\([[11,1,5]]\) quantum dodecacode[1]
Description
Eleven-qubit pure stabilizer code that is the smallest qubit stabilizer code to correct two-qubit errors.
See [3][2; Table 8.5] for its stabilizer generator matrix.
Protection
Smallest stabilizer code that protects against errors on any two qubits. Detects four-qubit errors.
Parents
Cousin
- Dodecacode — The dodecacode corresponds to a \([[12,0,6]]\) quantum code in the \(GF(4)\) representation [1]. The \([[11,1,5]]\) quantum dodecacode code corresponds to the shortened dodecacode [4]. A pure \([[10,1,4]]\) quantum code can be obtained from the doubly punctured dodecacode [4]. These codes are not obtained from the Hermitian construction since none of the classical codes are linear.
References
- [1]
- A. R. Calderbank et al., “Quantum Error Correction via Codes over GF(4)”, (1997) arXiv:quant-ph/9608006
- [2]
- D. Gottesman, “Stabilizer Codes and Quantum Error Correction”, (1997) arXiv:quant-ph/9705052
- [3]
- A. J. Scott, “Probabilities of Failure for Quantum Error Correction”, Quantum Information Processing 4, 399 (2005) arXiv:quant-ph/0406063 DOI
- [4]
- A. J. Scott, “Probabilities of Failure for Quantum Error Correction”, Quantum Information Processing 4, 399 (2005) DOI
Page edit log
- Victor V. Albert (2023-11-26) — most recent
Cite as:
“\([[11,1,5]]\) quantum dodecacode”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/stab_11_1_5