A simple family of nonadditive quantum codes
Quantum Physics
2009-11-13 v2
Abstract
Most known quantum codes are additive, meaning the codespace can be described as the simultaneous eigenspace of an abelian subgroup of the Pauli group. While in some scenarios such codes are strictly suboptimal, very little is understood about how to construct nonadditive codes with good performance. Here we present a family of nonadditive quantum codes for all odd blocklengths, n, that has a particularly simple form. Our codes correct single qubit erasures while encoding a higher dimensional space than is possible with an additive code or, for n of 11 or greater, any previous codes.
Keywords
Cite
@article{arxiv.quant-ph/0701065,
title = {A simple family of nonadditive quantum codes},
author = {John A. Smolin and Graeme Smith and Stephanie Wehner},
journal= {arXiv preprint arXiv:quant-ph/0701065},
year = {2009}
}
Comments
3 pages, new version with slight clarifications, no results are changed