\(((9,12,3))\) 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
- Codeword stabilized (CWS) code — The \(((9,12,3))\) qubit code is a cyclic CWS code [4,5].
- Cyclic quantum code
- Small-distance block quantum code
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
- [5]
- Cross, Andrew William. Fault-tolerant quantum computer architectures using hierarchies of quantum error-correcting codes. Diss. Massachusetts Institute of Technology, 2008.
Page edit log
- Victor V. Albert (2023-11-29) — most recent
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