\(((5,6,2))\) qubit code[1]
Description
Six-qubit cyclic CWS code detecting a single-qubit error. This code has a logical subspace whose dimension is larger than that of the \([[5,2,2]]\) code, the best five-qubit stabilizer code with the same distance [2].
Its codeword stabilizer consists of all cyclic shifts of \(ZXZII\). It's automorphism group is of size 3840 and given in Ref. [1] (see also [3; Corr. 18]).
Parents
- \(((5+2r,3\times 2^{2r+1},2))\) Rains code — The \(((5,6,2))\) code is the smallest nontrivial Rains code [3] (see also [5][4; Ex. 8]).
- \(((n,1+n(q-1),2))_q\) union stabilizer code — The \(((5,6,2))\) code is the \(((n,1+n(q-1),2))_q\) union stabilizer code for \(n=5\) and \(q=2\) [6].
- Cyclic quantum code
References
- [1]
- E. M. Rains et al., “A Nonadditive Quantum Code”, Physical Review Letters 79, 953 (1997) arXiv:quant-ph/9703002 DOI
- [2]
- S. Yu, Q. Chen, and C. H. Oh, “Graphical Quantum Error-Correcting Codes”, (2007) arXiv:0709.1780
- [3]
- E. M. Rains, “Quantum codes of minimum distance two”, (1997) arXiv:quant-ph/9704043
- [4]
- V. Aggarwal and A. R. Calderbank, “Boolean Functions, Projection Operators, and Quantum Error Correcting Codes”, IEEE Transactions on Information Theory 54, 1700 (2008) arXiv:cs/0610159 DOI
- [5]
- D. Hu et al., “Graphical nonbinary quantum error-correcting codes”, Physical Review A 78, (2008) arXiv:0801.0831 DOI
- [6]
- V. Arvind, P. P. Kurur, and K. R. Parthasarathy, “Nonstabilizer Quantum Codes from Abelian Subgroups of the Error Group”, (2002) arXiv:quant-ph/0210097
Page edit log
- Victor V. Albert (2023-02-01) — most recent
Cite as:
“\(((5,6,2))\) qubit code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/qubit_5_6_2