Study On Construction Methos Of Quantum LDPC Codes Based On Difference Family

Quantum information is sensitive to noise,and quantum error-correcting codes are means ofprotecting quantum information from noise and decoherence. Although the quantumerror-correction codes have some similarity to classical error-correcting codes, they are not asimple generalization of classical error-correcting codes. Actually, the coding methods are morecomplicated. At present, theories of quantum error correction codes have become more and moreperfect. Many counterparts of classical error correction code methods have been found inquantum area.Calderbank-Shor-Steane (CSS) codes is one of the fundamental methods of quantumerror-correcting codes, which can be constructed by a pair of classical linear codes. Takingadvantage of classical low density parity check codes based on difference family, we propose aclass of construction of quantum LDPC based on CSS ,and then a construction of irregularquantum LDPC codes. Here, (101,5,1) difference family are selected as examples to illustrate theconstruction. We then analyse and compare the performance of these codes. The simulationresults show that the quantum LDPC codes constructed by this method have a good performancein comparison with those ones constructed by Hagiwara with the similar parameters, and theperformance of irregular Quantum LDPC codes is better than the regular codes.On the other hand, arbitrary classical codes have been proven to be quantum errorcorrection codes with the assistant of entanglement. It is named entanglement-assisted quantumerror correction codes. We show that quantum entanglement assisted quantum codes formdifference family requires only one ebit to be shared between source and destination. Here,(31,3,1) difference family and (101,5,1) difference family are selected as examples to illustratethe construction. We then analyse and compare the performance of these codes. The simulationresults show that the quantum LDPC code constructed by this method have a good performancein comparison with those ones constructed by T. A. Brun with the similar parameters We furthergeneralize the concept of difference family to irregular Entanglement assisted quantum codes,.And then we proposed the used of cyclic difference sets to construct Entanglement assistedquantum codes who have shorter code length .