\([[13,1,5]]\) cyclic code[1]
Description
Thirteen-qubit twisted surface code for which there is a set of stabilizer generators consisting of cyclic permutations of the \(XZZX\)-type Pauli string \(XIZZIXIIIIIII\). The code can be thought of as a small twisted XZZX code [1; Ex. 11 and Fig. 3].
Transversal Gates
No non-Pauli transversal gates.
Parents
- Twisted XZZX toric code — The \([[13,1,5]]\) cyclic code is a small twisted XZZX toric code [1; Ex. 11 and Fig. 3].
- Frobenius code
- Small-distance block quantum code
Cousin
- Hermitian qubit code — A different cyclic \([[13,1,5]]\) code can be derived from a quaternary QR code using the Hermitian construction [2]; see [3; pg. 11] for details.
References
- [1]
- A. A. Kovalev, I. Dumer, and L. P. Pryadko, “Design of additive quantum codes via the code-word-stabilized framework”, Physical Review A 84, (2011) arXiv:1108.5490 DOI
- [2]
- E. Rains, private communication, April 1997.
- [3]
- F. Vatan, V. P. Roychowdhury, and M. P. Anantram, “Spatially Correlated Qubit Errors and Burst-Correcting Quantum Codes”, (1997) arXiv:quant-ph/9704019
Page edit log
- Simon Burton (2024-07-17) — most recent
- Victor V. Albert (2024-07-17)
- Victor V. Albert (2024-03-31)
Cite as:
“\([[13,1,5]]\) cyclic code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/stab_13_1_5