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GENERAL

Solving nonlinear Schrödinger equations and parameter discovery via extended mixed-training physics-informed neural networks
WANG Yuduo, CHEN Jiaxin, LI Biao
2025, 74 (16): 160201. doi: 10.7498/aps.74.20250422
Abstract +
In recent years, physics-informed neural networks (PINNs) have provided effcient data-driven methods for solving forward and inverse problems of partial differential equations (PDEs). However, when addressing complex PDEs, PINNs face significant challenges in computational efficiency and accuracy. In this study, we propose the extended mixed-training physics-informed neural networks (X-MTPINNs) as illustrated in the following figure, which effectively enhance the ability to solve nonlinear wave problems by integrating the domain decomposition technique of extended physics-informed neural networks (X-PINNs) in a mixed-training physics-informed neural networks (MTPINNs) framework. Compared with the classical PINNs model, the new model exhibits dual advantages: The first advantage is that the mixed-training framework significantly improves convergence properties by optimizing the handling mechanism of initial and boundary conditions, achieving higher fitting accuracy for nonlinear wave solutions while reducing the computation time by approximately 40%. And the second advantage is that the domain decomposition technique from X-PINNs strengthens the ability of the model to represent complex dynamical behaviors. Numerical experiments based on the nonlinear Schrödinger equation (NLSE) demonstrate that X-MTPINNs excel perform well in solving two bright solitons, third-order rogue waves, and parameter inversion tasks, with prediction accuracy improved by one to two orders of magnitude over traditional PINN. For inverse problems, the X-MTPINNs algorithm accurately identifies unknown parameters in the NLSE under noise-free, 2%, and 5% noisy conditions, solving the complete failure problem of NSLE parameter identification in classical PINNs in the studied scenario, thus demonstrating strong robustness.

SPECIAL TOPIC—Quantum information processing

Research status and prospects of quantum secret sharing
YIN Hualei, SHEN Jianyu, CHEN Nuo, CHEN Zengbing
2025, 74 (16): 160301. doi: 10.7498/aps.74.20250586
Abstract +
Quantum secret sharing (QSS), as a quantum extension of classical secret sharing, uses the basic principles of quantum mechanics to share information safely among multiple parties, providing a new paradigm for information security. As a key foundation for secure multiparty quantum communication and distributed quantum computing, QSS has attracted considerable attention since its emergence. Currently, research in this field includes both classical and quantum scenarios, and continuous progress has been made in both theoretical and experimental aspects. This paper first reviews the current development of QSS for classical information. In this regard, significant and parallel progress has been made in both discrete-variable QSS and continuous-variable QSS. The QSS protocols for sharing classical information, from entangled states to single photons and then to coherent light, have been continuously optimized to better utilize available resources and achieve more efficient implementation under current technological conditions. Meanwhile, round-robin, measurement-device-independent, and other protocols have been steadily improving the security of QSS. Next, one will focus on QSS scheme for quantum secrets, which begins with the symmetry of access structures and introduces basic (k, n) threshold protocols, dynamic schemes that support adaptive agent groups, and symmetric quantum information splitting through entanglement. It further introduces hierarchical quantum secret sharing schemes for asymmetric splitting of quantum information. Considering practical laboratory conditions of quantum states as resources, an overall discussion is conducted on quantum secret sharing with graph states. Afterwards, the design of a continuous-variable scheme for quantum secret sharing is outlined, and entanglement state sharing and quantum teleportation between multiple senders and receivers are introduced. Finally, this review discusses and outlines the future development directions of QSS, thereby inspiring readers to further study and explore the relevant subjects.

SPECIAL TOPIC—Quantum information processing

Research progress of nonlocal quantum entanglement preparation based on quantum multiplexing
LI Tao, WANG Xueqi, XIE Zhihao
2025, 74 (16): 160302. doi: 10.7498/aps.74.20250589
Abstract +
Nonlocal quantum entanglement is a fundamental resource for future quantum networks. However, the efficiency of generating nonlocal entanglement between distant nodes is severely limited by the exponential loss incurred when locally generated entangled states are distributed through lossy quantum channels. This limitation becomes more pronounced in practical scenarios requiring the simultaneous distribution of multiple entangled pairs. Although classical multiplexing approaches, such as spatial, temporal, and frequency multiplexing, can increase the nonlocal entanglement generation rate, they do not improve the single-shot transmission efficiency. In contrast, quantum multiplexing, which can be generated by high-dimensional encoding of single photons, allows for the parallel generation of multiple nonlocal entangled pairs in a single transmission round, thereby enhancing the overall efficiency of nonlocal entanglement generation. Quantum multiplexing thus presents a promising route toward scalable quantum networks. This review introduces the mechanisms of generating nonlocal entanglement through quantum multiplexing, and focuses on two main methods: using high-dimensional single-photon encoding and high-dimensional biphoton entanglement distribution. Then it examines how quantum multiplexing can accelerate the generation of nonlocal quantum logical entanglement. Finally, it briefly explores the potential of quantum multiplexing for building large-scale quantum networks.

GENERAL

Kalman filter based local local oscillator continuous-variable quantum secret sharing
LIAO Qin, FEI Zhuoying, WANG Yijun
2025, 74 (16): 160303. doi: 10.7498/aps.74.20250227
Abstract +
In a practical continuous-variable quantum secret sharing system, the local oscillator transmitted via an insecure channel may be subjected to security threats due to various targeted attacks. To solve this problem, this paper proposes a continuous-variable quantum secret sharing scheme with local intrinsic oscillator, in which the intrinsic oscillator is generated locally at the trusted end without being sent by each user, thus completely plugging the relevant security loopholes. The scheme consists of three stages: preparation, where users generate Gaussian-modulated coherent states and reference signals; measurement, where the dealer performs heterodyne detection by using the local intrinsic oscillator and reference phases; post-processing, which involves parameter estimation, phase compensation, and secure key extraction. On this basis, Kalman filter (KF) is utilized to estimate the minimum mean square error for each reference phase separately, reducing the phase drift estimation error and suppressing the phase measurement noise. Phase compensation methods for scalar KF and vector KF are developed respectively, where scalar KF requires additional block averaging for slow phase drift, while vector KF simultaneously models fast and slow drifts, enabling one-step compensation with minimized estimation errors. The excess noise of the filtered system including modulation noise, phase noise, photon leakage noise, and ADC quantization noise is modeled, with KF reducing phase measurement noise via dynamic gain optimization. Security bound against eavesdroppers and dishonest users is derived. Numerical simulations under practical parameters demonstrate significant improvements: vector KF achieves a maximum transmission distance of 82.6 km (vs. 67.3 km for block averaging) and supports 33 users (vs. 22), with excess noise reduced by 40% at 60 km. The scheme’s robustness is further validated under varying reference signal amplitudes, showing stable performance even at lower levels, minimizing interference with quantum signals. These results highlight that the proposed scheme has significant advantages in terms of maximum transmission distance and maximum number of supported users, and has the potential to build adaptive KF algorithms for dynamic user scenarios and quantum machine learning integration.

SPECIAL TOPIC—Quantum information processing

Recent progress on photon-integrated quantum key distribution and quantum random number generator
YU Jingchun, LU Wenbin, CHEN Bin, DU Yongqiang, XIE Feng, LI Wei, WEI Kejin
2025, 74 (16): 160304. doi: 10.7498/aps.74.20250791
Abstract +
Quantum key distribution (QKD) relies on the fundamental principles of quantum mechanics and can theoretically achieve unconditionally secure communication that is provable by information theory. Quantum random number generators, on the other hand, utilize the inherent randomness of quantum phenomena and are capable of generating a truly random entropy source that is unpredictable, unbiased and unrepeatable. These two technologies are crucial for building highly trustworthy and secure communication systems resistant to quantum attacks. However, their large-scale deployment still faces challenges such as system performance optimization, cost control and scale production.Relying on wafer-level fabrication platforms and micro-nanometer processing, integrated photonics technology integrates the core devices of traditional QKD systems (e.g., light source, modulator, and detector) in a single chip at high density. It significantly improves the miniaturization, operational stability and cost-effectiveness of the system, and enhances the intrinsic security, and becomes a key enabling platform to drive QKD and QRNG from laboratory to engineering applications.In this paper, we systematically review the recent breakthroughs of photonic integrated QKD based on different material platforms (SOI/InP/TFLN/Si3N4) in terms of core metrics, such as transmission distance and key rate, as well as the significant breakthroughs of integrated QRNG in terms of random number generation rate and system integration. Finally, the future development direction of this field is discussed and outlooked from the four dimensions of practical security of QKD systems, on-chip implementation of cutting-edge QKD protocols, practical fully-integrated QKD systems, and synergistic optimization of high performance and high integration of integrated QRNG.

DATA PAPER

Evaluation of the application of large language models in the entire process of battery research and development of a comprehensive database forinorganic solid electrolyte
WU Siyuan, LI Hong
2025, 74 (16): 160701. doi: 10.7498/aps.74.20250572
Abstract +
The emergence of large language models has significantly advanced scientific research. Representative models such as ChatGPT and DeepSeek R1 have brought notable changes to the paradigm of scientific research. While these models are general-purpose, they have demonstrated strong generalization capabilities in the field of batteries, especially in solid-state battery research. In this study, we systematically screen 5309268 articles from key journals up to 2024, and accurately extract 124021 papers related to batteries. Additionally, we comprehensively search through 17559750 patent applications and granted patents from the European Patent Office and the United States Patent and Trademark Office up to 2024, identifying 125716 battery-related patents. Utilizing these extensive literature and patents, we conduct numerous experiments to evaluate the structured output capabilities of knowledge base, contextual learning, instruction adherence, and language models. Through multi-dimensional model evaluations and analyses, the following points are found. First, the model exhibits high accuracy in screening literature on inorganic solid-state electrolytes, equivalent to the level of a doctoral student in the relevant field. Based on 10604 data entries, the model demonstrates good recognition capabilities in identifying literature on in-situ polymerization/solidification technology. However, its understanding accuracy for this emerging technology is slightly lower than that for solid-state electrolytes, requiring further fine-tuning to improve accuracy. Second, through testing with 10604 data entries, the model achieves reliable accuracy in extracting inorganic ionic conductivity data. Third, based on solid-state lithium battery patents from four companies in South Korea and Japan over the past 20 years, this model proves effective in analyzing historical patent trends and conducting comparative analyses. Furthermore, the model-generated personalized literature reports based on the latest publications also show high accuracy. Fourth, by utilizing the iterative strategy of the model, we enable DeepSeek to engage in self-reflection thinking, thereby providing more comprehensive responses. The research results indicate that language models possess strong capabilities in content summarization and trend analysis. However, we also observe that the model may occasionally experience issues with numerical hallucinations. Additionally, while processing a large number of battery-related data, there is still room for optimization in engineering applications. According to the characteristics of the model and the above test results, we utilize the DeepSeek V3-0324 model to extract data on inorganic solid electrolyte materials, including 5970 ionic conductivity entries, 387 diffusion coefficient entries, and 3094 migration barrier entries. Additionally, it includes over 1000 data entries related to chemical, electrochemical, and mechanical properties, covering nearly all physical, chemical, and electrochemical properties related to inorganic solid electrolytes. This also means that the application of large language models in scientific research has shifted from auxiliary research to actively promoting its development. The datasets presented in this paper may be available at the website: https://cmpdc.iphy.ac.cn/literature/SSE.html (DOI: https://doi.org/10.57760/sciencedb.j00213.00172).

GENERAL

Temperature-compensated hollow-core fiber Fabry-Perot strain sensor based on optimized particle swarm optimization-back propagation algorithm
SU Rui, GE Yixian, LIN Yongjie
2025, 74 (16): 160702. doi: 10.7498/aps.74.20250524
Abstract +
Ambient temperature fluctuations often induce measurement errors in fiber-optic Fabry-Perot strain sensors. To effectively compensate for the influence of temperature on measurement accuracy, this study proposes an optimized particle swarm optimization-back propagation (PSO-BP) neural network algorithm. The combined predictive model is applied to the monitoring data of a Fabry-Perot strain sensor based on a single-mode fiber-hollow-core fiber-single-mode fiber (SMF-HCF-SMF) structure. By preprocessing the data collected from the sensor, the temperature values and spectral valley shift data obtained from the fiber-optic Fabry-Perot strain sensor are directly used as input features to establish a temperature-compensated neural network model. Based on the traditional PSO-BP neural network algorithm, an optimization strategy incorporating adaptive adjustment of inertia weights and learning factors is employed to enhance global search capability and local convergence accuracy, thereby enabling effective compensation for temperature-induced effects.Experimental results demonstrate that in the entire temperature measurement range of the sensor, the optimized PSO-BP neural network achieves a mean absolute percentage error (MAPE) of about 1.2% and a root mean square error (RMSE) of about 5.9, significantly outperforming other methods. Comparative analysis with different model architectures reveals that compared with the BP, PSO-BP, RF, and GA-BP models, the optimized PSO-BP model improves MAPE by 57.14%, 45.45%, 73.91%, and 53.85%, respectively, while reducing RMSE by 68.11%, 52.42%, 72.94%, and 63.13%. Moreover, the coefficient of determination (R2) consistently exceeds 0.995 under various temperature conditions, indicating that the model effectively compensates for temperature-induced errors in the sensor under different thermal and strain conditions, and has excellent stability and adaptability.Therefore, the temperature compensation method proposed in this study not only offers a novel approach for improving the measurement accuracy of fiber-optic Fabry-Perot strain sensors, but also provides a valuable reference for studying the temperature compensation in related sensor technologies. Future research may further explore the applicability of this method to other types of sensors, thereby promoting the sustaining development of intelligent sensing technologies.

NUCLEAR PHYSICS

Research on u-d quark stars and their tidal deformaions under new mass scaling
XU Jianfeng, WANG Jingtao, XIA Chengjun
2025, 74 (16): 162101. doi: 10.7498/aps.74.20250535
Abstract +
Strange quark matter (SQM) is considered to be the true ground state of the strong interactions, but recent studies have shown that ordinary quark matter (u-d quark matter, u-d QM) may also be the ground state of the strong interactions. By inserting an attenuation factor of Woods-Saxon potential type into the quark mass scaling, the resulting calculations of equation of state of u-d QM based on equiv-particle model show that the stability window of model parameters for stable u-d QM can be significantly enlarged with proper model parameters, which can be seen in the following figure. In this figure, the red solid and dashed lines represent the curves of $ \sqrt{D} $ versus C with and without attenuation factor, respectively, when the minimum value of the average energy per baryon is set to 930 MeV; the blue solid and dashed lines represent the curves of $ \sqrt{D} $ versus C with and without attenuation factor, respectively, when $ m_\mathrm{u}=0 $. Thereby, the red and blue shaded areas are the absolute stable regions of u-d QM without and with attenuation factor in mass scaling. It is obvious that with the attenuation factor and proper model parameters, the absolute stable region (blue shaded area) for u-d QM can be much larger than that without the attenuation factor (red shaded area). The introduction of the attenuation factor allows the maximum mass of ordinary quark star (u-d quark star, u-d QS) to be larger than twice the solar mass, while the tidal deformability satisfies $ \varLambda_{1.4} \in [70,580] $, which is consistent with the current astronomical observations. Therefore, the pulsars may be essentially the u-d QSs. This result provides a possibility for understanding the nature of pulsars, and it also further deepens the understanding of the strong interactions.

NUCLEAR PHYSICS

Monte Carlo simulations of proton-induced displacement damage in SiGe alloys and SiGe/Si heterostructures
XING Tian, LIU Shuhuan, WANG Xuan, WANG Chao, ZHOU Junye, ZHANG Ximin, CHEN Wei
2025, 74 (16): 162401. doi: 10.7498/aps.74.20250162
Abstract +
SiGe-based electronics have a promising prospect in the field of space exploration due to the controllable bandgap of SiGe alloys and high compatibility with Si technology. However, they may be susceptible to the influence of energetic particles in space radiation environments. In order to explain the potential displacement damage in SiGe-based electronics, Monte Carlo simulations are conducted to investigate the displacement damage in SiGe alloys and SiGe/Si heterostructures induced by 1–1000 MeV protons. The displacement damage in SiGe alloys is studied by the energy spectra and types of proton-induced primary knock-on atoms (PKAs) and the related damage energy distribution, while the displacement damage in SiGe/Si heterostructures is studied by the damage energy distribution caused by forward- and reverse-incident protons. Low-energy protons (1–100 MeV) primarily generate Si PKAs and Ge PKAs in SiGe alloys through Coulomb scattering and elastic collisions, and the corresponding damage energy distribution exhibits a distinct Bragg peak at the end of the proton range. Meanwhile, high-energy protons (300–1000 MeV) cause significant inelastic collisions in SiGe alloys, leading to a series of other PKA types, with the associated damage energy distribution predominantly located in the front of the proton range. In addition, the damage energy in SiGe/Si heterostructures generally decreases as the proton energy increases, and compared with the forward-incident protons, the reverse-incident protons (10 MeV and 100 MeV) cause greater damage energy on the side of Si substrate at the interface, and result in more noticeable fluctuations in damage energy on both sides of the interface, probably leading to severe displacement damage. Besides, Ge content can affect the PKA type, damage energy distribution, and nonionizing energy loss. As for high-energy protons, high Ge content may lead to a great nonionizing energy loss in SiGe alloys, whereas the Ge content has an insignificant effect on the total damage energy of small-size SiGe/Si heterostructures. In summary, this work indicates that the proton-induced displacement damage in SiGe alloys and SiGe/Si heterostructures is greatly dependent on the proton energy, and low-energy protons are prone to generating massive self-recoil atoms, inducing significant displacement damage in small-size SiGe/Si heterostructures, which will provide theoretical basis and reference for studying displacement damage effect and developing radiation hardening techniques of SiGe-based electronics.

NUCLEAR PHYSICS

Control of microwave photon transmissions in microwave quantum networks by elastic scattering
MA Jun, OUYANG Penghui, CHAI Yaqiang, JIANG Qingquan, HE Qing, WEI Lianfu
2025, 74 (16): 162501. doi: 10.7498/aps.74.20250404
Abstract +
Elastic scattering is one of the useful methods to control the transmission behaviors of microwave photons transporting in microwave quantum networks without energy consumption. Therefore, it is of practical significance for developing microwave quantum devices and constructing multi-node microwave quantum networks. The transmission line embedded by a single Josephson junction can be described by different circuit models (series and parallel). In this work, we first theoretically analyze the transmission characteristics of microwave photons scattered by different elastic scattering models described by series or parallel embedding models, generated by a single LC loop or a nonlinear Josephson junction device, respectively. The classical microwave transport theory predicts that the series LC loop and the parallel LC loop lead to different elastic scattering behaviors of microwave photons, i.e. the series LC circuit yields the resonant reflection and the parallel LC circuit leads alternatively to the resonant transmission. Recently, the transport properties of microwave photons scattered by a Josephson junction embedded in a transmission line have been discussed, and the results suggested that the Josephson junction embedded in the transmission line can be described by a series embedding circuit, which implies the resonant reflection. We argue here that if the Josephson junction is embedded in parallel in the transmission line, the elastically scattered microwave photons should be transmitted by resonant transmission. In order to test which of the above two different embedding circuit models yielding the completely different elastic scattering behaviors, is physically correct, we then fabricate such a device, i.e. a single Joseph junction device embedded in a transmission line, and measure its elastic scattering transmission coefficient at an extremely low temperature. The results are consistent with the expected effect of the parallel embedding circuit model, but inconsistent with the behaviors predicted by the series embedding circuit model in the literature. According to the above theoretical and experimental analyses of the elastic scattering of a single Josephson junction device, we further propose a scheme to control the elastic scattering behavior of microwave photons by modulating a DC superconducting quantum interference device with a bypass current, which can be applied to the construction of a microwave quantum network based on elastic scattering node controls.
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