Study Of Quantum LDPC Code And Its Application

Quantum error correction coding is an important technique to protect quantum in-formation against decoherence and environmental noises, which exist in any quantuminformation processing system such as quantum computer, quantum communication, andquantum storage etc. By generalizing the Low-Density Parity-Check (LDPC) code inmodern channel coding theory to quantum information feld, quantum LDPC code hasbeen a hot research topic in recent years. In this dissertation, the author focuses onthe construction methods and iterative decoding algorithms of binary and non-binaryquantum LDPC codes, and obtains main results as follows.(1) The construction methods of CSS structural and non-CSS structural binary quan-tum LDPC codes are provided together with their sparse graph models. Due to theunavoidable short cycles (especially cycle-fours) in the graphs of quantum LDPCcodes with standard stabilizer formalism, a jointly-check method is proposed toimprove their iterative decoding performances under standard belief-propagationalgorithm. By changing the iterative updating messages of some check nodes in-volved in cycle-fours, the decoding process of quantum LDPC codes can be efcientlyconverged to the correct output results. After simulating the present binary quan-tum LDPC codes with various decoding algorithms, it is shown that jointly-checkmethod can improve the performance of standard BP algorithm.(2) Based on non-binary stabilizer coding theory over multi-level quantum system, stan-dard stabilizer-ary quantum LDPC codes are depicted with their2-ary sparsegraph models over fnite feld GF(2). By using-ary sparse cyclic matrix overfnite feld GF(), a class of-ary quantum LDPC codes is constructed with dual-containing CSS structures. By iteratively decoding these-ary quantum LDPCcodes with-ary sum-product algorithms, their error correcting performances aresimulated over depolarizing channels. The simulation results show that the pro-posed non-binary quantum LDPC codes have better performances than the presentbinary quantum sparse graph LDPC codes.(3) Generalizing the entanglement-assisted stabilizer coding theory to multi-level quan-tum system, non-binary entanglement-assisted stabilizer codes are proposed. Byusing algebraic fnite feld method, a class of quasi-cyclic entanglement-assisted-ary quantum LDPC codes is constructed. With simulation results, the constructedentanglement-assisted-ary quantum LDPC codes have shown better performancesthan the present binary quantum LDPC codes. (4) By utilizing the quantum LDPC coding technique to quantum communication sys-tem, an efcient quantum secure direct communication (QSDC) scheme is proposedto improve the communication reliability of the present Ping-Pong protocol overnoisy quantum channels. Entanglement-assisted quantum LDPC code is used asa forward error correcting code to protect the encoded quantum state sequenceagainst the channel noises, which improves the reliability of the QSDC system. Fur-thermore, a quantum ARQ protocol with quantum error detection code is used todetect the strong channel noise efect, which improves the communication efciency.And two steps of eavesdropping detection are taken to ensure the security of theproposed QSDC system.