Research On Construction And Performance Of Quantum LDPC Codes Based On Finite Geometry

Quantum coherence plays an essential role in the field of quantum information,including quantum computing and quantum communication.The quantum state interacts with the environment inevitably during the channel transmission,resulting in the quantum decoherence,and quantum decoherence causes the error of the quantum bit occurrence.Quantum error correction coding is an effective means to overcome the quantum decoherence,and it is the most popular research topic in the field of quantum information.The most commonly used method of obtaining quantum error correcting codes is based on their corresponding classical error correcting codes,which combines classical error correcting codes with quantum coding technology to get quantum error correcting codes.In this paper,a low density parity check code that approximated the Shannon capacity limit in the classical error correction theory is extended to the field of quantum information.The constributions of the dissertation are outline as follows:1.We construct symmetric quantum LDPC codes based on Euclidean geometry.We analyze the properties of the Euclidean geometry,and proposed two schemes for constructing quantum codes.The first scheme is to use the characteristics of the Euclidean geometry to construct the parity check matrix of the quasi-cyclic LDPC code.then transform the check matrix to satisfy the self duality,and combined with CSS construction theorem to construct quantum LDPC codes.The second is to construct symmetric quantum LDPC codes by combining two classical LDPC codes with Steane construction.Meanwhile,we simulate the performance of several examples of new construction quantum LDPC codes.2.We construct asymmetric quantum LDPC codes via two classical quasi-cyclic LDPC codes.We make use of the characteristics of the Euclidean geometry to construct classical quasi-cyclic LDPC codes,using the CSS constructions generate new families of asymmetric quantum LDPC codes.We simulate the performance of new construction asymmetric quantum codes.3.We construct entanglement-assisted quantum LDPC codes based on quantum entanglement.With the help of a certain number of shared entanglement bits,we construct a corresponding quantum error correcting code by any classical error correcting code.Quantum entanglement improve the performance of quantum stabilizer codes,and construct a quantum error correcting code without the classical code with dual relations.