2013/02/28 by Yingkai Ouyang · 2 citations
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.1103/physreva.90.062317
published as Phys. Rev. A 90, 062317 (2014) · Figures are still available in this version. Introduction is revised, elementary proofs removed, and paper is close to its final form
arxiv created 2014/12/10 · arxiv updated 2014/12/16
A quantum code is a subspace of a Hilbert space of a physical system chosen to be correctable against a given class of errors, where information can be encoded. Ideally, the quantum code lies within the ground space of the physical system. When the physical model is the Heisenberg ferromagnet in the absence of an external magnetic field, the corresponding ground-space contains all permutation-invariant states. We use techniques from combinatorics and operator theory to construct families of permutation-invariant quantum codes. These codes have length proportional to t2; one family of codes perfectly corrects arbitrary weight t errors, while the other family of codes approximately correct t spontaneous decay errors. The analysis of our codes' performance with respect to spontaneous decay errors utilizes elementary matrix analysis, where we revisit and extend the quantum error correction criterion of Knill and Laflamme, and Leung, Chuang, Nielsen and Yamamoto.