Description
A block code on \(n\) subsystems that either detects or corrects errors on only a single subsystem. These two cases correspond to distance \(d=2\) or \(d=3\) block quantum codes, respectively.
All single error-correcting qubit stabilizer codes have been classified [1]. See Ref. [2] for single error-detecting qubit stabilizer codes.
Parent
Children
- Kitaev current-mirror qubit code
- Three-rotor code
- Zero-pi qubit code
- Five-rotor code
- Braunstein five-mode code
- Lloyd-Slotine nine-mode code
- Tetron Majorana code
- \(((7,2,3))\) permutation-invariant code
- \([[2^r-1, 1, 3]]\) quantum Reed-Muller code
- \([[k+4,k,2]]\) H code
- \([[2m,2m-2,2]]\) error-detecting code
- \([[2^r, 2^r-r-2, 3]]\) quantum Hamming code
- \(((5,6,2))\) qubit code
- \([[8,3,2]]\) code
- Transverse-field Ising model (TFIM) code
- Bring's code
- \([[2^r-1, 2^r-2r-1, 3]]_p\) prime-qudit CSS code
- \([[5,1,3]]_{\mathbb{Z}_q}\) modular-qudit code
- Three-qutrit code
- \([[9,1,3]]_{\mathbb{Z}_q}\) modular-qudit code
- \([[5,1,3]]_q\) Galois-qudit code
References
- [1]
- S. Yu et al., “All the stabilizer codes of distance 3”, (2011) arXiv:0901.1968
- [2]
- E. M. Rains, “Quantum codes of minimum distance two”, (1997) arXiv:quant-ph/9704043
Page edit log
- Victor V. Albert (2023-02-01) — most recent
Cite as:
“Small-distance block quantum code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/small_distance