In this paper,we construct three classes of Clifford subsystem maximum distance separable(MDS)codes based on Reed-Solomon codes and extended generalized Reed-Solomon codes over finite fields Fq for specific code lengt...In this paper,we construct three classes of Clifford subsystem maximum distance separable(MDS)codes based on Reed-Solomon codes and extended generalized Reed-Solomon codes over finite fields Fq for specific code lengths.Moreover,our Clifford subsystem MDS codes are new because their parameters differ from the previously known ones.展开更多
Quantum error-correcting codes are essential for fault-tolerant quantum computing,as they effectively detect and correct noise-induced errors by distributing information across multiple physical qubits.The subsystem s...Quantum error-correcting codes are essential for fault-tolerant quantum computing,as they effectively detect and correct noise-induced errors by distributing information across multiple physical qubits.The subsystem surface code with three-qubit check operators demonstrates significant application potential due to its simplified measurement operations and low logical error rates.However,the existing minimum-weight perfect matching(MWPM)algorithm exhibits high computational complexity and lacks flexibility in large-scale systems.Therefore,this paper proposes a decoder based on a graph attention network(GAT),representing error syndromes as undirected graphs with edge weights,and employing a multihead attention mechanism to efficiently aggregate node features and enable parallel computation.Compared to MWPM,the GAT decoder exhibits linear growth in computational complexity,adapts to different quantum code structures,and demonstrates stronger robustness under high physical error rates.The experimental results demonstrate that the proposed decoder achieves an overall accuracy of 89.95%under various small code lattice sizes(L=2,3,4,5),with the logical error rate threshold increasing to 0.0078,representing an improvement of approximately 13.04%compared to the MWPM decoder.This result significantly outperforms traditional methods,showcasing superior performance under small code lattice sizes and providing a more efficient decoding solution for large-scale quantum error correction.展开更多
Two code constructions generating new families of good nonbinary asymmetric quantum BCH codes and good nonbinary subsystem BCH codes are presented in this paper.The first one is derived from q-ary Steane's enlarge...Two code constructions generating new families of good nonbinary asymmetric quantum BCH codes and good nonbinary subsystem BCH codes are presented in this paper.The first one is derived from q-ary Steane's enlargement of CSS codes applied to nonnarrow-sense BCH codes.The second one is derived from the method of defining sets of classical cyclic codes.The asymmetric quantum BCH codes and subsystem BCH codes here have better parameters than the ones available in the literature.展开更多
基金Supported by Research Funds of Hubei Province(D20144401 and Q20174503)。
文摘In this paper,we construct three classes of Clifford subsystem maximum distance separable(MDS)codes based on Reed-Solomon codes and extended generalized Reed-Solomon codes over finite fields Fq for specific code lengths.Moreover,our Clifford subsystem MDS codes are new because their parameters differ from the previously known ones.
基金Project supported by the Natural Science Foundation of Shandong Province,China(Grant No.ZR2021MF049)the Joint Fund of the Natural Science Foundation of Shandong Province,China(Grant Nos.ZR2022LLZ012 and ZR2021LLZ001)the Key Research and Development Program of Shandong Province,China(Grant No.2023CXGC010901)。
文摘Quantum error-correcting codes are essential for fault-tolerant quantum computing,as they effectively detect and correct noise-induced errors by distributing information across multiple physical qubits.The subsystem surface code with three-qubit check operators demonstrates significant application potential due to its simplified measurement operations and low logical error rates.However,the existing minimum-weight perfect matching(MWPM)algorithm exhibits high computational complexity and lacks flexibility in large-scale systems.Therefore,this paper proposes a decoder based on a graph attention network(GAT),representing error syndromes as undirected graphs with edge weights,and employing a multihead attention mechanism to efficiently aggregate node features and enable parallel computation.Compared to MWPM,the GAT decoder exhibits linear growth in computational complexity,adapts to different quantum code structures,and demonstrates stronger robustness under high physical error rates.The experimental results demonstrate that the proposed decoder achieves an overall accuracy of 89.95%under various small code lattice sizes(L=2,3,4,5),with the logical error rate threshold increasing to 0.0078,representing an improvement of approximately 13.04%compared to the MWPM decoder.This result significantly outperforms traditional methods,showcasing superior performance under small code lattice sizes and providing a more efficient decoding solution for large-scale quantum error correction.
基金supported by the National High Technology Research and Development Program of China (Grant No. 2011AA010803)the National Natural Science Foundation of China (Grant No. 60403004)the Outstanding Youth Foundation of Henan Province (Grant No. 0612000500)
文摘Two code constructions generating new families of good nonbinary asymmetric quantum BCH codes and good nonbinary subsystem BCH codes are presented in this paper.The first one is derived from q-ary Steane's enlargement of CSS codes applied to nonnarrow-sense BCH codes.The second one is derived from the method of defining sets of classical cyclic codes.The asymmetric quantum BCH codes and subsystem BCH codes here have better parameters than the ones available in the literature.
