npj Quantum Information最新文献

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Characterizing quantum codes via the coefficients in Knill-Laflamme conditions 利用Knill-Laflamme条件下的系数表征量子码
IF 7.6 1区 物理与天体物理
npj Quantum Information Pub Date : 2025-12-12 DOI: 10.1038/s41534-025-01155-1
Mengxin Du, Chao Zhang, Yiu Tung Poon, Bei Zeng
{"title":"Characterizing quantum codes via the coefficients in Knill-Laflamme conditions","authors":"Mengxin Du, Chao Zhang, Yiu Tung Poon, Bei Zeng","doi":"10.1038/s41534-025-01155-1","DOIUrl":"https://doi.org/10.1038/s41534-025-01155-1","url":null,"abstract":"Quantum error correction (QEC) is essential for protecting quantum information against noise, yet understanding the structure of the Knill-Laflamme (KL) coefficients (left{{lambda }_{ij}right}) from the condition (P{E}_{i}^{dagger }{E}_{j}P={lambda }_{ij}P) remains challenging, particularly for nonadditive codes. In this work, we introduce the signature vector (overrightarrow{lambda }(P)), composed of the off-diagonal KL coefficients (left{{lambda }_{ij}right}), where each coefficient corresponds to equivalence classes of errors counted only once. We define its Euclidean norm λ*(P) as a scalar measure representing the total strength of error correlations within the code subspace defined by the projector P. We parameterize P on a Stiefel manifold and formulate an optimization problem based on the KL conditions to systematically explore possible values of λ*. Moreover, we show that, for ((n, K, d)) codes, λ* is invariant under local unitary transformations. Applying our approach to the ((6, 2, 3)) quantum code, we find that ({lambda }_{min }^{* }=sqrt{0.6}) and ({lambda }_{max }^{* }=1), with λ* = 1 corresponding to a known degenerate stabilizer code. We construct continuous families of new nonadditive codes parameterized by vectors in ({{mathbb{R}}}^{5}), with λ* varying over the interval ([sqrt{0.6},1]). For the ((7, 2, 3)) code, we identify ({lambda }_{min }^{* }=0) (corresponding to the non-degenerate Steane code) and ({lambda }_{max }^{* }=sqrt{7}) (corresponding to the permutation-invariant code by Pollatsek and Ruskai), and we demonstrate continuous paths connecting these extremes via cyclic codes characterized solely by λ*. Our findings provide new insights into the structure of quantum codes, advance the theoretical foundations of QEC, and open new avenues for investigating intricate relationships between code subspaces and error correlations.","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"112 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2025-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145746789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The origins of noise in the Zeeman splitting of spin qubits in natural-silicon devices 天然硅器件中自旋量子位的塞曼分裂中噪音的来源
IF 7.6 1区 物理与天体物理
npj Quantum Information Pub Date : 2025-12-09 DOI: 10.1038/s41534-025-01150-6
Juan S. Rojas-Arias, Yohei Kojima, Kenta Takeda, Peter Stano, Takashi Nakajima, Jun Yoneda, Akito Noiri, Takashi Kobayashi, Daniel Loss, Seigo Tarucha
{"title":"The origins of noise in the Zeeman splitting of spin qubits in natural-silicon devices","authors":"Juan S. Rojas-Arias, Yohei Kojima, Kenta Takeda, Peter Stano, Takashi Nakajima, Jun Yoneda, Akito Noiri, Takashi Kobayashi, Daniel Loss, Seigo Tarucha","doi":"10.1038/s41534-025-01150-6","DOIUrl":"https://doi.org/10.1038/s41534-025-01150-6","url":null,"abstract":"We measure and analyze noise-induced energy-fluctuations of spin qubits defined in quantum dots made of isotopically natural silicon. Combining Ramsey, time-correlation of single-shot measurements, and CPMG experiments, we cover the qubit noise power spectrum over a frequency range of nine orders of magnitude without any gaps. We find that the low-frequency noise spectrum is similar across three different devices suggesting that it is dominated by the hyperfine coupling to nuclei. The effects of charge noise are smaller, but not negligible, and are device dependent as confirmed from the noise cross-correlations. We also observe differences to spectra reported in GaAs [Phys. Rev. Lett. 118, 177702 (2017), Phys. Rev. Lett. 101, 236803 (2008)], which we attribute to the presence of the valley degree of freedom in silicon. Finally, we observe ({T}_{2}^{* }) to increase upon increasing the external magnetic field, which we speculate is due to the increasing field gradient of the micromagnet suppressing nuclear spin diffusion.","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"27 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2025-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145705088","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Room-temperature hybrid 2D-3D quantum spin system for enhanced magnetic sensing and many-body dynamics 用于增强磁传感和多体动力学的室温混合2D-3D量子自旋系统
IF 7.6 1区 物理与天体物理
npj Quantum Information Pub Date : 2025-12-06 DOI: 10.1038/s41534-025-01152-4
Haoyu Sun, Pei Yu, Xu Zhou, Xiangyu Ye, Mengqi Wang, Zhaoxin Liu, Yuhang Guo, Wenzhao Liu, You Huang, Pengfei Wang, Fazhan Shi, Kangwei Xia, and Ya Wang
{"title":"Room-temperature hybrid 2D-3D quantum spin system for enhanced magnetic sensing and many-body dynamics","authors":"Haoyu Sun, Pei Yu, Xu Zhou, Xiangyu Ye, Mengqi Wang, Zhaoxin Liu, Yuhang Guo, Wenzhao Liu, You Huang, Pengfei Wang, Fazhan Shi, Kangwei Xia, and Ya Wang","doi":"10.1038/s41534-025-01152-4","DOIUrl":"https://doi.org/10.1038/s41534-025-01152-4","url":null,"abstract":"Advances in hybrid quantum systems and their precise control are pivotal for developing advanced quantum technologies. Two-dimensional (2D) materials with optically accessible spin defects have emerged as a promising platform for building integrated quantum spin systems due to their exceptional flexibility and scalability. However, experimentally realizing such systems and demonstrating their superiority remains challenging. Here, we present a hybrid spin system operating under ambient conditions, integrating boron vacancy ( <jats:inline-formula> <jats:alternatives> <jats:tex-math>$${{rm{V}}}_{{rm{B}}}^{-}$$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msubsup> <mml:mrow> <mml:mi>V</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>B</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> </jats:alternatives> </jats:inline-formula> ) spins in 2D hexagonal boron nitride flakes with a single nitrogen vacancy (NV) center in 3D single-crystal diamonds. This combined system achieves full controllability and exhibits enhanced performance for nanoscale magnetic sensing, including an improved dynamic range. Moreover, we investigate the rich many-body spin dynamics within the hybrid system, which enables us to estimate the concentration of <jats:inline-formula> <jats:alternatives> <jats:tex-math>$${{rm{V}}}_{{rm{B}}}^{-}$$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msubsup> <mml:mrow> <mml:mi>V</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>B</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> </jats:alternatives> </jats:inline-formula> spins. This work provides a critical foundation for advancing the development of 2D-3D integrated quantum spin systems.","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"21 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2025-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145680172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fault-tolerant operation and materials science with neutral atom logical qubits 中性原子逻辑量子比特的容错操作与材料科学
IF 7.6 1区 物理与天体物理
npj Quantum Information Pub Date : 2025-12-05 DOI: 10.1038/s41534-025-01095-w
Woo Chang Chung, Daniel C. Cole, Pranav Gokhale, Eric B. Jones, Kevin W. Kuper, David Mason, Victory Omole, Alexander G. Radnaev, Rich Rines, Mariesa H. Teo, Matt J. Bedalov, Matt Blakely, Peter D. Buttler, Caitlin Carnahan, Frederic T. Chong, Palash Goiporia, Bettina Heim, Garrett T. Hickman, Ryan A. Jones, Pradnya Khalate, Jin-Sung Kim, Martin T. Lichtman, Stephanie Lee, Nathan A. Neff-Mallon, Thomas W. Noel, Mark Saffman, Efrat Shabtai, Bharath Thotakura, Teague Tomesh, Angela K. Tucker
{"title":"Fault-tolerant operation and materials science with neutral atom logical qubits","authors":"Woo Chang Chung, Daniel C. Cole, Pranav Gokhale, Eric B. Jones, Kevin W. Kuper, David Mason, Victory Omole, Alexander G. Radnaev, Rich Rines, Mariesa H. Teo, Matt J. Bedalov, Matt Blakely, Peter D. Buttler, Caitlin Carnahan, Frederic T. Chong, Palash Goiporia, Bettina Heim, Garrett T. Hickman, Ryan A. Jones, Pradnya Khalate, Jin-Sung Kim, Martin T. Lichtman, Stephanie Lee, Nathan A. Neff-Mallon, Thomas W. Noel, Mark Saffman, Efrat Shabtai, Bharath Thotakura, Teague Tomesh, Angela K. Tucker","doi":"10.1038/s41534-025-01095-w","DOIUrl":"https://doi.org/10.1038/s41534-025-01095-w","url":null,"abstract":"We report on the fault-tolerant operation of logical qubits on a neutral atom quantum computer, with logical performance surpassing physical performance for multiple circuits including Bell state preparation (12x error reduction), random circuits (15x), and a prototype Anderson Impurity Model ground state solver for materials science applications (up to 6x, non-fault-tolerantly). The logical qubits are implemented via the [[4, 2, 2]] code (C <jats:sub>4</jats:sub> ). Our work constitutes the first complete realization of the benchmarking protocol proposed by <jats:italic>Gottesman 2016</jats:italic> demonstrating results consistent with fault tolerance. In light of recent advances on applying concatenated C <jats:sub>4</jats:sub> /C <jats:sub>6</jats:sub> detection codes to achieve error correction with high code rates and thresholds, our work can be regarded as a building block towards a practical scheme for fault tolerant quantum computation. Our demonstration of a materials science application with logical qubits particularly demonstrates the immediate value of these techniques on current experiments.","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"35 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2025-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145680055","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Provable super-exponential quantum advantage for learning secrets in Mastermind 可证明的超指数量子优势学习秘密的策划者
IF 7.6 1区 物理与天体物理
npj Quantum Information Pub Date : 2025-12-05 DOI: 10.1038/s41534-025-01148-0
Yongzhen Xu, Jingquan Luo, Lvzhou Li
{"title":"Provable super-exponential quantum advantage for learning secrets in Mastermind","authors":"Yongzhen Xu, Jingquan Luo, Lvzhou Li","doi":"10.1038/s41534-025-01148-0","DOIUrl":"https://doi.org/10.1038/s41534-025-01148-0","url":null,"abstract":"","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"8 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2025-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145680054","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Efficient Lindblad synthesis for noise model construction 高效Lindblad合成噪声模型构建
IF 7.6 1区 物理与天体物理
npj Quantum Information Pub Date : 2025-12-04 DOI: 10.1038/s41534-025-01139-1
Moein Malekakhlagh, Alireza Seif, Daniel Puzzuoli, Luke C. G. Govia, Ewout van den Berg
{"title":"Efficient Lindblad synthesis for noise model construction","authors":"Moein Malekakhlagh, Alireza Seif, Daniel Puzzuoli, Luke C. G. Govia, Ewout van den Berg","doi":"10.1038/s41534-025-01139-1","DOIUrl":"https://doi.org/10.1038/s41534-025-01139-1","url":null,"abstract":"","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"5 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2025-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145680173","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Tracking spin qubit frequency variations over 912 days 跟踪912天内自旋量子比特频率的变化
IF 7.6 1区 物理与天体物理
npj Quantum Information Pub Date : 2025-12-03 DOI: 10.1038/s41534-025-01134-6
Kenji Capannelli, Brennan Undseth, Irene Fernández de Fuentes, Eline Raymenants, Florian K. Unseld, Oriol Pietx-Casas, Stephan G. J. Philips, Mateusz T. Mądzik, Sergey V. Amitonov, Larysa Tryputen, Giordano Scappucci, Lieven M. K. Vandersypen
{"title":"Tracking spin qubit frequency variations over 912 days","authors":"Kenji Capannelli, Brennan Undseth, Irene Fernández de Fuentes, Eline Raymenants, Florian K. Unseld, Oriol Pietx-Casas, Stephan G. J. Philips, Mateusz T. Mądzik, Sergey V. Amitonov, Larysa Tryputen, Giordano Scappucci, Lieven M. K. Vandersypen","doi":"10.1038/s41534-025-01134-6","DOIUrl":"https://doi.org/10.1038/s41534-025-01134-6","url":null,"abstract":"Solid-state qubits are sensitive to their microscopic environment, causing the qubit properties to fluctuate on a wide range of timescales. The sub-Hz end of the spectrum is usually dealt with by repeated background calibrations, which bring considerable overhead. It is thus important to characterize and understand the low-frequency variations of the relevant qubit characteristics. In this study, we investigate the stability of spin qubit frequencies in the Si/SiGe quantum dot platform. We find that the calibrated qubit frequencies of a six-qubit device vary by up to ±100 MHz while performing a variety of experiments over a span of 912 days. These variations are sensitive to the precise voltage settings of the gate electrodes, however when these are kept constant to within 15 <jats:italic>µ</jats:italic> V, the qubit frequencies vary by less than ±7 MHz over periods up to 36 days. During overnight scans, the qubit frequencies of ten qubits across two different devices show a standard deviation below 200 kHz within a 1-hour time window. The qubit frequency noise spectral density shows roughly a 1 <jats:italic>/f</jats:italic> trend above 10 <jats:sup>−4</jats:sup> Hz and, strikingly, a steeper trend at even lower frequencies.","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"365 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2025-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145664768","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
High-resolution and wide-frequency-range magnetic spectroscopy with solid-state spin ensembles 高分辨率和宽频率范围的磁性光谱与固态自旋合奏
IF 7.6 1区 物理与天体物理
npj Quantum Information Pub Date : 2025-12-03 DOI: 10.1038/s41534-025-01137-3
Zechuan Yin, Justin J. Welter, Connor A. Hart, Paul V. Petruzzi, Ronald L. Walsworth
{"title":"High-resolution and wide-frequency-range magnetic spectroscopy with solid-state spin ensembles","authors":"Zechuan Yin, Justin J. Welter, Connor A. Hart, Paul V. Petruzzi, Ronald L. Walsworth","doi":"10.1038/s41534-025-01137-3","DOIUrl":"https://doi.org/10.1038/s41534-025-01137-3","url":null,"abstract":"","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"2017 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2025-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145664963","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Modular architectures and entanglement schemes for error-corrected distributed quantum computation 纠错分布式量子计算的模块化体系结构和纠缠方案
IF 7.6 1区 物理与天体物理
npj Quantum Information Pub Date : 2025-12-02 DOI: 10.1038/s41534-025-01146-2
Siddhant Singh, Fenglei Gu, Sébastian de Bone, Eduardo Villaseñor, David Elkouss, Johannes Borregaard
{"title":"Modular architectures and entanglement schemes for error-corrected distributed quantum computation","authors":"Siddhant Singh, Fenglei Gu, Sébastian de Bone, Eduardo Villaseñor, David Elkouss, Johannes Borregaard","doi":"10.1038/s41534-025-01146-2","DOIUrl":"https://doi.org/10.1038/s41534-025-01146-2","url":null,"abstract":"Connecting multiple smaller qubit modules by generating high-fidelity entanglement is a promising path for scaling quantum computing hardware. The performance of such a modular quantum computer depends on the quality and rate of entanglement generation. However, identifying optimal architectures and entanglement generation protocols remains an open question. How can modular quantum architectures be designed to achieve fault tolerance while requiring only feasible entanglement rates and hardware? Focusing on solid-state quantum hardware, we investigate the threshold and logical failure rate of a fully distributed surface code. We consider both emission-based and scattering-based entanglement schemes between the modules to link the performance to the physical hardware and identify the regime for fault tolerance. We compare architectures with one or two data qubits per module. For some entanglement schemes, thresholds nearing the thresholds of non-distributed implementations (~ 0.4%) appear feasible with future parameters minimizing the performance gap between modular and monolithic quantum processors.","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"5 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2025-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145664771","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Security of practical modulator-free quantum key distribution 实用无调制器量子密钥分发的安全性
IF 7.6 1区 物理与天体物理
npj Quantum Information Pub Date : 2025-11-28 DOI: 10.1038/s41534-025-01131-9
Álvaro Navarrete, Víctor Zapatero, Marcos Curty
{"title":"Security of practical modulator-free quantum key distribution","authors":"Álvaro Navarrete, Víctor Zapatero, Marcos Curty","doi":"10.1038/s41534-025-01131-9","DOIUrl":"https://doi.org/10.1038/s41534-025-01131-9","url":null,"abstract":"Recent advancements in quantum key distribution have led to the development of various modulator-free transmitters. Among their advantages, they offer enhanced security against Trojan-horse attacks. However, practical implementations emit residual pulses that, while not used in the quantum communication, still carry information about Alice’s state preparation process. While the intensity of these pulses is typically attenuated, the extinction ratio of practical intensity modulators is always finite, and therefore it remains crucial to account for the residual information leakage at the security-proof level. In this work, we prove the security of these transmitters in such setting and evaluate their performance. We find that the secret-key rate of the protocol is severely affected when the information leakage is not sufficiently small, which highlights the importance of taking into account this imperfection.","PeriodicalId":19212,"journal":{"name":"npj Quantum Information","volume":"29 1","pages":""},"PeriodicalIF":7.6,"publicationDate":"2025-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145611510","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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