Quantum Code Constructions

Jian Liu

Quantum error-correcting codes protect quantum information against undesirable noise in quantum computation and quantum communication.It is one of important problems that constructing very good quantum codes.There are two methods that use binary codes to construct quantum codes,one is CSS construction,another is Steane construction.These two methods are all based on the construction of binary self-orthogonal codes.Combinational construction of binary self-orthogonal codes is investigated in this paper.From known codes chains of binary self-orthogonal codes and their dual codes chains with given dual distance,new binary self-orthogonal codes of dual distance three,four,five and six are constructed.Based on these results,for each satisfying,S-chains with parameters and are constructed.According to Steane's construction,many very good quantum codes of distance five and six are constructed by the obtained S-chains,some of these quantum codes are new and some of these quantum codes have improved parameters than previously known codes.

Hao Chen

Gabriele Nebe, Eric M. Rains, Neil J.A. Sloane

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.

Sankalpa Khadka

Lingfei Jin, Chaoping Xing

There have been various constructions of classical codes from polynomial valuations in literature [2], [7], [8], [10], [11]. In this paper, we present a construction of classical codes based on polynomial construction again. One of the features of this construction is that not only the classical codes arisen from the construction have good parameters, but also quantum codes with reasonably good parameters can be produced from these classical codes. In particular, some new quantum codes are constructed (see Examples V.5 and V.6).