Using the graph method proposed by Schlingemann and Werner, this paper introduces a technique to construct nonbinary quantum cyclic codes and provides a specific example. We also construct the quantum codes [[8, 2, 4]...Using the graph method proposed by Schlingemann and Werner, this paper introduces a technique to construct nonbinary quantum cyclic codes and provides a specific example. We also construct the quantum codes [[8, 2, 4]]p and [[n, n - 2, 2]]p for all odd primes p by the graph method.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
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
The dual-containing (or self-orthogonal) formalism of Calderbank-Shor-Steane (CSS) codes provides a universal connection between a classical linear code and a Quantum Error-Correcting Code (QECC). We propose a novel c...The dual-containing (or self-orthogonal) formalism of Calderbank-Shor-Steane (CSS) codes provides a universal connection between a classical linear code and a Quantum Error-Correcting Code (QECC). We propose a novel class of quantum Low Density Parity Check (LDPC) codes constructed from cyclic classes of lines in Euclidean Geometry (EG). The corresponding constructed parity check matrix has quasi-cyclic structure that can be encoded flexibility, and satisfies the requirement of dual-containing quantum code. Taking the advantage of quasi-cyclic structure, we use a structured approach to construct Generalized Parity Check Matrix (GPCM). This new class of quantum codes has higher code rate, more sparse check matrix, and exactly one four-cycle in each pair of two rows. Ex-perimental results show that the proposed quantum codes, such as EG(2,q)II-QECC, EG(3,q)II-QECC, have better performance than that of other methods based on EG, over the depolarizing channel and decoded with iterative decoding based on the sum-product decoding algorithm.展开更多
In this paper,we develop a novel hybrid automatic-repeat-request(ARQ)protocol for the quantum communication system using quantum stabilizer codes.The quantum information is encoded by stabilizer codes to against the c...In this paper,we develop a novel hybrid automatic-repeat-request(ARQ)protocol for the quantum communication system using quantum stabilizer codes.The quantum information is encoded by stabilizer codes to against the channel noise.The twophoton entangled state is prepared for codeword secure transmission.Hybrid ARQ protocol rules the recognition and retransmission of error codewords.In this protocol,the property of quantum entangled state ensures the security of information,the theory of hybrid ARQ system improves the reliability of transmission,the theory of quantum stabilizer codes corrects the flipping errors of codewords.Finally,we verify the security and throughput efficiency of this protocol.展开更多
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
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
Quantum error correction, a technique that relies on the principle of redundancy to encode logical information into additional qubits to better protect the system from noise, is necessary to design a viable quantum co...Quantum error correction, a technique that relies on the principle of redundancy to encode logical information into additional qubits to better protect the system from noise, is necessary to design a viable quantum computer. For this new topological stabilizer code-XYZ^(2) code defined on the cellular lattice, it is implemented on a hexagonal lattice of qubits and it encodes the logical qubits with the help of stabilizer measurements of weight six and weight two. However topological stabilizer codes in cellular lattice quantum systems suffer from the detrimental effects of noise due to interaction with the environment. Several decoding approaches have been proposed to address this problem. Here, we propose the use of a state-attention based reinforcement learning decoder to decode XYZ^(2) codes, which enables the decoder to more accurately focus on the information related to the current decoding position, and the error correction accuracy of our reinforcement learning decoder model under the optimisation conditions can reach 83.27% under the depolarizing noise model, and we have measured thresholds of 0.18856 and 0.19043 for XYZ^(2) codes at code spacing of 3–7 and 7–11, respectively. our study provides directions and ideas for applications of decoding schemes combining reinforcement learning attention mechanisms to other topological quantum error-correcting codes.展开更多
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
The paper analyzes the basic principles of stabilizer codes, focusing on how to construct stabilizer codes for achieving the continuous-variable quantum error correction. Stabilizer codes can be used in the reconcilia...The paper analyzes the basic principles of stabilizer codes, focusing on how to construct stabilizer codes for achieving the continuous-variable quantum error correction. Stabilizer codes can be used in the reconciliation of continuous-variable quantum key distribution system. The construction method of stabilizer codes is very important and it can be turned into finding the check matrix for stabilizer codes. In this paper, a new algorithm called region elimination algorithm for finding the check matrix of stabilizer codes was presented which can seek the voluntary check matrix for continu-ous-variable stabilizer codes within 8 bit code length quickly and effectively, and it was simulated by Visual C++. The algorithm is mainly realized by initializing search region, reducing the search region and then keeping searching till finding all the commuting generators. The finding of check matrix of stabilizer codes lays important foundations for the further development of stabilizer codes in the con-tinuous-variable quantum key distribution.展开更多
We study mathematical,physical and computational aspects of the stabilizer formalism arising in quantum information and quantum computation.The measurement process of Pauli observables with its algorithm is given.It i...We study mathematical,physical and computational aspects of the stabilizer formalism arising in quantum information and quantum computation.The measurement process of Pauli observables with its algorithm is given.It is shown that to detect genuine entanglement we need a full set of stabilizer generators and the stabilizer witness is coarser than the GHZ(Greenberger-Horne-Zeilinger)witness.We discuss stabilizer codes and construct a stabilizer code from a given linear code.We also discuss quantum error correction,error recovery criteria and syndrome extraction.The symplectic structure of the stabilizer formalism is established and it is shown that any stabilizer code is unitarily equivalent to a trivial code.The structure of graph codes as stabilizer codes is identified by obtaining the respective stabilizer generators.The distance of embeddable stabilizer codes in lattices is obtained.We discuss the Knill-Gottesman theorem,tableau representation and frame representation.The runtime of simulating stabilizer gates is obtained by applying stabilizer matrices.Furthermore,an algorithm for updating global phases is given.Resolution of quantum channels into stabilizer channels is shown.We discuss capacity achieving codes to obtain the capacity of the quantum erasure channel.Finally,we discuss the shadow tomography problem and an algorithm for constructing classical shadow is given.展开更多
In this paper,the quantum error-correcting codes are generalized to the inhomogenous quantumstate space Cq1 Cq2 ··· Cqn,where qi(1 i n) are arbitrary positive integers.By attaching an abelian group Ai ...In this paper,the quantum error-correcting codes are generalized to the inhomogenous quantumstate space Cq1 Cq2 ··· Cqn,where qi(1 i n) are arbitrary positive integers.By attaching an abelian group Ai of order qi to the space Cqi(1 i n),we present the stabilizer construction of such inhomogenous quantum codes,called additive quantum codes,in term of the character theory of the abelian group A = A1⊕A2⊕···⊕An.As usual case,such construction opens a way to get inhomogenous quantum codes from the classical mixed linear codes.We also present Singleton bound for inhomogenous additive quantum codes and show several quantum codes to meet such bound by using classical mixed algebraic-geometric codes.展开更多
Multi-party quantum communication has gradually attracted widespread attention.To realize the perfect transmission of quantum states among multiple participants,a novel multi-party controlled cyclic remote preparation...Multi-party quantum communication has gradually attracted widespread attention.To realize the perfect transmission of quantum states among multiple participants,a novel multi-party controlled cyclic remote preparation protocol for arbitrary single-qubit states with three senders is proposed.With the permission of one controller,each sender can transmit an arbitrary singlequbit state to its neighbor.In addition,we give a universal protocol for multi-party controlled cyclic remote preparation of arbitrary single-qubit states in the case of multiple senders,which can realize deterministic cyclic preparation of multiple quantum states in one direction.The scheme shows that the communication task can be successfully achieved only if all senders cooperate with the controller,and there is no need for the senders to employ information splitting and additional operations before performing measurements.Finally,we discuss the cyclic remote preparation protocol with three senders under five types of noisy environment,and the closeness between the output state and original state is measured by calculating fidelity.展开更多
This paper discusses optimal binary codes and pure binary quantum codes created using Steane construction. First, a local search algorithm for a special subclass of quasi-cyclic codes is proposed, then five binary qua...This paper discusses optimal binary codes and pure binary quantum codes created using Steane construction. First, a local search algorithm for a special subclass of quasi-cyclic codes is proposed, then five binary quasi-cyclic codes are built. Second, three classical construction methods are generalized for new codes from old such that they are suitable for constructing binary self-orthogonal codes, and 62 binary codes and six subcode chains of obtained self-orthogonal codes are designed. Third, six pure binary quantum codes are constructed from the code pairs obtained through Steane construction. There are 66 good binary codes that include 12 optimal linear codes, 45 known optimal linear codes, and nine known optimal self-orthogonal codes. The six pure binary quantum codes all achieve the performance of their additive counterparts constructed by quaternary construction and thus are known optimal codes.展开更多
基金This work was supported by the National Natural Science Foundation of China(Grant No．60373059)the National Research Foundation for the Doctoral Program of Higher Education of China(Grant No．20040013007)the ISN Open Foundation, and the National Laboratory for Moderm Communications Science Foun-dation of China (Grant No.51436020103DZ4001).
文摘Using the graph method proposed by Schlingemann and Werner, this paper introduces a technique to construct nonbinary quantum cyclic codes and provides a specific example. We also construct the quantum codes [[8, 2, 4]]p and [[n, n - 2, 2]]p for all odd primes p by the graph method.
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supported by the National Basic Research Program of China (Grant No.2010CB328300)the National Natural Science Foundation of China (Grant Nos.60972046 and 60902030)+4 种基金the Program for Changjiang Scholars and Innovative Research Team in University (Grant No.IRT0852)the Natural Science Foundation of Shaanxi Province (Grant No.2010JQ8025)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No.20100203120004)the 111 Program (Grant No.B08038)the China Scholarship Council (Grant No.[2008]3019)
文摘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.
基金Supported by the National Natural Science Foundation ofChina (No. 61071145,41074090)the Specialized Research Fund for the Doctoral Program of Higher Education (200802880014)
文摘The dual-containing (or self-orthogonal) formalism of Calderbank-Shor-Steane (CSS) codes provides a universal connection between a classical linear code and a Quantum Error-Correcting Code (QECC). We propose a novel class of quantum Low Density Parity Check (LDPC) codes constructed from cyclic classes of lines in Euclidean Geometry (EG). The corresponding constructed parity check matrix has quasi-cyclic structure that can be encoded flexibility, and satisfies the requirement of dual-containing quantum code. Taking the advantage of quasi-cyclic structure, we use a structured approach to construct Generalized Parity Check Matrix (GPCM). This new class of quantum codes has higher code rate, more sparse check matrix, and exactly one four-cycle in each pair of two rows. Ex-perimental results show that the proposed quantum codes, such as EG(2,q)II-QECC, EG(3,q)II-QECC, have better performance than that of other methods based on EG, over the depolarizing channel and decoded with iterative decoding based on the sum-product decoding algorithm.
基金The work is supported by was supported by the Shandong Province Higher Educational Science and Technology Program(Grant No.J18KZ012)the National Natural Science Foundation of China(Grant No.11975132,61772295)the Shandong Provincial Natural Science Foundation,China(Grant No.ZR2019YQ01).
文摘In this paper,we develop a novel hybrid automatic-repeat-request(ARQ)protocol for the quantum communication system using quantum stabilizer codes.The quantum information is encoded by stabilizer codes to against the channel noise.The twophoton entangled state is prepared for codeword secure transmission.Hybrid ARQ protocol rules the recognition and retransmission of error codewords.In this protocol,the property of quantum entangled state ensures the security of information,the theory of hybrid ARQ system improves the reliability of transmission,the theory of quantum stabilizer codes corrects the flipping errors of codewords.Finally,we verify the security and throughput efficiency of this protocol.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61671087 and 61962009)the Fundamental Research Funds for the Central Universities,China(Grant No.2019XD-A02)+1 种基金Huawei Technologies Co.Ltd(Grant No.YBN2020085019)the Open Foundation of Guizhou Provincial Key Laboratory of Public Big Data(Grant No.2018BDKFJJ018)。
文摘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.
基金Supported by the National Natural Science Foundation of China under Grant No.61170321the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20110092110024the Scientific Research Innovation Plan for College Graduates of Jiangsu Province under Grant No.CXZZ13 0105
文摘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.
基金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)。
文摘Quantum error correction, a technique that relies on the principle of redundancy to encode logical information into additional qubits to better protect the system from noise, is necessary to design a viable quantum computer. For this new topological stabilizer code-XYZ^(2) code defined on the cellular lattice, it is implemented on a hexagonal lattice of qubits and it encodes the logical qubits with the help of stabilizer measurements of weight six and weight two. However topological stabilizer codes in cellular lattice quantum systems suffer from the detrimental effects of noise due to interaction with the environment. Several decoding approaches have been proposed to address this problem. Here, we propose the use of a state-attention based reinforcement learning decoder to decode XYZ^(2) codes, which enables the decoder to more accurately focus on the information related to the current decoding position, and the error correction accuracy of our reinforcement learning decoder model under the optimisation conditions can reach 83.27% under the depolarizing noise model, and we have measured thresholds of 0.18856 and 0.19043 for XYZ^(2) codes at code spacing of 3–7 and 7–11, respectively. our study provides directions and ideas for applications of decoding schemes combining reinforcement learning attention mechanisms to other topological quantum error-correcting codes.
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Supported by the Science and Technology Foundation of the Education Department of Fujian Province(No.JA08001)
文摘The paper analyzes the basic principles of stabilizer codes, focusing on how to construct stabilizer codes for achieving the continuous-variable quantum error correction. Stabilizer codes can be used in the reconciliation of continuous-variable quantum key distribution system. The construction method of stabilizer codes is very important and it can be turned into finding the check matrix for stabilizer codes. In this paper, a new algorithm called region elimination algorithm for finding the check matrix of stabilizer codes was presented which can seek the voluntary check matrix for continu-ous-variable stabilizer codes within 8 bit code length quickly and effectively, and it was simulated by Visual C++. The algorithm is mainly realized by initializing search region, reducing the search region and then keeping searching till finding all the commuting generators. The finding of check matrix of stabilizer codes lays important foundations for the further development of stabilizer codes in the con-tinuous-variable quantum key distribution.
文摘We study mathematical,physical and computational aspects of the stabilizer formalism arising in quantum information and quantum computation.The measurement process of Pauli observables with its algorithm is given.It is shown that to detect genuine entanglement we need a full set of stabilizer generators and the stabilizer witness is coarser than the GHZ(Greenberger-Horne-Zeilinger)witness.We discuss stabilizer codes and construct a stabilizer code from a given linear code.We also discuss quantum error correction,error recovery criteria and syndrome extraction.The symplectic structure of the stabilizer formalism is established and it is shown that any stabilizer code is unitarily equivalent to a trivial code.The structure of graph codes as stabilizer codes is identified by obtaining the respective stabilizer generators.The distance of embeddable stabilizer codes in lattices is obtained.We discuss the Knill-Gottesman theorem,tableau representation and frame representation.The runtime of simulating stabilizer gates is obtained by applying stabilizer matrices.Furthermore,an algorithm for updating global phases is given.Resolution of quantum channels into stabilizer channels is shown.We discuss capacity achieving codes to obtain the capacity of the quantum erasure channel.Finally,we discuss the shadow tomography problem and an algorithm for constructing classical shadow is given.
基金supported by National Natural Science Foundation of China (Grant No.10990011)
文摘In this paper,the quantum error-correcting codes are generalized to the inhomogenous quantumstate space Cq1 Cq2 ··· Cqn,where qi(1 i n) are arbitrary positive integers.By attaching an abelian group Ai of order qi to the space Cqi(1 i n),we present the stabilizer construction of such inhomogenous quantum codes,called additive quantum codes,in term of the character theory of the abelian group A = A1⊕A2⊕···⊕An.As usual case,such construction opens a way to get inhomogenous quantum codes from the classical mixed linear codes.We also present Singleton bound for inhomogenous additive quantum codes and show several quantum codes to meet such bound by using classical mixed algebraic-geometric codes.
基金the National Natural Science Foundation of China(Nos.62172341,62172196,62272208)。
文摘Multi-party quantum communication has gradually attracted widespread attention.To realize the perfect transmission of quantum states among multiple participants,a novel multi-party controlled cyclic remote preparation protocol for arbitrary single-qubit states with three senders is proposed.With the permission of one controller,each sender can transmit an arbitrary singlequbit state to its neighbor.In addition,we give a universal protocol for multi-party controlled cyclic remote preparation of arbitrary single-qubit states in the case of multiple senders,which can realize deterministic cyclic preparation of multiple quantum states in one direction.The scheme shows that the communication task can be successfully achieved only if all senders cooperate with the controller,and there is no need for the senders to employ information splitting and additional operations before performing measurements.Finally,we discuss the cyclic remote preparation protocol with three senders under five types of noisy environment,and the closeness between the output state and original state is measured by calculating fidelity.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant No. 11071255） and Science Foundation for young teachers in Science College, Air Force Engineering University. The authors are very grateful to the anonymous referees and the editors for their valuable comments and suggestions, which help to improve the manuscript significantly.
文摘This paper discusses optimal binary codes and pure binary quantum codes created using Steane construction. First, a local search algorithm for a special subclass of quasi-cyclic codes is proposed, then five binary quasi-cyclic codes are built. Second, three classical construction methods are generalized for new codes from old such that they are suitable for constructing binary self-orthogonal codes, and 62 binary codes and six subcode chains of obtained self-orthogonal codes are designed. Third, six pure binary quantum codes are constructed from the code pairs obtained through Steane construction. There are 66 good binary codes that include 12 optimal linear codes, 45 known optimal linear codes, and nine known optimal self-orthogonal codes. The six pure binary quantum codes all achieve the performance of their additive counterparts constructed by quaternary construction and thus are known optimal codes.
