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Quantum toric code decoding method based on syndrome-preliminary error fusion module and ResNet architecture 认领 引用
1
作者 Nai-Hua Ji Ping-Li Song +2 位作者 Wei Wang Hui-Qian Sun Hong-Yang Ma 《Chinese Physics B》 SCIE EI CAS CSCD 2026年第6期649-659,共11页
Quantum error correction technology is based on the principle of redundant encoding,encoding logical quantum information into multiple physical qubits to provide important support for the stable operation of quantum c... Quantum error correction technology is based on the principle of redundant encoding,encoding logical quantum information into multiple physical qubits to provide important support for the stable operation of quantum computers.To address the issues of low decoding accuracy and limited feature extraction in quantum error correction,this paper proposes a toric code decoder based on a syndrome-preliminary error fusion module(SPEFM)and a ResNet architecture.This decoder takes full advantage of the correlations between X and Z errors.In the SPEFM,the syndrome and preliminary error predictions are deeply fused,while a unidirectional Swin transformer architecture is incorporated to extract global error features from the syndrome data,signiffiificantly improving both decoding accuracy and computational efffiificiency.In addition,this paper further extracts local error features from the fused features using the deep residual structure of ResNet,enhancing the decoder's ability to capture quantum error patterns.Experimental results show that the decoder is applicable to different code distances(d=4,6,8,10)under the depolarizing noise model.Its bit error rate is lower than that of the minimum weight perfect matching(MWPM)algorithm,and its logical error rate is lower than both the MWPM algorithm and the ResNet18 decoder.Furthermore,the decoding threshold is increased to 0.163,representing a 3.82%improvement over the MWPM algorithm threshold of 0.157. 展开更多
关键词 quantum error correction toric code ResNet Swin transformer
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Global receptive field transformer decoder method on quantum surface code data and syndrome error correction 认领 引用 被引量：1
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作者 Ao-Qing Li Ce-Wen Tian +2 位作者 Xiao-Xuan Xu Hong-Yang Ma Jun-Qing Liang 《Chinese Physics B》 SCIE EI CAS CSCD 2025年第3期267-276,共10页
Quantum computing has the potential to solve complex problems that are inefficiently handled by classical computation.However,the high sensitivity of qubits to environmental interference and the high error rates in cu... Quantum computing has the potential to solve complex problems that are inefficiently handled by classical computation.However,the high sensitivity of qubits to environmental interference and the high error rates in current quantum devices exceed the error correction thresholds required for effective algorithm execution.Therefore,quantum error correction technology is crucial to achieving reliable quantum computing.In this work,we study a topological surface code with a two-dimensional lattice structure that protects quantum information by introducing redundancy across multiple qubits and using syndrome qubits to detect and correct errors.However,errors can occur not only in data qubits but also in syndrome qubits,and different types of errors may generate the same syndromes,complicating the decoding task and creating a need for more efficient decoding methods.To address this challenge,we used a transformer decoder based on an attention mechanism.By mapping the surface code lattice,the decoder performs a self-attention process on all input syndromes,thereby obtaining a global receptive field.The performance of the decoder was evaluated under a phenomenological error model.Numerical results demonstrate that the decoder achieved a decoding accuracy of 93.8%.Additionally,we obtained decoding thresholds of 5%and 6.05%at maximum code distances of 7 and 9,respectively.These results indicate that the decoder used demonstrates a certain capability in correcting noise errors in surface codes. 展开更多
关键词 quantum error correction surface code transformer decoder
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An empirical study on cross-phase code modification behaviors in incremental programming projects 认领 引用
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作者 Jing Jiang Chenhong Ji +1 位作者 Li Zhang Haiyan Yang 《计算机教育》 2026年第6期280-291,共12页
This paper conducts an empirical study on students'code modification behaviors in incremental programming projects by analyzing 40771 code submissions from 371 students through abstract syntax tree(AST)difference ... This paper conducts an empirical study on students'code modification behaviors in incremental programming projects by analyzing 40771 code submissions from 371 students through abstract syntax tree(AST)difference analysis and manual annotation.The study investigates the distribution of code modification types to prior-phase code during iterative development,identifies cross-phase error types,and analyzes refactoring strategies.The findings reveal that error correction and code refactoring constitute the primary types of cross-phase code modifications.Among cross-phase latent errors,special case neglect represents the dominant error type,indicating insufficient coverage of special scenarios in existing test suites.Variable renaming emerges as the most prevalent refactoring behavior,reflecting students'emphasis on code readability.These research findings provide empirical evidence for optimizing incremental curriculum design,improving test cases,and cultivating students'code maintenance capabilities in programming education. 展开更多
关键词 Incremental projects Code modification Error correction Code refactoring Computer science education
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一种校验码独立存储的EDAC设计 认领 引用
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作者 徐文龙 李洪昌 +2 位作者 许峥 姚进 周昕杰 《电子与封装》 2026年第5期58-62,共5页
引入校验码的检错与纠错机制可有效提升存储器的抗单粒子翻转能力。然而,在传统架构中,校验码与数据码共置于同一存储单元,存在高能粒子同时诱发二者翻转的潜在风险。针对该问题,提出一种基于SRAM的校验码独立存储架构,采用专用存储器... 引入校验码的检错与纠错机制可有效提升存储器的抗单粒子翻转能力。然而,在传统架构中,校验码与数据码共置于同一存储单元,存在高能粒子同时诱发二者翻转的潜在风险。针对该问题,提出一种基于SRAM的校验码独立存储架构,采用专用存储器单元管理校验码。仿真结果表明,该设计可有效纠正1位错误并检测2位错误;在性能方面,面积与功耗无显著增加,故障注入仿真中的单粒子翻转率由3.96%降至0.00%。 展开更多
关键词 单粒子翻转 汉明码 检错纠错 校验码 独立存储
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Determination of quantum toric error correction code threshold using convolutional neural network decoders 认领 引用 被引量：3
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作者 Hao-Wen Wang Yun-Jia Xue +2 位作者 Yu-Lin Ma Nan Hua Hong-Yang Ma 《Chinese Physics B》 SCIE EI CAS CSCD 2022年第1期136-142,共7页
Quantum error correction technology is an important solution to solve the noise interference generated during the operation of quantum computers.In order to find the best syndrome of the stabilizer code in quantum err... Quantum error correction technology is an important solution to solve the noise interference generated during the operation of quantum computers.In order to find the best syndrome of the stabilizer code in quantum error correction,we need to find a fast and close to the optimal threshold decoder.In this work,we build a convolutional neural network(CNN)decoder to correct errors in the toric code based on the system research of machine learning.We analyze and optimize various conditions that affect CNN,and use the RestNet network architecture to reduce the running time.It is shortened by 30%-40%,and we finally design an optimized algorithm for CNN decoder.In this way,the threshold accuracy of the neural network decoder is made to reach 10.8%,which is closer to the optimal threshold of about 11%.The previous threshold of 8.9%-10.3%has been slightly improved,and there is no need to verify the basic noise. 展开更多
关键词 quantum error correction toric code convolutional neural network(CNN)decoder
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A Comparison of Error Correction Models for Student’s Error Codes Based on Deep Learning 认领 引用 被引量：1
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作者 Tao Lin Jian Wang +2 位作者 Qifan Jian Zhiming Wu Zhenbo Zhang 《计算机教育》 2022年第12期137-142,共6页
Automatically correcting students’code errors using deep learning is an effective way to reduce the burden of teachers and to enhance the effects of students’learning.However,code errors vary greatly,and the adaptab... Automatically correcting students’code errors using deep learning is an effective way to reduce the burden of teachers and to enhance the effects of students’learning.However,code errors vary greatly,and the adaptability of fixing techniques may vary for different types of code errors.How to choose the appropriate methods to fix different types of errors is still an unsolved problem.To this end,this paper first classifies code errors by Java novice programmers based on Delphi analysis,and compares the effectiveness of different deep learning models(CuBERT,GraphCodeBERT and GGNN)fixing different types of errors.The results indicated that the 3 models differed significantly in their classification accuracy on different error codes,while the error correction model based on the Bert structure showed better code correction potential for beginners’codes. 展开更多
关键词 Deep learning Code error correction Code error classification
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Low-overhead fault-tolerant error correction scheme based on quantum stabilizer codes 认领 引用
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作者 Xiu-Bo Chen Li-Yun Zhao +4 位作者 Gang Xu Xing-Bo Pan Si-Yi Chen Zhen-Wen Cheng Yi-Xian Yang 《Chinese Physics B》 SCIE EI CAS CSCD 2022年第4期143-150,共8页
Fault-tolerant error-correction(FTEC)circuit is the foundation for achieving reliable quantum computation and remote communication.However,designing a fault-tolerant error correction scheme with a solid error-correcti... Fault-tolerant error-correction(FTEC)circuit is the foundation for achieving reliable quantum computation and remote communication.However,designing a fault-tolerant error correction scheme with a solid error-correction ability and low overhead remains a significant challenge.In this paper,a low-overhead fault-tolerant error correction scheme is proposed for quantum communication systems.Firstly,syndrome ancillas are prepared into Bell states to detect errors caused by channel noise.We propose a detection approach that reduces the propagation path of quantum gate fault and reduces the circuit depth by splitting the stabilizer generator into X-type and Z-type.Additionally,a syndrome extraction circuit is equipped with two flag qubits to detect quantum gate faults,which may also introduce errors into the code block during the error detection process.Finally,analytical results are provided to demonstrate the fault-tolerant performance of the proposed FTEC scheme with the lower overhead of the ancillary qubits and circuit depth. 展开更多
关键词 fault-tolerant error correction quantum stabilizer code gate fault quantum circuit
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Approximate error correction scheme for three-dimensional surface codes based reinforcement learning 认领 引用
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作者 曲英杰 陈钊 +1 位作者 王伟杰 马鸿洋 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第10期229-240,共12页
Quantum error correction technology is an important method to eliminate errors during the operation of quantum computers.In order to solve the problem of influence of errors on physical qubits,we propose an approximat... Quantum error correction technology is an important method to eliminate errors during the operation of quantum computers.In order to solve the problem of influence of errors on physical qubits,we propose an approximate error correction scheme that performs dimension mapping operations on surface codes.This error correction scheme utilizes the topological properties of error correction codes to map the surface code dimension to three dimensions.Compared to previous error correction schemes,the present three-dimensional surface code exhibits good scalability due to its higher redundancy and more efficient error correction capabilities.By reducing the number of ancilla qubits required for error correction,this approach achieves savings in measurement space and reduces resource consumption costs.In order to improve the decoding efficiency and solve the problem of the correlation between the surface code stabilizer and the 3D space after dimension mapping,we employ a reinforcement learning(RL)decoder based on deep Q-learning,which enables faster identification of the optimal syndrome and achieves better thresholds through conditional optimization.Compared to the minimum weight perfect matching decoding,the threshold of the RL trained model reaches 0.78%,which is 56%higher and enables large-scale fault-tolerant quantum computation. 展开更多
关键词 fault-tolerant quantum computing surface code approximate error correction reinforcement learning
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Quantum decoder design for subsystem surface code based on multi-head graph attention and edge weighting 认领 引用
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作者 Nai-Hua Ji Hui-Qian Sun +2 位作者 Bo Xiao Ping-Li Song Hong-Yang Ma 《Chinese Physics B》 SCIE EI CAS CSCD 2025年第2期165-176,共12页
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
关键词 quantum error correction graph attention network subsystem surface code circuit-level noise
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Neural network-based decoding for bias-tailored quantum codes over quantum channels with asymmetric noise 认领 引用
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作者 Jihao Fan Qianhui Zhang +1 位作者 Zhihua Zhang Jun Li 《Communications in Theoretical Physics》 SCIE CAS CSCD 2025年第12期32-42,共11页
To improve the decoding performance of quantum error-correcting codes in asymmetric noise channels,a neural network-based decoding algorithm for bias-tailored quantum codes is proposed.The algorithm consists of a bias... To improve the decoding performance of quantum error-correcting codes in asymmetric noise channels,a neural network-based decoding algorithm for bias-tailored quantum codes is proposed.The algorithm consists of a biased noise model,a neural belief propagation decoder,a convolutional optimization layer,and a multi-objective loss function.The biased noise model simulates asymmetric error generation,providing a training dataset for decoding.The neural network,leveraging dynamic weight learning and a multi-objective loss function,mitigates error degeneracy.Additionally,the convolutional optimization layer enhances early-stage convergence efficiency.Numerical results show that for bias-tailored quantum codes,our decoder performs much better than the belief propagation(BP)with ordered statistics decoding(BP+OSD).Our decoder achieves an order of magnitude improvement in the error suppression compared to higher-order BP+OSD.Furthermore,the decoding threshold of our decoder for surface codes reaches a high threshold of 20%. 展开更多
关键词 quantum error correction quantum channels asymmetric noise neural networkbased decoding bias-tailored quantum codes
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Performance analysis and design of MIMO-OFDM system using concatenated forward error correction codes 认领 引用 被引量：3
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作者 Arun Agarwal Saurabh N.Mehta 《Journal of Central South University》 SCIE EI CAS CSCD 2017年第6期1322-1343,共22页
This work investigates the performance of various forward error correction codes, by which the MIMO-OFDM system is deployed. To ensure fair investigation, the performance of four modulations, namely, binary phase shif... This work investigates the performance of various forward error correction codes, by which the MIMO-OFDM system is deployed. To ensure fair investigation, the performance of four modulations, namely, binary phase shift keying(BPSK), quadrature phase shift keying(QPSK), quadrature amplitude modulation(QAM)-16 and QAM-64 with four error correction codes(convolutional code(CC), Reed-Solomon code(RSC)+CC, low density parity check(LDPC)+CC, Turbo+CC) is studied under three channel models(additive white Guassian noise(AWGN), Rayleigh, Rician) and three different antenna configurations(2×2, 2×4, 4×4). The bit error rate(BER) and the peak signal to noise ratio(PSNR) are taken as the measures of performance. The binary data and the color image data are transmitted and the graphs are plotted for various modulations with different channels and error correction codes. Analysis on the performance measures confirm that the Turbo + CC code in 4×4 configurations exhibits better performance. 展开更多
关键词 bit error rate (BER) convolutional code (CC) forward error correction peak signal to noise ratio (PSNR) Turbo code
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A Quantum Error-Correction Circuit Based on Cyclic Code 认领 引用 被引量：1
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作者 Lü Hongjun ZHANG Zhike XIE Guangjun 《Wuhan University Journal of Natural Sciences》 CAS 2013年第5期413-417,共5页
In this paper, the cyclic code of the classic circuit is transformed and transplanted; then, the quantum encoding scheme based on cyclic code and quantum error-correction circuit is constructed. The proposed circuit c... In this paper, the cyclic code of the classic circuit is transformed and transplanted; then, the quantum encoding scheme based on cyclic code and quantum error-correction circuit is constructed. The proposed circuit can correct one-bit error, and the use of redundant bits to encode more than one-bit quantum information breaks the previous limitations of many bits encoding a quantum bit. Compared with the existing coding circuits （Shor code, Steane code and five stable subcode）, it shows obvious superiority in the quantum coding efficiency and transmission efficiency. 展开更多
关键词 quantum information quantum error-correction code cyclic code redundant bit
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Matroidal Error Correction Networks and Linear Network Error Correction MDS Codes 认领 引用
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作者 ZHOU Hang LIU Guangjun 《Wuhan University Journal of Natural Sciences》 CAS 2013年第6期477-483,共7页
In this paper, we further study the connections between linear network error correction codes and representable matroids. We extend the concept of matroidal network introduced by Dougherty et al. to a generalized case... In this paper, we further study the connections between linear network error correction codes and representable matroids. We extend the concept of matroidal network introduced by Dougherty et al. to a generalized case when errors occur in multi- ple channels. Importantly, we show the necessary and sufficient conditions on the existence of linear network error correction mul- ticast/broadcast/dispersion maximum distance separable （MDS） code on a matroidal error correction network. 展开更多
关键词 network error correction code error pattern imagi-nary error channels extended network matroid
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Generalized Minimum Rank Distance of Variable-Rate Linear Network Error Correction Codes 认领 引用
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作者 ZHOU Hang 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2021年第1期19-23,共5页
By extending the notion of the minimum distance for linear network error correction code(LNEC), this paper introduces the concept of generalized minimum rank distance(GMRD) of variable-rate linear network error correc... By extending the notion of the minimum distance for linear network error correction code(LNEC), this paper introduces the concept of generalized minimum rank distance(GMRD) of variable-rate linear network error correction codes. The basic properties of GMRD are investigated. It is proved that GMRD can characterize the error correction/detection capability of variable-rate linear network error correction codes when the source transmits the messages at several different rates. 展开更多
关键词 network error correction code error pattern generalized minimum distance variable-rate
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A graph neural network and multi-task learning-based decoding algorithm for enhancing XZZX code stability in biased noise 认领 引用
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作者 Bo Xiao Zai-Xu Fan +2 位作者 Hui-Qian Sun Hong-Yang Ma Xing-Kui Fan 《Chinese Physics B》 SCIE EI CAS CSCD 2025年第5期250-257,共8页
Quantum error correction is a technique that enhances a system’s ability to combat noise by encoding logical information into additional quantum bits,which plays a key role in building practical quantum computers.The... Quantum error correction is a technique that enhances a system’s ability to combat noise by encoding logical information into additional quantum bits,which plays a key role in building practical quantum computers.The XZZX surface code,with only one stabilizer generator on each face,demonstrates significant application potential under biased noise.However,the existing minimum weight perfect matching(MWPM)algorithm has high computational complexity and lacks flexibility in large-scale systems.Therefore,this paper proposes a decoding method that combines graph neural networks(GNN)with multi-classifiers,the syndrome is transformed into an undirected graph,and the features are aggregated by convolutional layers,providing a more efficient and accurate decoding strategy.In the experiments,we evaluated the performance of the XZZX code under different biased noise conditions(bias=1,20,200)and different code distances(d=3,5,7,9,11).The experimental results show that under low bias noise(bias=1),the GNN decoder achieves a threshold of 0.18386,an improvement of approximately 19.12%compared to the MWPM decoder.Under high bias noise(bias=200),the GNN decoder reaches a threshold of 0.40542,improving by approximately 20.76%,overcoming the limitations of the conventional decoder.They demonstrate that the GNN decoding method exhibits superior performance and has broad application potential in the error correction of XZZX code. 展开更多
关键词 quantum error correction XZZX code biased noise graph neural network
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Investigation of Heavy Ion Induced Failure Modes of Flash Memory with Error Correct Code 认领 引用
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作者 CHEN Qiyu LIU Jie +7 位作者 YAO Liwen YAN Xiaoyu JIAO Yang LI Xinyu ZHAI Pengfei YE Bing ZHAO Peixiong SUN Youmei 《原子核物理评论》 CAS CSCD 北大核心 2025年第4期749-756,共8页
The Error Correcting Code(ECC)is one of the most used hardening methods in Flash memory.In this study,the effect of ECC failure modes on memory error cross section has been investigated.The errors are counted in the s... The Error Correcting Code(ECC)is one of the most used hardening methods in Flash memory.In this study,the effect of ECC failure modes on memory error cross section has been investigated.The errors are counted in the situations of ECC function enabled and disabled separately after heavy ion irradiation.The results show that the upset cross section is a constant value in different ion fluences when the ECC function is disabled.With the ECC function enabled,the error cross section increases with the increase of ion fluences because the ECC failure modes lead to the increase in the number of errors.Moreover,all ECC failure modes are simulated,and their probability is calculated separately.The results help to understand the impact of ECC failure modes on Flash memory’s error cross section induced by irradiation.Some possible mitigation approaches are provided in response to this phenomenon. 展开更多
关键词 flash memory single event upset(SEU) heavy ion irradiation error correcting code(ECC) hamming code
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Secret Data-Driven Carrier-Free Secret Sharing Scheme Based on Error Correction Blocks of QR Codes 认领 引用
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作者 Song Wan Yuliang Lu +2 位作者 Xuehu Yan Hanlin Liu Longdan Tan 《国际计算机前沿大会会议论文集》 EI 2017年第1期56-57,共2页
In this paper,a novel secret data-driven carrier-free(semi structural formula)visual secret sharing(VSS)scheme with(2,2)threshold based on the error correction blocks of QR codes is investigated.The proposed scheme is... In this paper,a novel secret data-driven carrier-free(semi structural formula)visual secret sharing(VSS)scheme with(2,2)threshold based on the error correction blocks of QR codes is investigated.The proposed scheme is to search two QR codes that altered to satisfy the secret sharing modules in the error correction mechanism from the large datasets of QR codes according to the secret image,which is to embed the secret image into QR codes based on carrier-free secret sharing.The size of secret image is the same or closest with the region from the coordinate of(7,7)to the lower right corner of QR codes.In this way,we can find the QR codes combination of embedding secret information maximization with secret data-driven based on Big data search.Each output share is a valid QR code which can be decoded correctly utilizing a QR code reader and it may reduce the likelihood of attracting the attention of potential attackers.The proposed scheme can reveal secret image visually with the abilities of stacking and XOR decryptions.The secret image can be recovered by human visual system(HVS)without any computation based on stacking.On the other hand,if the light-weight computation device is available,the secret image can be lossless revealed based on XOR operation.In addition,QR codes could assist alignment for VSS recovery.The experimental results show the effectiveness of our scheme. 展开更多
关键词 Visual secret sharing QR code Error correction blocks Carrier-free Big data Data-driven Multiple decryptions
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Estimation of Two-Dimensional Correction Factors for Min-Sum Decoding of Regular LDPC Code 认领 引用
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作者 Ahmed A. Hamad 《Wireless Engineering and Technology》 2013年第4期181-187,共7页
In this paper, two-dimensional (2-D) correction scheme is proposed to improve the performance of conventional Min-Sum (MS) decoding of regular low density parity check codes. The adopted algorithm to obtain the correc... In this paper, two-dimensional (2-D) correction scheme is proposed to improve the performance of conventional Min-Sum (MS) decoding of regular low density parity check codes. The adopted algorithm to obtain the correction factors is simply based on estimating the mean square difference (MSD) between the transmitted codeword and the posteriori information of both bit and check node that produced at the MS decoder. Semi-practical tests using software-defined radio (SDR) and specific code simulations show that the proposed quasi-optimal algorithm provides a comparable error performance as Sum-Product (SP) decoding while requiring less complexity. 展开更多
关键词 LDPC Code Sum-Product Min-Sum 2-D Correction Factors Software-Defined Radio (SDR)
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基于码转换的表面码容错通用量子计算实现方法 认领 引用
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作者 权东晓 王贞理 程龙祥 《物理学报》 SCIE EI CAS CSCD 北大核心 2026年第8期260-275,共16页
量子计算在处理某类特定问题时展现出巨大潜力,但其易受噪声干扰的特性要求高效的量子纠错方案.表面码是一种重要的量子纠错码,其中二维(2D)表面码易于实现Clifford门集,而三维(3D)表面码可横截实现CCZ门和CZ门,通过两者之间的码转换可... 量子计算在处理某类特定问题时展现出巨大潜力,但其易受噪声干扰的特性要求高效的量子纠错方案.表面码是一种重要的量子纠错码,其中二维(2D)表面码易于实现Clifford门集,而三维(3D)表面码可横截实现CCZ门和CZ门,通过两者之间的码转换可高效实现容错通用门集.本文旨在优化3D表面码的编码线路设计,并研究其与2D表面码之间的码转换机制,以降低容错通用量子计算的资源开销.采用基于稳定子实现的编码线路设计及时隙优化方法,实现了高效的逻辑态编码;进一步提出基于融合与分割操作的码转换方案,并在Qiskit平台上对码距为2的实例进行仿真验证.结果表明,所设计的编码线路可以在较少时隙内正确编码,码转换方案能够有效实现任意逻辑态在2D表面码与3D表面码间的相互传输.本方案避免了魔幻态蒸馏过程,为高效实现容错通用量子计算提供了一种新途径. 展开更多
关键词 容错通用量子计算 量子纠错码 量子表面码 码转换
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面向高可靠低时延通信的顺序统计译码(OSD)关键技术综述 认领 引用
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作者 王千帆 郭延庚 +3 位作者 毕胜 王义文 宋林琦 马啸 《电子学报》 EI CAS CSCD 北大核心 2026年第1期466-478,共13页
高可靠低时延通信(Ultra-Reliable Low-Latency Communication,URLLC)是5G的三大核心场景之一,其增强版本极高可靠极低时延通信(Hyper-Reliable Low-Latency Communication,HRLLC)场景也已成为6G六大场景之一。高可靠低时延类通信场景... 高可靠低时延通信(Ultra-Reliable Low-Latency Communication,URLLC)是5G的三大核心场景之一,其增强版本极高可靠极低时延通信(Hyper-Reliable Low-Latency Communication,HRLLC)场景也已成为6G六大场景之一。高可靠低时延类通信场景对传输时延与可靠性提出了极致要求,这为短码编译码技术带来了新的机遇与挑战。顺序统计译码(Ordered Statistics Decoding,OSD)是一种近似最大似然(Near-Maximum-Likelihood,Near-ML)译码性能的通用短码译码算法,其在该类场景中具有重要潜力,但过高的计算复杂度严重制约了OSD算法的实际应用。本文系统综述了OSD算法中测试错误模式(Test Error Pattern,TEP)在测试顺序、跳过机制与提前终止策略等方面的代表性成果和最新研究进展,并对未来潜在研究方向进行了总结展望。具体地,首先讨论了汉明重量顺序、软重量顺序及基于有序可靠位的逻辑重量顺序对译码性能与复杂度的影响,指出逻辑权重顺序可以获得可靠性和实现复杂度间的有效折中。其次,分类总结了几种跳过与终止机制,阐明其基本思想是通过动态软信息判断或概率决策来降低冗余重编码次数。进一步,重点探讨了基于软度量和基于额外校验的TEP生成、跳过、终止机制及其联合设计,表明此类方法通过结构性约束与混合判断策略,在几乎不损失误帧率的前提下,将平均重编码次数降低1~2个数量级。数值结果显示,对于BCH(Bose-Chaudhuri-Hocquenghem)码[127,64],联合跳过机制在信噪比为4 dB处仅需十余次重编码,较原始OSD可减少超过90%的计算开销。最后,本文指出OSD在非二进制编码、时变信道适应性及硬件实现等方面仍面临挑战,尤其是对于码长更长的中码率区域,并展望了针对OSD算法的未来研究方向。 展开更多
关键词 纠错码 顺序统计译码 测试顺序 跳过机制 终止机制
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