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\(((10,24,3))\) qubit code[1]

Description

Ten-qubit nonadditive CWS code that is unique and optimal for its parameters [1]. It was constructed using the coding-clique graph-theoretic framework introduced in [1], which unifies additive and nonadditive code constructions.

The \(((10,24,3))\) qubit code can be combined to form an infinite family of distance-three qubit codes whose logical dimension is \(50\%\) larger than that of the optimal stabilizer code [2].

Member of code lists

Primary Hierarchy

Quantum Domain
Qubit Kingdom
Qubit codeQECC Quantum
Union stabilizer (USt) codeQECC Quantum
Codeword stabilized (CWS) codeQECC Quantum
Parents
Codeword stabilized (CWS) code
The \(((10,24,3))\) qubit code is a CWS code [3].
Small-distance block quantum codeQECC Quantum
The \(((10,24,3))\) qubit code can be combined to form an infinite family of distance-three qubit codes whose logical dimension is \(50\%\) larger than that of the optimal stabilizer code [2].
\(((10,24,3))\) qubit code

References

[1]
S. Yu, Q. Chen, and C. H. Oh, “Graphical Quantum Error-Correcting Codes”, (2007) arXiv:0709.1780
[2]
S. Yu, Q. Chen, and C. H. Oh, “Two infinite families of nonadditive quantum error-correcting codes”, (2009) arXiv:0901.1935
[3]
A. W. Cross. Fault-tolerant quantum computer architectures using hierarchies of quantum error-correcting codes. PhD thesis, Massachusetts Institute of Technology, 2008.
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Zoo Code ID: qubit_10_24_3

Cite as:
“\(((10,24,3))\) qubit code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/qubit_10_24_3
BibTeX:
@incollection{eczoo_qubit_10_24_3, title={\(((10,24,3))\) qubit code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/qubit_10_24_3} }
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Permanent link:
https://errorcorrectionzoo.org/c/qubit_10_24_3

Cite as:

“\(((10,24,3))\) qubit code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/qubit_10_24_3

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/small_distance/small/10/qubit_10_24_3.yml.