2007) arXiv:quant-ph/0703213 DOI
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Zoo Code ID: galois_subsystem_stabilizer

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
BibTeX:
@incollection{eczoo_galois_subsystem_stabilizer, title={Subsystem Galois-qudit stabilizer code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/galois_subsystem_stabilizer} }
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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/edit/main/codes/quantum/qudits_galois/subsystem/galois_subsystem_stabilizer.yml.