Pub Date : 2025-11-26DOI: 10.1007/s11433-025-2770-8
Zhong-Ming Xie, Hai-Chao Yuan, Yong Tang
The nature of dark matter (DM) remains mysterious despite the substantial evidence from astrophysical and cosmological observations. While the majority of DM in our universe is non-relativistic, collisionless and its equation of state (EoS) is approximately pressureless p ≃ 0, DM becomes relativistic near the massive black holes (BHs) in galactic center. Yet its EoS is seldom discussed in the relativistic regime. Here we initially explore the possible EoS for DM in the vicinity of Schwarzschild BHs. We work in a spherical and quasi-static background spacetime, and describe DM as a perfect fluid in equilibrium. By numerically solving the Tolman-Oppenheimer-Volkoff equations with physical spatial initial conditions, we show that DM can have static profiles near BHs and its pressure should be negative in order to support the viable density profiles ρ. We illustrate with two simple general EoSs, namely the polytropic–like p ∝ ργ and the radius-dependent p ∝ r · ρ, and compare them with the observations of the Milky Way. Our findings provide insights into the model-building of DM, which should incorporate the possibility of negative pressure in the relativistic regime around BHs if such shallower DM profiles are probed by future gravitational-wave detectors in space.
{"title":"On equation of state of dark matter around massive black holes","authors":"Zhong-Ming Xie, Hai-Chao Yuan, Yong Tang","doi":"10.1007/s11433-025-2770-8","DOIUrl":"10.1007/s11433-025-2770-8","url":null,"abstract":"<div><p>The nature of dark matter (DM) remains mysterious despite the substantial evidence from astrophysical and cosmological observations. While the majority of DM in our universe is non-relativistic, collisionless and its equation of state (EoS) is approximately pressureless <i>p</i> ≃ 0, DM becomes relativistic near the massive black holes (BHs) in galactic center. Yet its EoS is seldom discussed in the relativistic regime. Here we initially explore the possible EoS for DM in the vicinity of Schwarzschild BHs. We work in a spherical and quasi-static background spacetime, and describe DM as a perfect fluid in equilibrium. By numerically solving the Tolman-Oppenheimer-Volkoff equations with physical spatial initial conditions, we show that DM can have static profiles near BHs and its pressure should be negative in order to support the viable density profiles <i>ρ</i>. We illustrate with two simple general EoSs, namely the polytropic–like <i>p</i> ∝ <i>ρ</i><sup><i>γ</i></sup> and the radius-dependent <i>p</i> ∝ <i>r</i> · <i>ρ</i>, and compare them with the observations of the Milky Way. Our findings provide insights into the model-building of DM, which should incorporate the possibility of negative pressure in the relativistic regime around BHs if such shallower DM profiles are probed by future gravitational-wave detectors in space.</p></div>","PeriodicalId":774,"journal":{"name":"Science China Physics, Mechanics & Astronomy","volume":"69 1","pages":""},"PeriodicalIF":7.5,"publicationDate":"2025-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145612557","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}
Pub Date : 2025-11-24DOI: 10.1007/s11433-025-2780-1
Pan Sun, Kai Cao, Shuang Li
This paper reviews the recent advances of practical techniques within different method frameworks for improved uncertainty propagation in orbital dynamics. The uncertainty propagation problem has been explored in many applications in orbital dynamics, such as orbit determination, relative motion, space debris removal, and small body exploration. In recent years, to further improve the accuracy and efficiency of uncertainty propagation, many practical techniques have been presented within different method frameworks. Among these, most techniques are within the frameworks of the continuity equation, the Gaussian mixture model, and the surrogate model. To facilitate the research work for nonlinear uncertainty propagation in orbital dynamics, a classification of the present method frameworks and the practical techniques for improved uncertainty propagation within different method frameworks is given and discussed in this paper.
{"title":"Recent advances of practical techniques for nonlinear uncertainty propagation in orbital dynamics","authors":"Pan Sun, Kai Cao, Shuang Li","doi":"10.1007/s11433-025-2780-1","DOIUrl":"10.1007/s11433-025-2780-1","url":null,"abstract":"<div><p>This paper reviews the recent advances of practical techniques within different method frameworks for improved uncertainty propagation in orbital dynamics. The uncertainty propagation problem has been explored in many applications in orbital dynamics, such as orbit determination, relative motion, space debris removal, and small body exploration. In recent years, to further improve the accuracy and efficiency of uncertainty propagation, many practical techniques have been presented within different method frameworks. Among these, most techniques are within the frameworks of the continuity equation, the Gaussian mixture model, and the surrogate model. To facilitate the research work for nonlinear uncertainty propagation in orbital dynamics, a classification of the present method frameworks and the practical techniques for improved uncertainty propagation within different method frameworks is given and discussed in this paper.</p></div>","PeriodicalId":774,"journal":{"name":"Science China Physics, Mechanics & Astronomy","volume":"69 1","pages":""},"PeriodicalIF":7.5,"publicationDate":"2025-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145612295","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}
Pub Date : 2025-11-14DOI: 10.1007/s11433-025-2766-4
Jinjie Shi, Chenkai Liu, Hongchen Chu, Xiaozhou Liu, Yun Lai
Broadband undistorted transmission is one of the criteria to preserve the information carried by incident waves and pulses, allowing imaging formation and source detection. For transmission through artificial materials like metasurfaces, undistorted transmission usually requires each meta-atom to possess exactly the same transmission amplitude and phase. Here, we consider a special acoustic metasurface consisting of meta-atoms with the same transmission phase but different transmittance. Interestingly, we find that when the meta-atoms are of subwavelength scale, the difference in transmittance would not induce substantial distortion in the transmitted wavefront. Based on this observation, we numerically and experimentally demonstrate acoustic metasurfaces that exhibit undistorted transmission and configurable arbitrary reflection. Two distinct types of reflection, i.e., anomalous reflection and diffuse reflection, are numerically and experimentally demonstrated with the transmission wavefront undistorted through a broad spectrum. Our work reveals a more general condition for realizing broadband undistorted transmission and configurable reflection with metasurfaces, which has potential implications in acoustic field manipulation and novel sonar domes.
{"title":"Acoustic metasurfaces with amplitude-diverse meta-atoms for broadband undistorted transmission and configurable reflection","authors":"Jinjie Shi, Chenkai Liu, Hongchen Chu, Xiaozhou Liu, Yun Lai","doi":"10.1007/s11433-025-2766-4","DOIUrl":"10.1007/s11433-025-2766-4","url":null,"abstract":"<div><p>Broadband undistorted transmission is one of the criteria to preserve the information carried by incident waves and pulses, allowing imaging formation and source detection. For transmission through artificial materials like metasurfaces, undistorted transmission usually requires each meta-atom to possess exactly the same transmission amplitude and phase. Here, we consider a special acoustic metasurface consisting of meta-atoms with the same transmission phase but different transmittance. Interestingly, we find that when the meta-atoms are of subwavelength scale, the difference in transmittance would not induce substantial distortion in the transmitted wavefront. Based on this observation, we numerically and experimentally demonstrate acoustic metasurfaces that exhibit undistorted transmission and configurable arbitrary reflection. Two distinct types of reflection, i.e., anomalous reflection and diffuse reflection, are numerically and experimentally demonstrated with the transmission wavefront undistorted through a broad spectrum. Our work reveals a more general condition for realizing broadband undistorted transmission and configurable reflection with metasurfaces, which has potential implications in acoustic field manipulation and novel sonar domes.</p></div>","PeriodicalId":774,"journal":{"name":"Science China Physics, Mechanics & Astronomy","volume":"69 1","pages":""},"PeriodicalIF":7.5,"publicationDate":"2025-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145561265","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}
Pub Date : 2025-11-14DOI: 10.1007/s11433-025-2751-2
Xiaoyu Hong, Weiren Wu, Qinghui Liu, Dengyun Yu, Chi Wang, Tao Shuai, Weiye Zhong, Renjie Zhu, Yonghui Xie, Lihua Zhang, Liang Xiong, Yuhua Tang, Yongliao Zou, Haitao Li, Guangli Wang, Jianfeng Xie, Changbin Xue, Hao Geng, Juan Zhang, Xiaojing Wu, Yong Huang, Weimin Zheng, Lei Liu, Fang Wu, Xiuzhong Zhang, Tao An, Xiaolong Yang, Fengxian Tong, Leonid I. Gurvits, Yong Zheng, Minfeng Gu, Xiaofei Ma, Liang Li, Peijia Li, Shanshan Zhao, Ping Rui, Luojing Chen, Guohui Chen, Ke Li, Chao Zhang, Yuanqi Liu, Yongchen Jiang, Jinqing Wang, Wenbin Wang, Yan Sun, Longfei Hao, Lang Cui, Dongrong Jiang, Zhihan Qian, Shuhua Ye
The Lunar Orbital VLBI Experiment (LOVEX) is a scientific component of the Chinese Lunar Exploration Project (CLEP) Chang’E-7. The spaceborne component of LOVEX is implemented onboard the relay satellite QueQiao-2, which was launched on 20 March 2024, and later placed into an elliptical selenocentric orbit. The LOVEX-specific payload consists of an X-band cryogenic receiver, a hydrogen maser frequency standard, and VLBI data formatting and acquisition electronics. Several components of the QueQiao-2 nominal onboard instrumentation, such as the 4.2-m antenna, the data storage device, and the downlink communication system, contribute to the overall spaceborne VLBI instrumentation. This allows us to form a space radio telescope capable of co-observing with Earth-based radio telescopes in VLBI mode. In this space VLBI system, the length of the baseline extends up to approximately 380000 km. This paper presents the LOVEX scientific objectives, architecture, instrumentation, prelaunch tests, in-flight verification and calibration, and the first in-flight detections of interferometric response (“fringes”) achieved through observations of the quasar AO 0235+164 and the Chang’E-6 orbital module, positioned at the Sun-Earth Lagrange point L2. These initial results demonstrate the successful performance of LOVEX, verifying its capability for both astronomical and spacecraft tracking observations at ultra-long VLBI baselines.
{"title":"Lunar Orbital VLBI Experiment: Motivation, scientific purposes and status","authors":"Xiaoyu Hong, Weiren Wu, Qinghui Liu, Dengyun Yu, Chi Wang, Tao Shuai, Weiye Zhong, Renjie Zhu, Yonghui Xie, Lihua Zhang, Liang Xiong, Yuhua Tang, Yongliao Zou, Haitao Li, Guangli Wang, Jianfeng Xie, Changbin Xue, Hao Geng, Juan Zhang, Xiaojing Wu, Yong Huang, Weimin Zheng, Lei Liu, Fang Wu, Xiuzhong Zhang, Tao An, Xiaolong Yang, Fengxian Tong, Leonid I. Gurvits, Yong Zheng, Minfeng Gu, Xiaofei Ma, Liang Li, Peijia Li, Shanshan Zhao, Ping Rui, Luojing Chen, Guohui Chen, Ke Li, Chao Zhang, Yuanqi Liu, Yongchen Jiang, Jinqing Wang, Wenbin Wang, Yan Sun, Longfei Hao, Lang Cui, Dongrong Jiang, Zhihan Qian, Shuhua Ye","doi":"10.1007/s11433-025-2751-2","DOIUrl":"10.1007/s11433-025-2751-2","url":null,"abstract":"<div><p>The Lunar Orbital VLBI Experiment (LOVEX) is a scientific component of the Chinese Lunar Exploration Project (CLEP) Chang’E-7. The spaceborne component of LOVEX is implemented onboard the relay satellite QueQiao-2, which was launched on 20 March 2024, and later placed into an elliptical selenocentric orbit. The LOVEX-specific payload consists of an X-band cryogenic receiver, a hydrogen maser frequency standard, and VLBI data formatting and acquisition electronics. Several components of the QueQiao-2 nominal onboard instrumentation, such as the 4.2-m antenna, the data storage device, and the downlink communication system, contribute to the overall spaceborne VLBI instrumentation. This allows us to form a space radio telescope capable of co-observing with Earth-based radio telescopes in VLBI mode. In this space VLBI system, the length of the baseline extends up to approximately 380000 km. This paper presents the LOVEX scientific objectives, architecture, instrumentation, prelaunch tests, in-flight verification and calibration, and the first in-flight detections of interferometric response (“fringes”) achieved through observations of the quasar AO 0235+164 and the Chang’E-6 orbital module, positioned at the Sun-Earth Lagrange point L2. These initial results demonstrate the successful performance of LOVEX, verifying its capability for both astronomical and spacecraft tracking observations at ultra-long VLBI baselines.</p></div>","PeriodicalId":774,"journal":{"name":"Science China Physics, Mechanics & Astronomy","volume":"69 1","pages":""},"PeriodicalIF":7.5,"publicationDate":"2025-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11433-025-2751-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145561264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The nonmagnetic kagome metal ScV6Sn6 displays an unconventional charge order (CO) accompanied by signatures of an anomalous Hall effect, hidden magnetism, and multiple lattice instabilities. In this study, we report the observation of unconventional anomalous thermoelectric properties. Notably, unexpected anomalous transverse Nernst signals reach a peak value of ∼4 µV/K near the TCDW ∼92 K in ScV6Sn6, and these signals persist in the charge-ordered state as the temperature decreases to 10 K. Furthermore, both thermopower and thermal conductivity exhibit significant changes under magnetic fields, even in the nonmagnetic ground state. These observations strongly suggest the emergence of time-reversal symmetry breaking in ScV6Sn6, as supported by muon spin relaxation (µSR) measurements. While hidden magnetism represents the most plausible origin, alternative mechanisms involving orbital currents and chiral charge order remain possible.
{"title":"Anomalous nernst effect and its implications for time-reversal symmetry breaking in kagome metal ScV6Sn6","authors":"Yazhou Li, Saizheng Cao, Jiaxing Liao, Jiajun Ma, Yuwei Zhang, Tao Li, Jialu Wang, Chenchao Xu, Jianhui Dai, Chao Cao, Yu Song, Peijie Sun, Yuke Li","doi":"10.1007/s11433-025-2767-6","DOIUrl":"10.1007/s11433-025-2767-6","url":null,"abstract":"<div><p>The nonmagnetic kagome metal ScV<sub>6</sub>Sn<sub>6</sub> displays an unconventional charge order (CO) accompanied by signatures of an anomalous Hall effect, hidden magnetism, and multiple lattice instabilities. In this study, we report the observation of unconventional anomalous thermoelectric properties. Notably, unexpected anomalous transverse Nernst signals reach a peak value of ∼4 µV/K near the <i>T</i><sub>CDW</sub> ∼92 K in ScV<sub>6</sub>Sn<sub>6</sub>, and these signals persist in the charge-ordered state as the temperature decreases to 10 K. Furthermore, both thermopower and thermal conductivity exhibit significant changes under magnetic fields, even in the nonmagnetic ground state. These observations strongly suggest the emergence of time-reversal symmetry breaking in ScV<sub>6</sub>Sn<sub>6</sub>, as supported by muon spin relaxation (µSR) measurements. While hidden magnetism represents the most plausible origin, alternative mechanisms involving orbital currents and chiral charge order remain possible.</p></div>","PeriodicalId":774,"journal":{"name":"Science China Physics, Mechanics & Astronomy","volume":"69 1","pages":""},"PeriodicalIF":7.5,"publicationDate":"2025-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145560874","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}
Gravitational waves (GWs) originating from cosmological sources offer direct insights into the physics of the primordial Universe, the fundamental nature of gravity, and the cosmic expansion of the Universe. In this review paper, we present a comprehensive overview of our recent advances in GW cosmology, supported by the national key research and development program of China, focusing on cosmological GW sources and their implications for fundamental physics and cosmology. We first discuss the generation mechanisms and characteristics of stochastic gravitational wave backgrounds generated by physical processes that occurred in the early Universe, including those from inflation, phase transitions, and topological defects, and summarize current and possible future constraints from pulsar timing arrays and space-based detectors. Next, we explore the formation and observational prospects of primordial black holes as GW sources and their potential connection to dark matter. We then analyze how GWs are affected by large-scale structure, cosmological perturbations, and possible modifications of gravity on GW propagation, and how these effects can be used to test fundamental symmetry of gravity. Finally, we discuss the application of GW standard sirens in measuring the Hubble constant, the expansion history, and dark energy parameters, including their combination with electromagnetic observations. These topics together show how GW observations, especially with upcoming space-based detectors, such as LISA, Taiji, and TianQin, can provide new information about the physics of the early Universe, cosmological evolution, and the nature of gravity.
{"title":"Gravitational wave cosmology","authors":"Ligong Bian, Rong-Gen Cai, Yu-Qi Dong, Qing Gao, Yungui Gong, Zong-Kuan Guo, Qing-Guo Huang, Zhaofeng Kang, Li Li, Jing Liu, Lang Liu, Yu-Xiao Liu, Xuchen Lu, Zhi-Zhang Peng, Jin Qiao, Puxun Wu, Yue-Liang Wu, Jiang-Hao Yu, Chen Yuan, Chao Zhang, Tao Zhu","doi":"10.1007/s11433-025-2740-8","DOIUrl":"10.1007/s11433-025-2740-8","url":null,"abstract":"<div><p>Gravitational waves (GWs) originating from cosmological sources offer direct insights into the physics of the primordial Universe, the fundamental nature of gravity, and the cosmic expansion of the Universe. In this review paper, we present a comprehensive overview of our recent advances in GW cosmology, supported by the national key research and development program of China, focusing on cosmological GW sources and their implications for fundamental physics and cosmology. We first discuss the generation mechanisms and characteristics of stochastic gravitational wave backgrounds generated by physical processes that occurred in the early Universe, including those from inflation, phase transitions, and topological defects, and summarize current and possible future constraints from pulsar timing arrays and space-based detectors. Next, we explore the formation and observational prospects of primordial black holes as GW sources and their potential connection to dark matter. We then analyze how GWs are affected by large-scale structure, cosmological perturbations, and possible modifications of gravity on GW propagation, and how these effects can be used to test fundamental symmetry of gravity. Finally, we discuss the application of GW standard sirens in measuring the Hubble constant, the expansion history, and dark energy parameters, including their combination with electromagnetic observations. These topics together show how GW observations, especially with upcoming space-based detectors, such as LISA, Taiji, and TianQin, can provide new information about the physics of the early Universe, cosmological evolution, and the nature of gravity.</p></div>","PeriodicalId":774,"journal":{"name":"Science China Physics, Mechanics & Astronomy","volume":"69 1","pages":""},"PeriodicalIF":7.5,"publicationDate":"2025-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145560875","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}
Pub Date : 2025-11-12DOI: 10.1007/s11433-025-2760-y
Yu Xiao, Jingyi Chen, Nengyin Wang, Xu Wang, Yong Li
Degenerate states including exceptional points (EPs) and diabolic points (DPs) arise due to the underlying symmetry in physical systems. The interplay between different symmetry breakings opens a promising route for exceptional wave manipulation. Here, we conceptually demonstrate and experimentally prove that breaking parity symmetry and time-reversal symmetry through spatial perturbation and non-Hermitian perturbation, respectively, result in the evolution of EPs in pairs in a scattering system. These pairwise scattering EPs, which are orthogonal to each other and can be interconverted by mirror inversion, evolve continuously in the perturbation space and ultimately merge into a special non-Hermitian degenerate state—a non-Hermitian DP. The EPs and DP observed here exhibit distinct topological structures from different planes in the perturbation space, thus both carrying hybrid topological charges. Based on these findings, we show that metasurfaces at EPs can encode differences in scattering asymmetry, allowing for a complete yet arbitrary wave manipulation beyond previously reported non-Hermitian scattering metasurfaces. Our findings establish a general framework for exploring extreme wave scattering through combined-perturbation-driven degeneration evolution.
{"title":"Evolution of pairwise scattering exceptional points via acoustic metasurfaces","authors":"Yu Xiao, Jingyi Chen, Nengyin Wang, Xu Wang, Yong Li","doi":"10.1007/s11433-025-2760-y","DOIUrl":"10.1007/s11433-025-2760-y","url":null,"abstract":"<div><p>Degenerate states including exceptional points (EPs) and diabolic points (DPs) arise due to the underlying symmetry in physical systems. The interplay between different symmetry breakings opens a promising route for exceptional wave manipulation. Here, we conceptually demonstrate and experimentally prove that breaking parity symmetry and time-reversal symmetry through spatial perturbation and non-Hermitian perturbation, respectively, result in the evolution of EPs in pairs in a scattering system. These pairwise scattering EPs, which are orthogonal to each other and can be interconverted by mirror inversion, evolve continuously in the perturbation space and ultimately merge into a special non-Hermitian degenerate state—a non-Hermitian DP. The EPs and DP observed here exhibit distinct topological structures from different planes in the perturbation space, thus both carrying hybrid topological charges. Based on these findings, we show that metasurfaces at EPs can encode differences in scattering asymmetry, allowing for a complete yet arbitrary wave manipulation beyond previously reported non-Hermitian scattering metasurfaces. Our findings establish a general framework for exploring extreme wave scattering through combined-perturbation-driven degeneration evolution.</p></div>","PeriodicalId":774,"journal":{"name":"Science China Physics, Mechanics & Astronomy","volume":"69 1","pages":""},"PeriodicalIF":7.5,"publicationDate":"2025-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145560986","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}
In the noisy intermediate-scale quantum era, emerging classical-quantum hybrid optimization algorithms, such as variational quantum algorithms (VQAs), can leverage the unique characteristics of quantum devices to accelerate computations tailored to specific problems with shallow circuits. However, these algorithms encounter biases and iteration difficulties due to significant noise in quantum processors. These difficulties can only be partially addressed without error correction by optimizing hardware, reducing circuit complexity, or fitting and extrapolating. A compelling solution is applying probabilistic error cancellation (PEC), a quantum error mitigation technique that enables unbiased results without full error correction. Traditional PEC is challenging to apply in VQAs due to its variance amplification, contradicting iterative process assumptions. This paper proposes a novel noise-adaptable strategy that combines PEC with the quantum approximate optimization algorithm (QAOA). It is implemented through invariant sampling circuits (invariant-PEC, or IPEC) and substantially reduces iteration variance. This strategy marks the first successful integration of PEC and QAOA, resulting in efficient convergence. Moreover, we introduce adaptive partial PEC (APPEC), which modulates the error cancellation proportion of IPEC during iteration. We experimentally validate this technique on a superconducting quantum processor, cutting sampling cost by 90.1%. Notably, we find that dynamic adjustments of error levels via APPEC can enhance the ability to escape from local minima and reduce sampling costs. These results open promising avenues for executing VQAs with large-scale, low-noise quantum circuits, paving the way for practical quantum computing advancements.
{"title":"Variational quantum algorithms with invariant probabilistic error cancellation on noisy quantum processors","authors":"Yulin Chi, Hongyi Shi, Wen Zheng, Haoyang Cai, Yu Zhang, Xinsheng Tan, Shaoxiong Li, Jianwei Wang, Jiangyu Cui, Man-Hong Yung, Yang Yu","doi":"10.1007/s11433-025-2779-x","DOIUrl":"10.1007/s11433-025-2779-x","url":null,"abstract":"<div><p>In the noisy intermediate-scale quantum era, emerging classical-quantum hybrid optimization algorithms, such as variational quantum algorithms (VQAs), can leverage the unique characteristics of quantum devices to accelerate computations tailored to specific problems with shallow circuits. However, these algorithms encounter biases and iteration difficulties due to significant noise in quantum processors. These difficulties can only be partially addressed without error correction by optimizing hardware, reducing circuit complexity, or fitting and extrapolating. A compelling solution is applying probabilistic error cancellation (PEC), a quantum error mitigation technique that enables unbiased results without full error correction. Traditional PEC is challenging to apply in VQAs due to its variance amplification, contradicting iterative process assumptions. This paper proposes a novel noise-adaptable strategy that combines PEC with the quantum approximate optimization algorithm (QAOA). It is implemented through invariant sampling circuits (invariant-PEC, or IPEC) and substantially reduces iteration variance. This strategy marks the first successful integration of PEC and QAOA, resulting in efficient convergence. Moreover, we introduce adaptive partial PEC (APPEC), which modulates the error cancellation proportion of IPEC during iteration. We experimentally validate this technique on a superconducting quantum processor, cutting sampling cost by 90.1%. Notably, we find that dynamic adjustments of error levels via APPEC can enhance the ability to escape from local minima and reduce sampling costs. These results open promising avenues for executing VQAs with large-scale, low-noise quantum circuits, paving the way for practical quantum computing advancements.</p></div>","PeriodicalId":774,"journal":{"name":"Science China Physics, Mechanics & Astronomy","volume":"69 1","pages":""},"PeriodicalIF":7.5,"publicationDate":"2025-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145560877","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}