\(((9,12,3))\) qubit code[1] 

Description

Nine-qubit cyclic CWS code correcting a single-qubit error. This code has a logical subspace whose dimension is larger than that of the \([[9,3,3]]\) code, the best nine-qubit stabilizer code with the same distance [2].

Its codeword stabilizer consists of all cyclic shifts of \(ZXZIIIIII\).

Decoding

Fault-tolerant scheme that converts the required POVM into 10 binary measurements whose redundancy is guaranteed by a classical code [3].

Parents

References

[1]
S. Yu et al., “Nonadditive Quantum Error-Correcting Code”, Physical Review Letters 101, (2008) arXiv:0704.2122 DOI
[2]
A. R. Calderbank et al., “Quantum Error Correction via Codes over GF(4)”, (1997) arXiv:quant-ph/9608006
[3]
Y. Ouyang, “Robust projective measurements through measuring code-inspired observables”, (2024) arXiv:2402.04093
[4]
A. Cross et al., “Codeword Stabilized Quantum Codes”, IEEE Transactions on Information Theory 55, 433 (2009) arXiv:0708.1021 DOI
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Zoo Code ID: qubit_9_12_3

Cite as:
\(((9,12,3))\) qubit code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/qubit_9_12_3
BibTeX:
@incollection{eczoo_qubit_9_12_3, title={\(((9,12,3))\) qubit code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/qubit_9_12_3} }
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Cite as:

\(((9,12,3))\) qubit code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/qubit_9_12_3

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/small_distance/small/qubit_9_12_3.yml.