\([[2(m+1),m,2]]\) single-loss AD code[1]
Description
A member of a class of \([[2(m+1),m,2]]\) CSS codes for \(m\geq 1\) that generalizes the \([[4,1,2]]\) approximate amplitude-damping code of Ref. [2]. Its \(Z\)-type generators are \(m+1\) pairwise products, with each qubit participating in only one check; the single \(X\)-type generator is the all-\(X\) string.Cousin
- \([[4,2,2]]\) Four-qubit code— The \([[4,1,2]]\) Leung-Nielsen-Chuang-Yamamoto subcode \(\{|\overline{00}\rangle,|\overline{10}\rangle\}\) (approximately) corrects a single AD error [2] and is the smallest member of the amplitude-damping stabilizer family of Ref. [1].
Primary Hierarchy
Parents
The \([[2(m+1),m,2]]\) single-loss AD code is self-complementary, with the all-\(X\) stabilizer enforcing the complement-pair structure of the codewords [1].
Small-distance qubit stabilizer codeStabilizer Hamiltonian-based Qubit Small-distance block quantum QECC Quantum
\([[2(m+1),m,2]]\) single-loss AD code
References
- [1]
- A. S. Fletcher, P. W. Shor, and M. Z. Win, “Channel-Adapted Quantum Error Correction for the Amplitude Damping Channel”, (2007) arXiv:0710.1052
- [2]
- D. W. Leung, M. A. Nielsen, I. L. Chuang, and Y. Yamamoto, “Approximate quantum error correction can lead to better codes”, Physical Review A 56, 2567 (1997) arXiv:quant-ph/9704002 DOI
Page edit log
- Victor V. Albert (2026-03-30) — most recent
Cite as:
“\([[2(m+1),m,2]]\) single-loss AD code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/ampdamp_stabilizer