In quantum information, the gnu code refers to a particular family of quantum error correcting codes, with the special property of being invariant under permutations of the qubits. Given integers g (the gap), n (the occupancy), and m (the length of the code), the two codewords are

where are the Dicke states consisting of a uniform superposition of all weight-k words on m qubits, e.g.

The real parameter scales the density of the code. The length , hence the name of the code. For odd and , the gnu code is capable of correcting erasure errors,[1] or deletion errors.[2]

References

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  1. ^ Ouyang, Yingkai (2014-12-10). "Permutation-invariant quantum codes". Physical Review A. 90 (6): 062317. arXiv:1302.3247. Bibcode:2014PhRvA..90f2317O. doi:10.1103/physreva.90.062317. ISSN 1050-2947. S2CID 119114455.
  2. ^ Ouyang, Yingkai (2021-02-04). "Permutation-invariant quantum coding for quantum deletion channels". arXiv:2102.02494v1 [quant-ph].