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
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-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
Orthogonal frequency division multiplexing passive optical network(OFDM-PON) has superior anti-dispersion property to operate in the C-band of fiber for increased optical power budget. However,the downlink broadcast e...Orthogonal frequency division multiplexing passive optical network(OFDM-PON) has superior anti-dispersion property to operate in the C-band of fiber for increased optical power budget. However,the downlink broadcast exposes the physical layer vulnerable to the threat of illegal eavesdropping. Quantum noise stream cipher(QNSC) is a classic physical layer encryption method and well compatible with the OFDM-PON. Meanwhile, it is indispensable to exploit forward error correction(FEC) to control errors in data transmission. However, when QNSC and FEC are jointly coded, the redundant information becomes heavier and thus the code rate of the transmitted signal will be largely reduced. In this work, we propose a physical layer encryption scheme based on polar-code-assisted QNSC. In order to improve the code rate and security of the transmitted signal, we exploit chaotic sequences to yield the redundant bits and utilize the redundant information of the polar code to generate the higher-order encrypted signal in the QNSC scheme with the operation of the interleaver.We experimentally demonstrate the encrypted 16/64-QAM, 16/256-QAM, 16/1024-QAM, 16/4096-QAM QNSC signals transmitted over 30-km standard single mode fiber. For the transmitted 16/4096-QAM QNSC signal, compared with the conventional QNSC method, the proposed method increases the code rate from 0.1 to 0.32 with enhanced security.展开更多
In this paper,we first give the definition of the Euclidean sums of linear codes,and prove that the Euclidean sums of linear codes are Euclidean dual-containing.Then we construct two new classes of optimal asymmetric ...In this paper,we first give the definition of the Euclidean sums of linear codes,and prove that the Euclidean sums of linear codes are Euclidean dual-containing.Then we construct two new classes of optimal asymmetric quantum error-correcting codes based on Euclidean sums of the Reed-Solomon codes,and two new classes of optimal asymmetric quantum error-correcting codes based on Euclidean sums of linear codes generated by Vandermonde matrices over finite fields.Moreover,these optimal asymmetric quantum errorcorrecting codes constructed in this paper are different from the ones in the literature.展开更多
In this paper, we propose the approach of employing circulant permutation matrices to construct quantum quasicyclic （QC） low-density parity-check （LDPC） codes. Using the proposed approach one may construct some ne...In this paper, we propose the approach of employing circulant permutation matrices to construct quantum quasicyclic （QC） low-density parity-check （LDPC） codes. Using the proposed approach one may construct some new quantum codes with various lengths and rates of no cycles-length 4 in their Tanner graphs. In addition, these constructed codes have the advantages of simple implementation and low-complexity encoding. Finally, the decoding approach for the proposed quantum QC LDPC is investigated.展开更多
Quantum secret sharing（QSS） is a procedure of sharing classical information or quantum information by using quantum states. This paper presents how to use a [2k- 1, 1, k] quantum error-correcting code （QECC） to im...Quantum secret sharing（QSS） is a procedure of sharing classical information or quantum information by using quantum states. This paper presents how to use a [2k- 1, 1, k] quantum error-correcting code （QECC） to implement a quantum （k, 2k-1） threshold scheme. It also takes advantage of classical enhancement of the [2k-1, 1, k] QECC to establish a QSS scheme which can share classical information and quantum information simultaneously. Because information is encoded into QECC, these schemes can prevent intercept-resend attacks and be implemented on some noisy channels.展开更多
In a recent paper, Hu et al. defined the complete weight distributions of quantum codes and proved the Mac Williams identities, and as applications they showed how such weight distributions may be used to obtain the s...In a recent paper, Hu et al. defined the complete weight distributions of quantum codes and proved the Mac Williams identities, and as applications they showed how such weight distributions may be used to obtain the singleton-type and hamming-type bounds for asymmetric quantum codes. In this paper we extend their study much further and obtain several new results concerning the complete weight distributions of quantum codes and applications. In particular, we provide a new proof of the Mac Williams identities of the complete weight distributions of quantum codes. We obtain new information about the weight distributions of quantum MDS codes and the double weight distribution of asymmetric quantum MDS codes. We get new identities involving the complete weight distributions of two different quantum codes. We estimate the complete weight distributions of quantum codes under special conditions and show that quantum BCH codes by the Hermitian construction from primitive, narrow-sense BCH codes satisfy these conditions and hence these estimate applies.展开更多
This paper demonstrates how channel coding can improve the robustness of spatial image watermarks against signal distortion caused by lossy data compression such as the JPEG scheme by taking advantage of the propertie...This paper demonstrates how channel coding can improve the robustness of spatial image watermarks against signal distortion caused by lossy data compression such as the JPEG scheme by taking advantage of the properties of Gray code. Two error-correction coding (ECC) schemes are used here: One scheme, referred to as the vertical ECC (VECC), is to encode information bits in a pixel by error-correction coding where the Gray code is used to improve the performance. The other scheme, referred to as the horizontal ECC (HECC), is to encode information bits in an image plane. In watermarking, HECC generates a codeword representing watermark bits, and each bit of the codeword is encoded by VECC. Simple single-error-correcting block codes are used in VECC and HECC. Several experiments of these schemes were conducted on test images. The result demonstrates that the error-correcting performance of HECC just depends on that of VECC, and accordingly, HECC enhances the capability of VECC. Consequently, HECC with appropriate codes can achieve stronger robustness to JPEG—caused distortions than non-channel-coding watermarking schemes.展开更多
In this paper, error-correction coding (ECC) in Gray codes is considered and its performance in the protecting of spatial image watermarks against lossy data compression is demonstrated. For this purpose, the differen...In this paper, error-correction coding (ECC) in Gray codes is considered and its performance in the protecting of spatial image watermarks against lossy data compression is demonstrated. For this purpose, the differences between bit patterns of two Gray codewords are analyzed in detail. On the basis of the properties, a method for encoding watermark bits in the Gray codewords that represent signal levels by a single-error-correcting (SEC) code is developed, which is referred to as the Gray-ECC method in this paper. The two codewords of the SEC code corresponding to respective watermark bits are determined so as to minimize the expected amount of distortion caused by the watermark embedding. The stochastic analyses show that an error-correcting capacity of the Gray-ECC method is superior to that of the ECC in natural binary codes for changes in signal codewords. Experiments of the Gray-ECC method were conducted on 8-bit monochrome images to evaluate both the features of watermarked images and the performance of robustness for image distortion resulting from the JPEG DCT-baseline coding scheme. The results demonstrate that, compared with a conventional averaging-based method, the Gray-ECC method yields watermarked images with less amount of signal distortion and also makes the watermark comparably robust for lossy data compression.展开更多
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
Quantum secure direct communication(QSDC) is a communication method based on quantum mechanics and it is used to transmit secret messages. Unlike quantum key distribution, secret messages can be transmitted directly o...Quantum secure direct communication(QSDC) is a communication method based on quantum mechanics and it is used to transmit secret messages. Unlike quantum key distribution, secret messages can be transmitted directly on a quantum channel with QSDC. Higher channel capacity and noise suppression capabilities are key to achieving longdistance quantum communication. Here, we report a continuous-variable QSDC scheme based on mask-coding and orbital angular momentum, in which the mask-coding is employed to protect the security of the transmitting messages and to suppress the influence of excess noise. The combination of orbital angular momentum and information block transmission effectively improves the secrecy capacity. In the 800 information blocks ×1310 bits length 10-km experiment, the results show a statistical average bit error rate of 0.38%, a system excess noise value of 0.0184 SNU, and a final secrecy capacity of 6.319×10~6 bps. Therefore, this scheme reduces error bits while increasing secrecy capacity, providing a solution for long-distance large-scale quantum communication, which is capable of transmitting text, images and other information of reasonable size.展开更多
Exploiting the encoding process of the stabilizer quantum code [[n, k, d]], a deterministic quantum communication scheme, in which n - 1 photons are distributed forward and backward in two-way channel, is proposed to ...Exploiting the encoding process of the stabilizer quantum code [[n, k, d]], a deterministic quantum communication scheme, in which n - 1 photons are distributed forward and backward in two-way channel, is proposed to transmit the secret messages with unconditional security. The present scheme can be implemented to distribute the secret quantum （or classical） messages with great capacity in imperfect quantum channel since the utilized code encodes k-qubit messages for each scheme run.展开更多
When the time variable in quantum signal processing is discrete, the Fourier transform exists on the vector space of n-tuples over the Galois field F2, which plays an important role in the investigation of quantum sig...When the time variable in quantum signal processing is discrete, the Fourier transform exists on the vector space of n-tuples over the Galois field F2, which plays an important role in the investigation of quantum signals. By using Fourier transforms, the idea of quantum coding theory can be described in a setting that is much different from that seen that far. Quantum BCH codes can be defined as codes whose quantum states have certain specified consecutive spectral components equal to zero and the error-correcting ability is also described by the number of the consecutive zeros. Moreover, the decoding of quantum codes can be described spectrally with more efficiency.展开更多
It is a regular way of constructing quantum error-correcting codes via codes with self-orthogonal property, and whether a classical Bose-Chaudhuri-Hocquenghem (BCH) code is self-orthogonal can be determined by its des...It is a regular way of constructing quantum error-correcting codes via codes with self-orthogonal property, and whether a classical Bose-Chaudhuri-Hocquenghem (BCH) code is self-orthogonal can be determined by its designed distance. In this paper, we give the sufficient and necessary condition for arbitrary classical BCH codes with self-orthogonal property through algorithms. We also give a better upper bound of the designed distance of a classical narrow-sense BCH code which contains its Euclidean dual. Besides these, we also give one algorithm to compute the dimension of these codes. The complexity of all algorithms is analyzed. Then the results can be applied to construct a series of quantum BCH codes via the famous CSS constructions.展开更多
In this paper, we discuss the concepts of quantum coding and error correction for a five-particle entangled state. Error correction can correct bit-reverse or phase-flip errors of one and two quantum states and is no ...In this paper, we discuss the concepts of quantum coding and error correction for a five-particle entangled state. Error correction can correct bit-reverse or phase-flip errors of one and two quantum states and is no longer limited to only one quantum state. We encode a single quantum state into a five-particle entangled state before being transferred to the sender. We designed an automatic error-correction circuit to correct errors caused by noise. We also simplify the design process for a multiple quantum error-correction circuit. We compare error-correction schemes for five and three entangled particles in terms of efficiency and capabilities. The results show that error-correction efficiency and fidelity are im- proved.展开更多
The theory of quantum error correcting codes is a primary tool for fighting decoherence and other quantum noise in quantum communication and quantum computation. Recently, the theory of quantum error correcting codes ...The theory of quantum error correcting codes is a primary tool for fighting decoherence and other quantum noise in quantum communication and quantum computation. Recently, the theory of quantum error correcting codes has developed rapidly and been extended to protect quantum information over asymmetric quantum channels, in which phase-shift and qubit-flip errors occur with different probabilities. In this paper, we generalize the construction of symmetric quantum codes via graphs (or matrices) to the asymmetric case, converting the construction of asymmetric quantum codes to finding matrices with some special properties. We also propose some asymmetric quantum Maximal Distance Separable (MDS) codes as examples constructed in this way.展开更多
We study the performances of quantum channel adaptive [4,1] code transmitting in a joint amplitude damping and dephasing channel, the [6,2] code transmitting in an amplitude damping channel by combining the encoding, ...We study the performances of quantum channel adaptive [4,1] code transmitting in a joint amplitude damping and dephasing channel, the [6,2] code transmitting in an amplitude damping channel by combining the encoding, noise process, and decoding as one effective channel. We explicitly obtain the entanglement fidelities. The recovery operators of the [6,2] code are given. The performance is nearly optimal compared with that of the optimal method of semidefinite programming.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
基金Supported by the National Natural Science Foundation of China (61271122)the Natural Science Foundation of Anhui Province(1208085MF102)
文摘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.
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 in part by the National Natural Science Foundation of China Project under Grant 62075147the Suzhou Industry Technological Innovation Projects under Grant SYG202348.
文摘Orthogonal frequency division multiplexing passive optical network(OFDM-PON) has superior anti-dispersion property to operate in the C-band of fiber for increased optical power budget. However,the downlink broadcast exposes the physical layer vulnerable to the threat of illegal eavesdropping. Quantum noise stream cipher(QNSC) is a classic physical layer encryption method and well compatible with the OFDM-PON. Meanwhile, it is indispensable to exploit forward error correction(FEC) to control errors in data transmission. However, when QNSC and FEC are jointly coded, the redundant information becomes heavier and thus the code rate of the transmitted signal will be largely reduced. In this work, we propose a physical layer encryption scheme based on polar-code-assisted QNSC. In order to improve the code rate and security of the transmitted signal, we exploit chaotic sequences to yield the redundant bits and utilize the redundant information of the polar code to generate the higher-order encrypted signal in the QNSC scheme with the operation of the interleaver.We experimentally demonstrate the encrypted 16/64-QAM, 16/256-QAM, 16/1024-QAM, 16/4096-QAM QNSC signals transmitted over 30-km standard single mode fiber. For the transmitted 16/4096-QAM QNSC signal, compared with the conventional QNSC method, the proposed method increases the code rate from 0.1 to 0.32 with enhanced security.
基金Supported by the Scientific Research Foundation of Hubei Provincial Education Department of China(Q20174503)the National Science Foundation of Hubei Polytechnic University of China(12xjz14A and 17xjz03A)。
文摘In this paper,we first give the definition of the Euclidean sums of linear codes,and prove that the Euclidean sums of linear codes are Euclidean dual-containing.Then we construct two new classes of optimal asymmetric quantum error-correcting codes based on Euclidean sums of the Reed-Solomon codes,and two new classes of optimal asymmetric quantum error-correcting codes based on Euclidean sums of linear codes generated by Vandermonde matrices over finite fields.Moreover,these optimal asymmetric quantum errorcorrecting codes constructed in this paper are different from the ones in the literature.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 60773085 and 60801051)the NSFC-KOSEF International Collaborative Research Funds (Grant Nos 60811140346 and F01-2008-000-10021-0)
文摘In this paper, we propose the approach of employing circulant permutation matrices to construct quantum quasicyclic （QC） low-density parity-check （LDPC） codes. Using the proposed approach one may construct some new quantum codes with various lengths and rates of no cycles-length 4 in their Tanner graphs. In addition, these constructed codes have the advantages of simple implementation and low-complexity encoding. Finally, the decoding approach for the proposed quantum QC LDPC is investigated.
基金Project supported by the National Natural Science Foundation of China (Grant No. 61072071)
文摘Quantum secret sharing（QSS） is a procedure of sharing classical information or quantum information by using quantum states. This paper presents how to use a [2k- 1, 1, k] quantum error-correcting code （QECC） to implement a quantum （k, 2k-1） threshold scheme. It also takes advantage of classical enhancement of the [2k-1, 1, k] QECC to establish a QSS scheme which can share classical information and quantum information simultaneously. Because information is encoded into QECC, these schemes can prevent intercept-resend attacks and be implemented on some noisy channels.
基金the National Natural Science Foundation of China (Grant Nos. 61972413, 61901525, and 62002385)the National Key R&D Program of China (Grant No. 2021YFB3100100)RGC under Grant No. N HKUST619/17 from Hong Kong, China。
文摘In a recent paper, Hu et al. defined the complete weight distributions of quantum codes and proved the Mac Williams identities, and as applications they showed how such weight distributions may be used to obtain the singleton-type and hamming-type bounds for asymmetric quantum codes. In this paper we extend their study much further and obtain several new results concerning the complete weight distributions of quantum codes and applications. In particular, we provide a new proof of the Mac Williams identities of the complete weight distributions of quantum codes. We obtain new information about the weight distributions of quantum MDS codes and the double weight distribution of asymmetric quantum MDS codes. We get new identities involving the complete weight distributions of two different quantum codes. We estimate the complete weight distributions of quantum codes under special conditions and show that quantum BCH codes by the Hermitian construction from primitive, narrow-sense BCH codes satisfy these conditions and hence these estimate applies.
文摘This paper demonstrates how channel coding can improve the robustness of spatial image watermarks against signal distortion caused by lossy data compression such as the JPEG scheme by taking advantage of the properties of Gray code. Two error-correction coding (ECC) schemes are used here: One scheme, referred to as the vertical ECC (VECC), is to encode information bits in a pixel by error-correction coding where the Gray code is used to improve the performance. The other scheme, referred to as the horizontal ECC (HECC), is to encode information bits in an image plane. In watermarking, HECC generates a codeword representing watermark bits, and each bit of the codeword is encoded by VECC. Simple single-error-correcting block codes are used in VECC and HECC. Several experiments of these schemes were conducted on test images. The result demonstrates that the error-correcting performance of HECC just depends on that of VECC, and accordingly, HECC enhances the capability of VECC. Consequently, HECC with appropriate codes can achieve stronger robustness to JPEG—caused distortions than non-channel-coding watermarking schemes.
文摘In this paper, error-correction coding (ECC) in Gray codes is considered and its performance in the protecting of spatial image watermarks against lossy data compression is demonstrated. For this purpose, the differences between bit patterns of two Gray codewords are analyzed in detail. On the basis of the properties, a method for encoding watermark bits in the Gray codewords that represent signal levels by a single-error-correcting (SEC) code is developed, which is referred to as the Gray-ECC method in this paper. The two codewords of the SEC code corresponding to respective watermark bits are determined so as to minimize the expected amount of distortion caused by the watermark embedding. The stochastic analyses show that an error-correcting capacity of the Gray-ECC method is superior to that of the ECC in natural binary codes for changes in signal codewords. Experiments of the Gray-ECC method were conducted on 8-bit monochrome images to evaluate both the features of watermarked images and the performance of robustness for image distortion resulting from the JPEG DCT-baseline coding scheme. The results demonstrate that, compared with a conventional averaging-based method, the Gray-ECC method yields watermarked images with less amount of signal distortion and also makes the watermark comparably robust for lossy data compression.
基金supported by the Natural Science Foundation of Shandong Province,China(Grant No.ZR2021MF049)the Joint Fund of Natural Science Foundation of Shandong Province,China(Grant Nos.ZR2022LL.Z012 and ZR2021LLZ001)the Key Research and Development Program of Shandong Province,China(Grant No.2023CXGC010901).
文摘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.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 62071381 and 62301430)Shaanxi Fundamental Science Research Project for Mathematics and Physics (Grant No. 23JSY014)+1 种基金Scientific Research Plan Project of Shaanxi Education Department (Natural Science Special Project (Grant No. 23JK0680)Young Talent Fund of Xi’an Association for Science and Technology (Grant No. 959202313011)。
文摘Quantum secure direct communication(QSDC) is a communication method based on quantum mechanics and it is used to transmit secret messages. Unlike quantum key distribution, secret messages can be transmitted directly on a quantum channel with QSDC. Higher channel capacity and noise suppression capabilities are key to achieving longdistance quantum communication. Here, we report a continuous-variable QSDC scheme based on mask-coding and orbital angular momentum, in which the mask-coding is employed to protect the security of the transmitting messages and to suppress the influence of excess noise. The combination of orbital angular momentum and information block transmission effectively improves the secrecy capacity. In the 800 information blocks ×1310 bits length 10-km experiment, the results show a statistical average bit error rate of 0.38%, a system excess noise value of 0.0184 SNU, and a final secrecy capacity of 6.319×10~6 bps. Therefore, this scheme reduces error bits while increasing secrecy capacity, providing a solution for long-distance large-scale quantum communication, which is capable of transmitting text, images and other information of reasonable size.
基金The project supported by National Natural Science Foundation of China under Grant Nos.60472018 and 60573127partly supported by the Postdoctoral Science Foundation of Central South University
文摘Exploiting the encoding process of the stabilizer quantum code [[n, k, d]], a deterministic quantum communication scheme, in which n - 1 photons are distributed forward and backward in two-way channel, is proposed to transmit the secret messages with unconditional security. The present scheme can be implemented to distribute the secret quantum （or classical） messages with great capacity in imperfect quantum channel since the utilized code encodes k-qubit messages for each scheme run.
基金The project supported by National Natural Science Foundation of China under Grant No. 60472018, and the Foundation of National Laboratory for Modern Communications
文摘When the time variable in quantum signal processing is discrete, the Fourier transform exists on the vector space of n-tuples over the Galois field F2, which plays an important role in the investigation of quantum signals. By using Fourier transforms, the idea of quantum coding theory can be described in a setting that is much different from that seen that far. Quantum BCH codes can be defined as codes whose quantum states have certain specified consecutive spectral components equal to zero and the error-correcting ability is also described by the number of the consecutive zeros. Moreover, the decoding of quantum codes can be described spectrally with more efficiency.
基金Supported by the National Natural Science Foundation of China (No.60403004)the Outstanding Youth Foundation of China (No.0612000500)
文摘It is a regular way of constructing quantum error-correcting codes via codes with self-orthogonal property, and whether a classical Bose-Chaudhuri-Hocquenghem (BCH) code is self-orthogonal can be determined by its designed distance. In this paper, we give the sufficient and necessary condition for arbitrary classical BCH codes with self-orthogonal property through algorithms. We also give a better upper bound of the designed distance of a classical narrow-sense BCH code which contains its Euclidean dual. Besides these, we also give one algorithm to compute the dimension of these codes. The complexity of all algorithms is analyzed. Then the results can be applied to construct a series of quantum BCH codes via the famous CSS constructions.
文摘In this paper, we discuss the concepts of quantum coding and error correction for a five-particle entangled state. Error correction can correct bit-reverse or phase-flip errors of one and two quantum states and is no longer limited to only one quantum state. We encode a single quantum state into a five-particle entangled state before being transferred to the sender. We designed an automatic error-correction circuit to correct errors caused by noise. We also simplify the design process for a multiple quantum error-correction circuit. We compare error-correction schemes for five and three entangled particles in terms of efficiency and capabilities. The results show that error-correction efficiency and fidelity are im- proved.
基金supported by the National High Technology Research and Development Program of China under Grant No. 2011AA010803
文摘The theory of quantum error correcting codes is a primary tool for fighting decoherence and other quantum noise in quantum communication and quantum computation. Recently, the theory of quantum error correcting codes has developed rapidly and been extended to protect quantum information over asymmetric quantum channels, in which phase-shift and qubit-flip errors occur with different probabilities. In this paper, we generalize the construction of symmetric quantum codes via graphs (or matrices) to the asymmetric case, converting the construction of asymmetric quantum codes to finding matrices with some special properties. We also propose some asymmetric quantum Maximal Distance Separable (MDS) codes as examples constructed in this way.
基金Project supported by the National Natural Science Foundation of China (Grant No. 60972071)the Natural Science Foundation of Zhejiang Province, China(Grant Nos. Y6100421 and LQ12F02012)the Zhejiang Province Science and Technology Project, China (Grant No. 2009C31060)
文摘We study the performances of quantum channel adaptive [4,1] code transmitting in a joint amplitude damping and dephasing channel, the [6,2] code transmitting in an amplitude damping channel by combining the encoding, noise process, and decoding as one effective channel. We explicitly obtain the entanglement fidelities. The recovery operators of the [6,2] code are given. The performance is nearly optimal compared with that of the optimal method of semidefinite programming.
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.
