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
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
A new Chien search method for shortened Reed-Solomon （RS） code is proposed, based on this, a versatile RS decoder for correcting both errors and erasures is designed. Compared with the traditional RS decoder, the we...A new Chien search method for shortened Reed-Solomon （RS） code is proposed, based on this, a versatile RS decoder for correcting both errors and erasures is designed. Compared with the traditional RS decoder, the weighted coefficient of the Chien search method is calculated sequentially through the three pipelined stages of the decoder. And therefore, the computation of the errata locator polynomial and errata evaluator polynomial needs to be modified. The versatile RS decoder with minimum distance 21 has been synthesized in the Xilinx Virtex-Ⅱ series field programmable gate array （FPGA） xe2v1000-5 and is used by coneatenated coding system for satellite communication. Results show that the maximum data processing rate can be up to 1.3 Gbit/s.展开更多
This paper proposes a steady-state errors correction(SSEC)method for eliminating measurement errors.This method is based on the detections of error signal E(s)and output C(s)which generate an expected output R(s).In c...This paper proposes a steady-state errors correction(SSEC)method for eliminating measurement errors.This method is based on the detections of error signal E(s)and output C(s)which generate an expected output R(s).In comparison with the conventional solutions which are based on detecting the expected output R(s)and output C(s)to obtain error signal E(s),the measurement errors are eliminated even the error might be at a significant level.Moreover,it is possible that the individual debugging by regulating the coefficient K for every member of the multiple objectives achieves the optimization of the open loop gain.Therefore,this simple method can be applied to the weak coupling and multiple objectives system,which is usually controlled by complex controller.The principle of eliminating measurement errors is derived analytically,and the advantages comparing with the conventional solutions are depicted.Based on the SSEC method analysis,an application of this method for an active power filter(APF)is investigated and the effectiveness and viability of the scheme are demonstrated through the simulation and experimental verifications.展开更多
For quantum sparse graph codes with stabilizer formalism, the unavoidable girth-four cycles in their Tanner graphs greatly degrade the iterative decoding performance with standard belief-propagation （BP） algorithm. ...For quantum sparse graph codes with stabilizer formalism, the unavoidable girth-four cycles in their Tanner graphs greatly degrade the iterative decoding performance with standard belief-propagation （BP） algorithm. In this paper, we present a jointly-check iterative algorithm suitable for decoding quantum sparse graph codes efficiently. Numerical simulations show that this modified method outperforms standard BP algorithm with an obvious performance improvement.展开更多
The decoding algorithm for the correction of errors of arbitrary Mannheim weight has discussed for Lattice constellations and codes from quadratic number fields.Following these lines,the decoding algorithms for the co...The decoding algorithm for the correction of errors of arbitrary Mannheim weight has discussed for Lattice constellations and codes from quadratic number fields.Following these lines,the decoding algorithms for the correction of errors of n=p−12 length cyclic codes(C)over quaternion integers of Quaternion Mannheim(QM)weight one up to two coordinates have considered.In continuation,the case of cyclic codes of lengths n=p−12 and 2n−1=p−2 has studied to improve the error correction efficiency.In this study,we present the decoding of cyclic codes of length n=ϕ(p)=p−1 and length 2n−1=2ϕ(p)−1=2p−3(where p is prime integer andϕis Euler phi function)over Hamilton Quaternion integers of Quaternion Mannheim weight for the correction of errors.Furthermore,the error correction capability and code rate tradeoff of these codes are also discussed.Thus,an increase in the length of the cyclic code is achieved along with its better code rate and an adequate error correction capability.展开更多
In this paper, we describe a hard-decision decoding technique based on Genetic Algorithms (HDGA), which is applicable to the general case of error correcting codes where the only known structure is given by the genera...In this paper, we describe a hard-decision decoding technique based on Genetic Algorithms (HDGA), which is applicable to the general case of error correcting codes where the only known structure is given by the generating matrix G. Then we present a new soft-decision decoding based on HDGA and the Chase algorithm (SDGA). The performance of some binary and non-binary Linear Block Codes are given for HDGA and SDGA over Gaussian and Rayleigh channels. The performances show that the HDGA decoder has the same performances as the Berlekamp-Massey Algorithm (BMA) in various transmission channels. On the other hand, the performances of SDGA are equivalent to soft-decision decoding using Chase algorithm and BMA (Chase-BMA). The complexity of decoders proposed is also discussed and compared to those of other decoders.展开更多
In this paper we present an efficient algorithm to decode linear block codes on binary channels. The main idea consists in using a vote procedure in order to elaborate artificial reliabilities of the binary received w...In this paper we present an efficient algorithm to decode linear block codes on binary channels. The main idea consists in using a vote procedure in order to elaborate artificial reliabilities of the binary received word and to present the obtained real vector r as inputs of a SIHO decoder (Soft In/Hard Out). The goal of the latter is to try to find the closest codeword to r in terms of the Euclidean distance. A comparison of the proposed algorithm over the AWGN channel with the Majority logic decoder, Berlekamp-Massey, Bit Flipping, Hartman-Rudolf algorithms and others show that it is more efficient in terms of performance. The complexity of the proposed decoder depends on the weight of the error to decode, on the code structure and also on the used SIHO decoder.展开更多
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
In view of the problems that the encoding complexity of quasi-cyclic low-density parity-check(QC-LDPC) codes is high and the minimum distance is not large enough which leads to the degradation of the error-correction ...In view of the problems that the encoding complexity of quasi-cyclic low-density parity-check(QC-LDPC) codes is high and the minimum distance is not large enough which leads to the degradation of the error-correction performance, the new irregular type-Ⅱ QC-LDPC codes based on perfect cyclic difference sets(CDSs) are constructed. The parity check matrices of these type-Ⅱ QC-LDPC codes consist of the zero matrices with weight of 0, the circulant permutation matrices(CPMs) with weight of 1 and the circulant matrices with weight of 2(W2CMs). The introduction of W2CMs in parity check matrices makes it possible to achieve the larger minimum distance which can improve the error-correction performance of the codes. The Tanner graphs of these codes have no girth-4, thus they have the excellent decoding convergence characteristics. In addition, because the parity check matrices have the quasi-dual diagonal structure, the fast encoding algorithm can reduce the encoding complexity effectively. Simulation results show that the new type-Ⅱ QC-LDPC codes can achieve a more excellent error-correction performance and have no error floor phenomenon over the additive white Gaussian noise(AWGN) channel with sum-product algorithm(SPA) iterative decoding.展开更多
基金Project supported by the Natural Science Foundation of Shandong Province,China(Grant No.ZR2021MF049)Joint Fund of Natural Science Foundation of Shandong Province(Grant Nos.ZR2022LLZ012 and ZR2021LLZ001)the Key R&D Program of Shandong Province,China(Grant No.2023CXGC010901)。
文摘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.
基金the National Natural Science Foundation of China(Grant Nos.11975132 and 61772295)the Natural Science Foundation of Shandong Province,China(Grant No.ZR2019YQ01)the Project of Shandong Province Higher Educational Science and Technology Program,China(Grant No.J18KZ012).
文摘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.
基金Sponsored by the Ministerial Level Advanced Research Foundation (20304)
文摘A new Chien search method for shortened Reed-Solomon （RS） code is proposed, based on this, a versatile RS decoder for correcting both errors and erasures is designed. Compared with the traditional RS decoder, the weighted coefficient of the Chien search method is calculated sequentially through the three pipelined stages of the decoder. And therefore, the computation of the errata locator polynomial and errata evaluator polynomial needs to be modified. The versatile RS decoder with minimum distance 21 has been synthesized in the Xilinx Virtex-Ⅱ series field programmable gate array （FPGA） xe2v1000-5 and is used by coneatenated coding system for satellite communication. Results show that the maximum data processing rate can be up to 1.3 Gbit/s.
基金National Natural Science Foundation of China(No.61273172)
文摘This paper proposes a steady-state errors correction(SSEC)method for eliminating measurement errors.This method is based on the detections of error signal E(s)and output C(s)which generate an expected output R(s).In comparison with the conventional solutions which are based on detecting the expected output R(s)and output C(s)to obtain error signal E(s),the measurement errors are eliminated even the error might be at a significant level.Moreover,it is possible that the individual debugging by regulating the coefficient K for every member of the multiple objectives achieves the optimization of the open loop gain.Therefore,this simple method can be applied to the weak coupling and multiple objectives system,which is usually controlled by complex controller.The principle of eliminating measurement errors is derived analytically,and the advantages comparing with the conventional solutions are depicted.Based on the SSEC method analysis,an application of this method for an active power filter(APF)is investigated and the effectiveness and viability of the scheme are demonstrated through the simulation and experimental verifications.
基金Project supported by the National Natural Science Foundation of China(Grant No.60972046)Grant from the National Defense Pre-Research Foundation of China
文摘For quantum sparse graph codes with stabilizer formalism, the unavoidable girth-four cycles in their Tanner graphs greatly degrade the iterative decoding performance with standard belief-propagation （BP） algorithm. In this paper, we present a jointly-check iterative algorithm suitable for decoding quantum sparse graph codes efficiently. Numerical simulations show that this modified method outperforms standard BP algorithm with an obvious performance improvement.
基金The authors extend their gratitude to the Deanship of Scientific Research at King Khalid University for funding this work through research groups program under grant number R.G.P.1/85/42.
文摘The decoding algorithm for the correction of errors of arbitrary Mannheim weight has discussed for Lattice constellations and codes from quadratic number fields.Following these lines,the decoding algorithms for the correction of errors of n=p−12 length cyclic codes(C)over quaternion integers of Quaternion Mannheim(QM)weight one up to two coordinates have considered.In continuation,the case of cyclic codes of lengths n=p−12 and 2n−1=p−2 has studied to improve the error correction efficiency.In this study,we present the decoding of cyclic codes of length n=ϕ(p)=p−1 and length 2n−1=2ϕ(p)−1=2p−3(where p is prime integer andϕis Euler phi function)over Hamilton Quaternion integers of Quaternion Mannheim weight for the correction of errors.Furthermore,the error correction capability and code rate tradeoff of these codes are also discussed.Thus,an increase in the length of the cyclic code is achieved along with its better code rate and an adequate error correction capability.
文摘In this paper, we describe a hard-decision decoding technique based on Genetic Algorithms (HDGA), which is applicable to the general case of error correcting codes where the only known structure is given by the generating matrix G. Then we present a new soft-decision decoding based on HDGA and the Chase algorithm (SDGA). The performance of some binary and non-binary Linear Block Codes are given for HDGA and SDGA over Gaussian and Rayleigh channels. The performances show that the HDGA decoder has the same performances as the Berlekamp-Massey Algorithm (BMA) in various transmission channels. On the other hand, the performances of SDGA are equivalent to soft-decision decoding using Chase algorithm and BMA (Chase-BMA). The complexity of decoders proposed is also discussed and compared to those of other decoders.
文摘In this paper we present an efficient algorithm to decode linear block codes on binary channels. The main idea consists in using a vote procedure in order to elaborate artificial reliabilities of the binary received word and to present the obtained real vector r as inputs of a SIHO decoder (Soft In/Hard Out). The goal of the latter is to try to find the closest codeword to r in terms of the Euclidean distance. A comparison of the proposed algorithm over the AWGN channel with the Majority logic decoder, Berlekamp-Massey, Bit Flipping, Hartman-Rudolf algorithms and others show that it is more efficient in terms of performance. The complexity of the proposed decoder depends on the weight of the error to decode, on the code structure and also on the used SIHO decoder.
基金supported by the National Natural Science Foundation of China(Grant Nos.62371240,61802175,62401266,and 12201300)the National Key R&D Program of China(Grant No.2022YFB3103800)+2 种基金the Natural Science Foundation of Jiangsu Province(Grant No.BK20241452)the Fundamental Research Funds for the Central Universities(Grant No.30923011014)the fund of Laboratory for Advanced Computing and Intelligence Engineering(Grant No.2023-LYJJ-01-009)。
文摘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%.
基金supported by the National Natural Science Foundation of China(No.61472464)the Research Foundation of Education Bureau of Hunan Province in China(No.16C0686)the Key Discipline Construction Project Funding for Hunan University of Science and Engineering(Electrical systems)
文摘In view of the problems that the encoding complexity of quasi-cyclic low-density parity-check(QC-LDPC) codes is high and the minimum distance is not large enough which leads to the degradation of the error-correction performance, the new irregular type-Ⅱ QC-LDPC codes based on perfect cyclic difference sets(CDSs) are constructed. The parity check matrices of these type-Ⅱ QC-LDPC codes consist of the zero matrices with weight of 0, the circulant permutation matrices(CPMs) with weight of 1 and the circulant matrices with weight of 2(W2CMs). The introduction of W2CMs in parity check matrices makes it possible to achieve the larger minimum distance which can improve the error-correction performance of the codes. The Tanner graphs of these codes have no girth-4, thus they have the excellent decoding convergence characteristics. In addition, because the parity check matrices have the quasi-dual diagonal structure, the fast encoding algorithm can reduce the encoding complexity effectively. Simulation results show that the new type-Ⅱ QC-LDPC codes can achieve a more excellent error-correction performance and have no error floor phenomenon over the additive white Gaussian noise(AWGN) channel with sum-product algorithm(SPA) iterative decoding.
