Nested Quantum Error Correction Codes via Subgraphs

Yuanli Cai, Mantao Xu, Qiang Sun

Graphical approach provides a more intuitive and simple way to construct error correction codes. How to obtain generator matrix is the key problem of constructing graphical quantum codes. In this paper, we further generalize the graphical quantum code construction method by entangling its disconnected subgraphs, so that the corresponding generator matrix of quantum nondegenerate codes can be easily obtained. By making use of the method of subgraphs entangling, we also point out its application in adjacency matrix constructions of larger colorable graph and graphical quantum nested codes.

황규호

Markus Grassl

Yue RAN, Juan XU, Hanwu Chen +2 more

Since Calderbank et al. established CRSS construction, which constructs quantum error-correcting codes (QECC) from classical error-correcting codes, many QECC demonstrating good performance have been constructed from classical error-correcting codes; these codes are referred to as quantum stabilizer codes. Recent physical experiments indicate that the probabilities of occurrence of qubit- ip errors are much less than those of phase- ip errors in most quantum mechanical systems. Error-correcting codes thus constructed are referred to as asymmetric quantum codes. In this paper, series of asymmetric quantum stabilizer codes are constructed using nested Goppa codes and dual contained Goppa codes. In the construction of asymmetric quantum codes based on nested Goppa codes, the choice of Goppa codes is limited to construct codes with analysis methods. In normal circumstances, the construction is executed with the help of mathematical software Matlab, which is used to compute the minimum distance of Goppa codes. In the construction of asymmetric quantum codes based on dual contained Goppa codes, the error correction ability of the codes constructed in this paper is re ected in the correction of Z-type errors

Harriet Pollatsek, Mary Beth Ruskai

Ji Fan

Since Calderbank et al.established CRSS construction,which constructs quantum error-correcting codes(QECC) from classical error-correcting codes,many QECC demonstrating good performance have been constructed from classical error-correcting codes;these codes are referred to as quantum stabilizer codes.Recent physical experiments indicate that the probabilities of occurrence of qubit-flip errors are much less than those of phase-flip errors in most quantum mechanical systems.Error-correcting codes thus constructed are referred to as asymmetric quantum codes.In this paper,series of asymmetric quantum stabilizer codes are constructed using nested Goppa codes and dual contained Goppa codes.In the construction of asymmetric quantum codes based on nested Goppa codes,the choice of Goppa codes is limited to construct codes with analysis methods.In normal circumstances,the construction is executed with the help of mathematical software Matlab,which is used to compute the minimum distance of Goppa codes.In the construction of asymmetric quantum codes based on dual contained Goppa codes,the error correction ability of the codes constructed in this paper is reflected in the correction of Z-type errors.