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Quantum secret sharing based on quantum error-correcting codes 认领 引用 被引量:3
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作者 张祖荣 刘伟涛 李承祖 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第5期91-95,共5页
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
关键词 quantum secret sharing quantum error-correcting code classically enhanced quantumerror-correcting code
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On the complete weight distributions of quantum error-correcting codes 认领 引用 被引量:1
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作者 杜超 马智 熊茂胜 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第5期272-287,共16页
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
关键词 quantum codes complete weight distributions Mac Williams identities BCH codes
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Quantum toric code decoding method based on syndrome-preliminary error fusion module and ResNet architecture 认领 引用
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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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New binary quantum stabilizer codes from classical quasi-cyclic codes of index two 认领 引用
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作者 Zhen-Hui Zhang Zhuo Li Li-Juan Xing 《Chinese Physics B》 SCIE EI CAS CSCD 2026年第4期253-264,共12页
We study the algebraic structures of a generalized class of quasi-cyclic codes of index two,and prove that any quasicyclic code of index two can be transformed into our proposed quasi-cyclic codes.We determine the gen... We study the algebraic structures of a generalized class of quasi-cyclic codes of index two,and prove that any quasicyclic code of index two can be transformed into our proposed quasi-cyclic codes.We determine the generator forms of the proposed quasi-cyclic codes and their Hermitian dual codes.We establish the necessary and sufficient conditions for Hermitian self-orthogonality and dual-containing property to construct quantum stabilizer codes via the Hermitian construction method.As an application,10 record-breaking quantum stabilizer codes are constructed. 展开更多
关键词 quasi-cyclic codes quantum stabilizer codes Hermitian inner product Hermitian construction
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Quantum quasi-cyclic low-density parity-check error-correcting codes 认领 引用 被引量:5
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作者 李渊 曾贵华 Moon Ho Leeb 《Chinese Physics B》 SCIE EI CAS 2009年第10期4154-4160,共7页
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
关键词 quantum LDPC code quasi-cycliC circulant permutation matrix CSS code
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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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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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An Error-Correcting Code-Based Robust Watermarking Scheme for Stereolithographic Files 认领 引用 被引量:2
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作者 Zhuorong Li Huawei Tian +2 位作者 Yanhui Xiao Yunqi Tang Anhong Wang 《Computer Systems Science & Engineering》 SCIE EI 2021年第5期247-263,共17页
Stereolithographic(STL)files have been extensively used in rapid prototyping industries as well as many other fields as watermarking algorithms to secure intellectual property and protect three-dimensional models from... Stereolithographic(STL)files have been extensively used in rapid prototyping industries as well as many other fields as watermarking algorithms to secure intellectual property and protect three-dimensional models from theft.However,to the best of our knowledge,few studies have looked at how watermarking can resist attacks that involve vertex-reordering.Here,we present a lossless and robust watermarking scheme for STL files to protect against vertexreordering attacks.Specifically,we designed a novel error-correcting code(ECC)that can correct the error of any one-bit in a bitstream by inserting several check digits.In addition,ECC is designed to make use of redundant information according to the characteristics of STL files,which introduces further robustness for defense against attacks.No modifications are made to the geometric information of the three-dimensional model,which respects the requirements of a highprecision model.The experimental results show that the proposed watermarking scheme can survive numerous kinds of attack,including rotation,scaling and translation(RST),facet reordering,and vertex-reordering attacks. 展开更多
关键词 Three-dimensional watermarking stereolithographic file robust watermarking error-correcting code
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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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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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ON CLASSICAL BCH CODES AND QUANTUM BCH CODES 认领 引用 被引量:4
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作者 Xu Yajie Ma Zhi Zhang Chunyuan 《Journal of Electronics(China)》 2009年第1期64-70,共7页
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
关键词 Quantum error-correcting codes Bose-Chaudhuri-Hocquenghem (BCH) codes Self-orthogonal Euclidean dual Hermitian dual
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USING ERROR-CORRECTING ENCODERS TO DESIGN LOCAL-RANDOM SEQUENCE GENERATORS 认领 引用
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作者 杨义先 《Journal of Electronics(China)》 1995年第1期9-14,共6页
This paper proved the statement that a good linear block encoder is in fact a good local-random sequence generator. Furthermore, this statement discovers the deep relationship between the error-correcting coding theor... This paper proved the statement that a good linear block encoder is in fact a good local-random sequence generator. Furthermore, this statement discovers the deep relationship between the error-correcting coding theory and the modern cryptography. 展开更多
关键词 Error-correcting coding Cryptography Random sequences
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A Construction of Quantum Error-Locating Codes 认领 引用
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作者 樊继豪 陈汉武 《Communications in Theoretical Physics》 SCIE CAS CSCD 2017年第1期37-40,共4页
We present the construction of quantum error-locating(QEL) codes based on classical error-locating(EL)codes. Similar to classical EL codes, QEL codes lie midway between quantum error-correcting codes and quantum error... We present the construction of quantum error-locating(QEL) codes based on classical error-locating(EL)codes. Similar to classical EL codes, QEL codes lie midway between quantum error-correcting codes and quantum errordetecting codes. Then QEL codes can locate qubit errors within one sub-block of the received qubit symbols but do not need to determine the exact locations of the erroneous qubits. We show that, an e-error-locating code derived from an arbitrary binary cyclic code with generator polynomial g(x), can lead to a QEL code with e error-locating abilities, only if g(x) does not contain the(1 + x)-factor. 展开更多
关键词 quantum error-correcting code error-locating code cyclic code
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A Novel Deterministic Quantum Communication Scheme Using Stabilizer Quantum Code 认领 引用 被引量:3
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作者 GUO Ying CHEN Zhi-Gang +1 位作者 HUANG Da-Zu ZENG Gui-Hua 《Communications in Theoretical Physics》 SCIE CAS 2008年第1期93-99,共7页
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
关键词 quantum key distribution quantum error-correction code quantum information
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Encoding entanglement-assisted quantum stabilizer codes 认领 引用 被引量:5
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作者 Wang Yun-Jiang Bai Bao-Ming +2 位作者 Li Zhuo Peng Jin-Ye Xiao He-Ling 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第2期88-93,共6页
We address the problem of encoding entanglement-assisted (EA) quantum error-correcting codes (QECCs) and of the corresponding complexity. We present an iterative algorithm from which a quantum circuit composed of ... We address the problem of encoding entanglement-assisted (EA) quantum error-correcting codes (QECCs) and of the corresponding complexity. We present an iterative algorithm from which a quantum circuit composed of CNOT, H, and S gates can be derived directly with complexity O(n2) to encode the qubits being sent. Moreover, we derive the number of each gate consumed in our algorithm according to which we can design EA QECCs with low encoding complexity. Another advantage brought by our algorithm is the easiness and efficiency of programming on classical computers. 展开更多
关键词 quantum error correction entanglement-assisted quantum stabilizer codes encodingcomplexity
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Constructing Non-binary Asymmetric Quantum Codes via Graphs 认领 引用 被引量:3
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作者 马智 冷日光 +1 位作者 魏正超 钟淑琴 《China Communications》 SCIE CSCD 2013年第2期33-41,共9页
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
关键词 asymmetric quantum codes quantum MDS codes graph construction
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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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Jointly-check iterative decoding algorithm for quantum sparse graph codes 认领 引用 被引量:2
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作者 邵军虎 白宝明 +1 位作者 林伟 周林 《Chinese Physics B》 SCIE EI CAS 2010年第8期116-122,共7页
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
关键词 quantum error correction sparse graph code iterative decoding belief-propagation algorithm
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Degenerate asymmetric quantum concatenated codes for correcting biased quantum errors 认领 引用
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作者 Ji-Hao Fan Jun Li +1 位作者 Han-Wu Chen Wen-Jie Liu 《Chinese Physics B》 SCIE EI CAS CSCD 2021年第12期206-213,共8页
In most practical quantum mechanical systems,quantum noise due to decoherence is highly biased towards dephasing.The quantum state suffers from phase flip noise much more seriously than from the bit flip noise.In this... In most practical quantum mechanical systems,quantum noise due to decoherence is highly biased towards dephasing.The quantum state suffers from phase flip noise much more seriously than from the bit flip noise.In this work,we construct new families of asymmetric quantum concatenated codes(AQCCs)to deal with such biased quantum noise.Our construction is based on a novel concatenation scheme for constructing AQCCs with large asymmetries,in which classical tensor product codes and concatenated codes are utilized to correct phase flip noise and bit flip noise,respectively.We generalize the original concatenation scheme to a more general case for better correcting degenerate errors.Moreover,we focus on constructing nonbinary AQCCs that are highly degenerate.Compared to previous literatures,AQCCs constructed in this paper show much better parameter performance than existed ones.Furthermore,we design the specific encoding circuit of the AQCCs.It is shown that our codes can be encoded more efficiently than standard quantum codes. 展开更多
关键词 asymmetric quantum codes concatenated code quantum channel degenerate code
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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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