Constraint satisfaction problems(CSPs)are a class of problems that are ubiquitous in science and engineering.They feature a collection of constraints specified over subsets of variables.A CSP can be solved either dire...Constraint satisfaction problems(CSPs)are a class of problems that are ubiquitous in science and engineering.They feature a collection of constraints specified over subsets of variables.A CSP can be solved either directly or by reducing it to other problems.This paper introduces the Julia ecosystem for solving and analyzing CSPs with a focus on the programming practices.We introduce some important CSPs and show how these problems are reduced to each other.We also show how to transform CSPs into tensor networks,how to optimize the tensor network contraction orders,and how to extract the solution space properties by contracting the tensor networks with generic element types.Examples are given,which include computing the entropy constant,analyzing the overlap gap property,and the reduction between CSPs.展开更多
Computing free energy is a fundamental problem in statistical physics.Recently,two distinct methods have been developed and have demonstrated remarkable success:the tensor-network-based contraction method and the neur...Computing free energy is a fundamental problem in statistical physics.Recently,two distinct methods have been developed and have demonstrated remarkable success:the tensor-network-based contraction method and the neural-network-based variational method.Tensor networks are accurate,but their application is often limited to low-dimensional systems due to the high computational complexity in high-dimensional systems.The neural network method applies to systems with general topology.However,as a variational method,it is not as accurate as tensor networks.In this work,we propose an integrated approach,tensor-network-based variational autoregressive networks(TNVAN),that leverages the strengths of both tensor networks and neural networks:combining the variational autoregressive neural network’s ability to compute an upper bound on free energy and perform unbiased sampling from the variational distribution with the tensor network’s power to accurately compute the partition function for small sub-systems,resulting in a robust method for precisely estimating free energy.To evaluate the proposed approach,we conducted numerical experiments on spin glass systems with various topologies,including two-dimensional lattices,fully connected graphs,and random graphs.Our numerical results demonstrate the superior accuracy of our method compared to existing approaches.In particular,it effectively handles systems with longrange interactions and leverages GPU efficiency without requiring singular value decomposition,indicating great potential in tackling statistical mechanics problems and simulating high-dimensional complex systems through both tensor networks and neural networks.展开更多
Tensor networks are used to describe the ground state wavefunction of the quantum many-body system.Recently,it has been shown that a tensor network can generate the anti-de Sitter(AdS)geometry by using the entanglemen...Tensor networks are used to describe the ground state wavefunction of the quantum many-body system.Recently,it has been shown that a tensor network can generate the anti-de Sitter(AdS)geometry by using the entanglement renormalization approach,which provides a new way to realize bulk reconstruction in the AdS/conformal field theory correspondence.However,whether the dynamical connections can be found between the tensor network and gravity is an important unsolved problem.In this paper,we give a novel proposal to integrate ideas from tensor networks,entanglement entropy,canonical quantization of quantum gravity and the holographic principle and argue that the gravitational dynamics can be generated from a tensor network if the wave function of the latter satisfies the Wheeler–DeWitt equation.展开更多
The prediction of the intensity of tropical cyclones(TCs)is crucial for weather forecasts and disaster prevention.Maximum sustained wind(MSW)is one of the main indexes of TC intensity.Analyzing multispectral images(MS...The prediction of the intensity of tropical cyclones(TCs)is crucial for weather forecasts and disaster prevention.Maximum sustained wind(MSW)is one of the main indexes of TC intensity.Analyzing multispectral images(MSIs)of cyclones by deep learning methods can increase MSW accuracy.However,existing methods are mostly designed for infrared images,not being able to leverage different band data or represent the rich temporal-spectral-spatial features in MSIs.Meanwhile,MSIs alone cannot provide all the necessary or accurate information of TCs as there are usually undesired variations or distortions in TC structures reflected by the images due to the uniqueness of each TC and positions of TCs and the satellites that capture images.Moreover,TC formation and evolution are affected by various physical factors that are not recorded in MSIs or cannot be easily derived from the images.To perform multimodal data fusion while making use of the most valuable information,we propose a novel model,Invalid-Band-Suppressed and Structure-Descriptor-Enhanced Temporal Tensor Network(ISSDTN).ISSDTN extracts features from the long-wavelength and the short-wavelength band images of each set of TC MSIs in two separate paths to suppress invalid band data.Finally,the paths are combined to fuse the multimodal information,i.e.,image features and Structure Descriptors(SDs)via cross-attentions to predict MSW.Experimental results show that ISSDTN outperforms many baselines and state-of-the-art methods in various cyclone datasets.The errors of 24 h MSW prediction by ISSDTN is as low as 4.49 m/s and 5.33 m/s for FY4A-TC and TCIR datasets,respectively.展开更多
The polaron problem is a very old problem in condensed matter physics that dates back to the thirties,but still remains largely unsolved today,especially when electron–electron interaction is taken into consideration...The polaron problem is a very old problem in condensed matter physics that dates back to the thirties,but still remains largely unsolved today,especially when electron–electron interaction is taken into consideration.The presence of both electron–electron and electron–phonon interactions in the problem invalidates most existing numerical methods,which are either computationally too expensive or simply intractable.The continuous-time quantum Monte Carlo(CTQMC)methods could tackle this problem,but they are only effective on the imaginarytime axis.In this work,we present a method based on tensor networks and the path integral formalism to solve polaron impurity problems.As both the electron and phonon baths can be integrated out via the Feynman–Vernon influence functional in the path integral formalism,our method is free of bath discretization error.It can also flexibly work on imaginary time,Keldysh contour,and L-shaped Kadanoff contour.In addition,our method can naturally resolve several long-existing challenges:(i)non-diagonal hybridization function;(ii)measuring multi-time correlations beyond single-particle Green’s functions.We demonstrate the effectiveness and accuracy of our method with extensive numerical examples against analytic solutions,exact diagonalization,and CTQMC.We also perform full-fledged real-time calculations that have never been done before to our knowledge,which could serve as a benchmarking baseline for future method developments.展开更多
Dear Editor,This letter proposes the graph tensor alliance attention network(GT-A^(2)T)to represent a dynamic graph(DG)precisely.Its main idea includes 1)Establishing a unified spatio-temporal message propagation fram...Dear Editor,This letter proposes the graph tensor alliance attention network(GT-A^(2)T)to represent a dynamic graph(DG)precisely.Its main idea includes 1)Establishing a unified spatio-temporal message propagation framework on a DG via the tensor product for capturing the complex cohesive spatio-temporal interdependencies precisely and 2)Acquiring the alliance attention scores by node features and favorable high-order structural correlations.展开更多
We propose a generalized Lanczos method to generate the many-body basis states of quantum lattice models using tensor-network states （TNS）. The ground-state wave function is represented as a linear superposition com...We propose a generalized Lanczos method to generate the many-body basis states of quantum lattice models using tensor-network states （TNS）. The ground-state wave function is represented as a linear superposition composed from a set of TNS generated by Lanczos iteration. This method improves significantly the accuracy of the tensor-network algorithm and provides an effective way to enlarge the maximal bond dimension of TNS. The ground state such obtained contains significantly more entanglement than each individual TNS, reproducing correctly the logarithmic size dependence of the entanglement entropy in a critical system. The method can be generalized to non-Hamiltonian systems and to the calculation of low-lying excited states, dynamical correlation functions, and other physical properties of strongly correlated systems.展开更多
This article discusses the covariance correlation tensor (CCT) in quantum network theory for four Bell bases in detail. Furthermore, it gives the expression of the density operator in terms of CCT for a quantum networ...This article discusses the covariance correlation tensor (CCT) in quantum network theory for four Bell bases in detail. Furthermore, it gives the expression of the density operator in terms of CCT for a quantum network of three nodes, thus gives the criterion of entanglement for this case, i.e. the conditions of complete separability and partial separability for a given quantum state of three bodies. Finally it discusses the general case for the quantum network of nodes.展开更多
This article discusses the separability of the pure states and mixed states of the quantum network of two nodes by means of the criterion of no entanglement in terms of the covariance correlation tensor in quantum net...This article discusses the separability of the pure states and mixed states of the quantum network of two nodes by means of the criterion of no entanglement in terms of the covariance correlation tensor in quantum network theory, i.e. for a composite system consisting of two nodes. The covariance correlation tensor is equal to zero for all possible and .展开更多
From the comparison of correlation tensor in the theory of quantum network, the Alexander relation matrix in the theory of knot crystals and the identical inversion relations under the action of Pauli matrices, we sho...From the comparison of correlation tensor in the theory of quantum network, the Alexander relation matrix in the theory of knot crystals and the identical inversion relations under the action of Pauli matrices, we show that there is a one to one correspondence between four Bell bases and four oriented links of the linkage in knot theory.展开更多
Temporal lobe resection is an important treatment option for epilepsy that involves removal of potentially essential brain regions. Selective amygdalohippocampectomy is a widely performed temporal lobe surgery. We sug...Temporal lobe resection is an important treatment option for epilepsy that involves removal of potentially essential brain regions. Selective amygdalohippocampectomy is a widely performed temporal lobe surgery. We suggest starting the incision for selective amygdalohippocampectomy at the inferior temporal gyrus based on diffusion magnetic resonance imaging（MRI） tractography. Diffusion MRI data from 20 normal participants were obtained from Parkinson＇s Progression Markers Initiative（PPMI） database（www.ppmi-info.org）. A tractography algorithm was applied to extract neuronal fiber information for the temporal lobe, hippocampus, and amygdala. Fiber information was analyzed in terms of the number of fibers and betweenness centrality. Distances between starting incisions and surgical target regions were also considered to explore the length of the surgical path. Middle temporal and superior temporal gyrus regions have higher connectivity values than the inferior temporal gyrus and thus are not good candidates for starting the incision. The distances between inferior temporal gyrus and surgical target regions were shorter than those between middle temporal gyrus and target regions. Thus, the inferior temporal gyrus is a good candidate for starting the incision. Starting the incision from the inferior temporal gyrus would spare the important（in terms of betweenness centrality values） middle region and shorten the distance to the target regions of the hippocampus and amygdala.展开更多
The piezoelectric materials enable the mutual conversion between mechanical and electrical energy,which drive a multi-billion dollar industry through their applications as sensors,actuators,and energy harvesters.The t...The piezoelectric materials enable the mutual conversion between mechanical and electrical energy,which drive a multi-billion dollar industry through their applications as sensors,actuators,and energy harvesters.The third-rank piezoelectric tensor is the core matrices for piezoelectric materials and their devices.However,the high costs of obtaining full piezoelectric tensor data through either experimental or computational methods make a significant challenge.Here,we propose an equivariant attention tensor graph neural network(EATGNN)that can identify crystal symmetry and remain independent of the reference frame,ultimately enabling the accurate prediction of the complete third-rank piezoelectric tensor.Especially,we perform an irreducible decomposition of the piezoelectric tensor into four irreducible representations to efficiently reserve the symmetry under group transformation operations.Our results further demonstrate that this model performs well in both bulk and twodimensional materials.Finally,combining EATGNN with first-principles calculations,we discovered several potential high-performance piezoelectric materials.展开更多
The Ryu-Takayanagi(RT)formula plays a large role in the current theory of gauge-gravity duality and emergent geometry phenomena.The recent reinterpretation of this formula in terms of a set of"bit threads"is...The Ryu-Takayanagi(RT)formula plays a large role in the current theory of gauge-gravity duality and emergent geometry phenomena.The recent reinterpretation of this formula in terms of a set of"bit threads"is an interesting effort in understanding holography.In this study,we investigate a quantum generalization of the"bit threads"based on a tensor network,with particular focus on the multi-scale entanglement renormalization ansatz(MERA).We demonstrate that,in the large c limit,isometries of the MERA can be regarded as"sources"(or"sinks")of the information flow,which extensively modifies the original picture of bit threads by introducing a new variableρ:density of the isometries.In this modified picture of information flow,the isometries can be viewed as generators of the flow.The strong subadditivity and related properties of the entanglement entropy are also obtained in this new picture.The large c limit implies that classical gravity can emerge from the information flow.展开更多
In this paper,we introduce a type of tensor neural network.For the first time,we propose its numerical integration scheme and prove the computational complexity to be the polynomial scale of the dimension.Based on the...In this paper,we introduce a type of tensor neural network.For the first time,we propose its numerical integration scheme and prove the computational complexity to be the polynomial scale of the dimension.Based on the tensor product structure,we develop an efficient numerical integration method by using fixed quadrature points for the functions of the tensor neural network.The corresponding machine learning method is also introduced for solving high-dimensional problems.Some numerical examples are also provided to validate the theoretical results and the numerical algorithm.展开更多
The spin-1/2 model system with antiferromagnetic(AF) couplings on a J1-J2checkerboard lattice, known as the planar pyrochlore model, is strongly frustrated and associated with a two-to-one dimensional crossover. Using...The spin-1/2 model system with antiferromagnetic(AF) couplings on a J1-J2checkerboard lattice, known as the planar pyrochlore model, is strongly frustrated and associated with a two-to-one dimensional crossover. Using the Projected Entangled Simplex States tensor network ansatz, we identify a large number of nearly degenerate states in the frustrated region(J_(1)<J_(2)).Specifically, we find the long-sought crossed-dimer valence bond solid(VBS) state to be the ground state at J_(1)≤J_(2), while various 1D AF correlated states take over the rest. We verify the stability of the VBS state against nematic perturbation. The corresponding bosonic picture provides an intuitive understanding of the low-energy physics. Particularly, it predicts weaker VBS states in the easy-plane limit, which we confirm numerically. Our results clarify the most essential ground state properties of this interesting system and demonstrate the usefulness of bosonic picture in dealing with frustrated magnetism.展开更多
The nature of the zero-temperature phase diagram of the spin-1/2 J_(1)-J_(2)Heisenberg model on a square lattice has been debated in the past three decades,and it remains one of the fundamental problems unsettled in t...The nature of the zero-temperature phase diagram of the spin-1/2 J_(1)-J_(2)Heisenberg model on a square lattice has been debated in the past three decades,and it remains one of the fundamental problems unsettled in the study of quantum many-body theory.By using the state-of-the-art tensor network method,specifically,the finite projected entangled pair state(PEPS)algorithm,to simulate the global phase diagram of the J_(1)-J_(2)Heisenberg model up to 24×24 sites,we provide very solid evidences to show that the nature of the intermediate nonmagnetic phase is a gapless quantum spin liquid(QSL),whose spin-spin and dimer-dimer correlations both decay with a power law behavior.There also exists a valence-bond solid(VBS)phase in a very narrow region 0.56■J_(2)/J_(1)≤0.61 before the system enters the well known collinear antiferromagnetic phase.We stress that we make the first detailed comparison between the results of PEPS and the well-established density matrix renormalization group(DMRG)method through one-to-one direct benchmark for small system sizes,and thus give rise to a very solid PEPS calculation beyond DMRG.Our numerical evidences explicitly demonstrate the huge power of PEPS for highly frustrated spin systems.Finally,an effective field theory is also proposed to understand the physical nature of the discovered gapless QSL and its relation to deconfined quantum critical point(DQCP).展开更多
The emergence of exotic quantum phenomena in frustrated magnets is rapidly driving the development of quantum many-body physics,raising fundamental questions on the nature of quantum phase transitions.Here we unveil t...The emergence of exotic quantum phenomena in frustrated magnets is rapidly driving the development of quantum many-body physics,raising fundamental questions on the nature of quantum phase transitions.Here we unveil the behaviour of emergent symmetry involving two extraordinarily representative phenomena,i.e.,the deconfined quantum critical point(DQCP)and the quantum spin liquid(QSL)state.Via large-scale tensor network simulations,we study a spatially anisotropic spin-1/2 square-lattice frustrated antiferromagnetic(AFM)model,namely the J1x-J1y-J2 model,which contains anisotropic nearestneighbor couplings J1x,J1y and the next nearest neighbor coupling J2.For small J1y/J1x,by tuning J2,a direct continuous transition between the AFM and valence bond solid phase is observed.With growing J1y/J1x,a gapless QSL phase gradually emerges between the AFM and VBS phases.We observe an emergent O(4)symmetry along the AFM–VBS transition line,which is consistent with the prediction of DQCP theory.Most surprisingly,we find that such an emergent O(4)symmetry holds for the whole QSL–VBS transition line as well.These findings reveal the intrinsic relationship between the QSL and DQCP from categorical symmetry point of view,and strongly constrain the quantum field theory description of the QSL phase.The phase diagram and critical exponents presented in this paper are of direct relevance to future experiments on frustrated magnets and cold atom systems.展开更多
Graph de-anonymization is a technique used to reveal connections between entities in anonymized graphs,which is crucial in detecting malicious activities,network analysis,social network analysis,and more.Despite its p...Graph de-anonymization is a technique used to reveal connections between entities in anonymized graphs,which is crucial in detecting malicious activities,network analysis,social network analysis,and more.Despite its paramount importance,conventional methods often grapple with inefficiencies and challenges tied to obtaining accurate query graph data.This paper introduces a neural-based inexact graph de-anonymization,which comprises an embedding phase,a comparison phase,and a matching procedure.The embedding phase uses a graph convolutional network to generate embedding vectors for both the query and anonymized graphs.The comparison phase uses a neural tensor network to ascertain node resemblances.The matching procedure employs a refined greedy algorithm to discern optimal node pairings.Additionally,we comprehensively evaluate its performance via well-conducted experiments on various real datasets.The results demonstrate the effectiveness of our proposed approach in enhancing the efficiency and performance of graph de-anonymization through the use of graph embedding vectors.展开更多
基金funded by the National Key R&D Program of China(Grant No.2024YFE0102500)the National Natural Science Foundation of China(Grant No.12404568)+1 种基金the Guangzhou Municipal Science and Technology Project(Grant No.2023A03J00904)the Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area,China and the Undergraduate Research Project from HKUST(Guangzhou).
文摘Constraint satisfaction problems(CSPs)are a class of problems that are ubiquitous in science and engineering.They feature a collection of constraints specified over subsets of variables.A CSP can be solved either directly or by reducing it to other problems.This paper introduces the Julia ecosystem for solving and analyzing CSPs with a focus on the programming practices.We introduce some important CSPs and show how these problems are reduced to each other.We also show how to transform CSPs into tensor networks,how to optimize the tensor network contraction orders,and how to extract the solution space properties by contracting the tensor networks with generic element types.Examples are given,which include computing the entropy constant,analyzing the overlap gap property,and the reduction between CSPs.
基金supported by Projects 12325501,12047503,and 12247104 of the National Natural Science Foundation of ChinaProject ZDRW-XX-2022-3-02 of the Chinese Academy of Sciencessupported by the Innovation Program for Quantum Science and Technology project 2021ZD0301900。
文摘Computing free energy is a fundamental problem in statistical physics.Recently,two distinct methods have been developed and have demonstrated remarkable success:the tensor-network-based contraction method and the neural-network-based variational method.Tensor networks are accurate,but their application is often limited to low-dimensional systems due to the high computational complexity in high-dimensional systems.The neural network method applies to systems with general topology.However,as a variational method,it is not as accurate as tensor networks.In this work,we propose an integrated approach,tensor-network-based variational autoregressive networks(TNVAN),that leverages the strengths of both tensor networks and neural networks:combining the variational autoregressive neural network’s ability to compute an upper bound on free energy and perform unbiased sampling from the variational distribution with the tensor network’s power to accurately compute the partition function for small sub-systems,resulting in a robust method for precisely estimating free energy.To evaluate the proposed approach,we conducted numerical experiments on spin glass systems with various topologies,including two-dimensional lattices,fully connected graphs,and random graphs.Our numerical results demonstrate the superior accuracy of our method compared to existing approaches.In particular,it effectively handles systems with longrange interactions and leverages GPU efficiency without requiring singular value decomposition,indicating great potential in tackling statistical mechanics problems and simulating high-dimensional complex systems through both tensor networks and neural networks.
基金supported by the National Natural Science Foundation of China under Grant No.11675272supported by China Postdoctoral Science Foundation(No.2019M653137)。
文摘Tensor networks are used to describe the ground state wavefunction of the quantum many-body system.Recently,it has been shown that a tensor network can generate the anti-de Sitter(AdS)geometry by using the entanglement renormalization approach,which provides a new way to realize bulk reconstruction in the AdS/conformal field theory correspondence.However,whether the dynamical connections can be found between the tensor network and gravity is an important unsolved problem.In this paper,we give a novel proposal to integrate ideas from tensor networks,entanglement entropy,canonical quantization of quantum gravity and the holographic principle and argue that the gravitational dynamics can be generated from a tensor network if the wave function of the latter satisfies the Wheeler–DeWitt equation.
基金supported by the National Natural Science Foundation of China under Grant 61702094 and the DHU Distinguished Young Professor Program under Grant LZB2025003.
文摘The prediction of the intensity of tropical cyclones(TCs)is crucial for weather forecasts and disaster prevention.Maximum sustained wind(MSW)is one of the main indexes of TC intensity.Analyzing multispectral images(MSIs)of cyclones by deep learning methods can increase MSW accuracy.However,existing methods are mostly designed for infrared images,not being able to leverage different band data or represent the rich temporal-spectral-spatial features in MSIs.Meanwhile,MSIs alone cannot provide all the necessary or accurate information of TCs as there are usually undesired variations or distortions in TC structures reflected by the images due to the uniqueness of each TC and positions of TCs and the satellites that capture images.Moreover,TC formation and evolution are affected by various physical factors that are not recorded in MSIs or cannot be easily derived from the images.To perform multimodal data fusion while making use of the most valuable information,we propose a novel model,Invalid-Band-Suppressed and Structure-Descriptor-Enhanced Temporal Tensor Network(ISSDTN).ISSDTN extracts features from the long-wavelength and the short-wavelength band images of each set of TC MSIs in two separate paths to suppress invalid band data.Finally,the paths are combined to fuse the multimodal information,i.e.,image features and Structure Descriptors(SDs)via cross-attentions to predict MSW.Experimental results show that ISSDTN outperforms many baselines and state-of-the-art methods in various cyclone datasets.The errors of 24 h MSW prediction by ISSDTN is as low as 4.49 m/s and 5.33 m/s for FY4A-TC and TCIR datasets,respectively.
基金supported by the National Natural Science Foundation of China(Grant No.12104328)。
文摘The polaron problem is a very old problem in condensed matter physics that dates back to the thirties,but still remains largely unsolved today,especially when electron–electron interaction is taken into consideration.The presence of both electron–electron and electron–phonon interactions in the problem invalidates most existing numerical methods,which are either computationally too expensive or simply intractable.The continuous-time quantum Monte Carlo(CTQMC)methods could tackle this problem,but they are only effective on the imaginarytime axis.In this work,we present a method based on tensor networks and the path integral formalism to solve polaron impurity problems.As both the electron and phonon baths can be integrated out via the Feynman–Vernon influence functional in the path integral formalism,our method is free of bath discretization error.It can also flexibly work on imaginary time,Keldysh contour,and L-shaped Kadanoff contour.In addition,our method can naturally resolve several long-existing challenges:(i)non-diagonal hybridization function;(ii)measuring multi-time correlations beyond single-particle Green’s functions.We demonstrate the effectiveness and accuracy of our method with extensive numerical examples against analytic solutions,exact diagonalization,and CTQMC.We also perform full-fledged real-time calculations that have never been done before to our knowledge,which could serve as a benchmarking baseline for future method developments.
基金supported in part by the National Natural Science Foundation of China(62372385).
文摘Dear Editor,This letter proposes the graph tensor alliance attention network(GT-A^(2)T)to represent a dynamic graph(DG)precisely.Its main idea includes 1)Establishing a unified spatio-temporal message propagation framework on a DG via the tensor product for capturing the complex cohesive spatio-temporal interdependencies precisely and 2)Acquiring the alliance attention scores by node features and favorable high-order structural correlations.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11190024 and 11474331)
文摘We propose a generalized Lanczos method to generate the many-body basis states of quantum lattice models using tensor-network states （TNS）. The ground-state wave function is represented as a linear superposition composed from a set of TNS generated by Lanczos iteration. This method improves significantly the accuracy of the tensor-network algorithm and provides an effective way to enlarge the maximal bond dimension of TNS. The ground state such obtained contains significantly more entanglement than each individual TNS, reproducing correctly the logarithmic size dependence of the entanglement entropy in a critical system. The method can be generalized to non-Hamiltonian systems and to the calculation of low-lying excited states, dynamical correlation functions, and other physical properties of strongly correlated systems.
文摘This article discusses the covariance correlation tensor (CCT) in quantum network theory for four Bell bases in detail. Furthermore, it gives the expression of the density operator in terms of CCT for a quantum network of three nodes, thus gives the criterion of entanglement for this case, i.e. the conditions of complete separability and partial separability for a given quantum state of three bodies. Finally it discusses the general case for the quantum network of nodes.
文摘This article discusses the separability of the pure states and mixed states of the quantum network of two nodes by means of the criterion of no entanglement in terms of the covariance correlation tensor in quantum network theory, i.e. for a composite system consisting of two nodes. The covariance correlation tensor is equal to zero for all possible and .
文摘From the comparison of correlation tensor in the theory of quantum network, the Alexander relation matrix in the theory of knot crystals and the identical inversion relations under the action of Pauli matrices, we show that there is a one to one correspondence between four Bell bases and four oriented links of the linkage in knot theory.
基金supported by the National Research Foundation of Korea,No.20100023233
文摘Temporal lobe resection is an important treatment option for epilepsy that involves removal of potentially essential brain regions. Selective amygdalohippocampectomy is a widely performed temporal lobe surgery. We suggest starting the incision for selective amygdalohippocampectomy at the inferior temporal gyrus based on diffusion magnetic resonance imaging（MRI） tractography. Diffusion MRI data from 20 normal participants were obtained from Parkinson＇s Progression Markers Initiative（PPMI） database（www.ppmi-info.org）. A tractography algorithm was applied to extract neuronal fiber information for the temporal lobe, hippocampus, and amygdala. Fiber information was analyzed in terms of the number of fibers and betweenness centrality. Distances between starting incisions and surgical target regions were also considered to explore the length of the surgical path. Middle temporal and superior temporal gyrus regions have higher connectivity values than the inferior temporal gyrus and thus are not good candidates for starting the incision. The distances between inferior temporal gyrus and surgical target regions were shorter than those between middle temporal gyrus and target regions. Thus, the inferior temporal gyrus is a good candidate for starting the incision. Starting the incision from the inferior temporal gyrus would spare the important（in terms of betweenness centrality values） middle region and shorten the distance to the target regions of the hippocampus and amygdala.
基金supported by the National Key R&D Program of China(2019YFE0112000)the Zhejiang Provincial Natural Science Foundation of China(LR21A040001,LDT23F04014F01)the National Natural Science Foundation of China(No.11974307).
文摘The piezoelectric materials enable the mutual conversion between mechanical and electrical energy,which drive a multi-billion dollar industry through their applications as sensors,actuators,and energy harvesters.The third-rank piezoelectric tensor is the core matrices for piezoelectric materials and their devices.However,the high costs of obtaining full piezoelectric tensor data through either experimental or computational methods make a significant challenge.Here,we propose an equivariant attention tensor graph neural network(EATGNN)that can identify crystal symmetry and remain independent of the reference frame,ultimately enabling the accurate prediction of the complete third-rank piezoelectric tensor.Especially,we perform an irreducible decomposition of the piezoelectric tensor into four irreducible representations to efficiently reserve the symmetry under group transformation operations.Our results further demonstrate that this model performs well in both bulk and twodimensional materials.Finally,combining EATGNN with first-principles calculations,we discovered several potential high-performance piezoelectric materials.
基金Supported in part by the National Natural Science Foundation of China(11975116,11665016,11563006)Jiangxi Science Foundation for Distinguished Young Scientists(20192BCB23007)。
文摘The Ryu-Takayanagi(RT)formula plays a large role in the current theory of gauge-gravity duality and emergent geometry phenomena.The recent reinterpretation of this formula in terms of a set of"bit threads"is an interesting effort in understanding holography.In this study,we investigate a quantum generalization of the"bit threads"based on a tensor network,with particular focus on the multi-scale entanglement renormalization ansatz(MERA).We demonstrate that,in the large c limit,isometries of the MERA can be regarded as"sources"(or"sinks")of the information flow,which extensively modifies the original picture of bit threads by introducing a new variableρ:density of the isometries.In this modified picture of information flow,the isometries can be viewed as generators of the flow.The strong subadditivity and related properties of the entanglement entropy are also obtained in this new picture.The large c limit implies that classical gravity can emerge from the information flow.
基金supported in part by the National Key Research and Development Program of China(Grant No.2019YFA0709601)by the National Center for Mathematics and Interdisciplinary Science,CAS.
文摘In this paper,we introduce a type of tensor neural network.For the first time,we propose its numerical integration scheme and prove the computational complexity to be the polynomial scale of the dimension.Based on the tensor product structure,we develop an efficient numerical integration method by using fixed quadrature points for the functions of the tensor neural network.The corresponding machine learning method is also introduced for solving high-dimensional problems.Some numerical examples are also provided to validate the theoretical results and the numerical algorithm.
基金supported by the National Natural Science Foundation of China(Grant No.12274126)supports from the National Natural Science Foundation of China(Grant Nos.12074031,and 12234016)+1 种基金supports from the National Natural Science Foundation of China(Grant Nos.12274287,and 12042507)the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0301900)。
文摘The spin-1/2 model system with antiferromagnetic(AF) couplings on a J1-J2checkerboard lattice, known as the planar pyrochlore model, is strongly frustrated and associated with a two-to-one dimensional crossover. Using the Projected Entangled Simplex States tensor network ansatz, we identify a large number of nearly degenerate states in the frustrated region(J_(1)<J_(2)).Specifically, we find the long-sought crossed-dimer valence bond solid(VBS) state to be the ground state at J_(1)≤J_(2), while various 1D AF correlated states take over the rest. We verify the stability of the VBS state against nematic perturbation. The corresponding bosonic picture provides an intuitive understanding of the low-energy physics. Particularly, it predicts weaker VBS states in the easy-plane limit, which we confirm numerically. Our results clarify the most essential ground state properties of this interesting system and demonstrate the usefulness of bosonic picture in dealing with frustrated magnetism.
基金supported by the National Natural Science Foundation of China(NSFC)/RGC Joint Research Scheme No.N-CUHK427/18the ANR/RGC Joint Research Scheme No.A-CUHK402/18 from the Hong Kong’s Research Grants Council+7 种基金the TNSTRONG ANR-16-CE30-0025,TNTOP ANR-18CE30-0026-01 grants awarded from the French Research Councilsupported by the NSFC(11874078 and 11834014)the Fundamental Research Funds for the Central Universitiessupported by the NSFC(11861161001)the Science,Technology and Innovation Commission of Shenzhen Municipality(ZDSYS20190902092905285)Guangdong Basic and Applied Basic Research Foundation(2020B1515120100)Shenzhen-Hong Kong Cooperation Zone for Technology and Innovation(HZQB-KCZYB-2020050)Center for Computational Science and Engineering at Southern University of Science and Technology。
文摘The nature of the zero-temperature phase diagram of the spin-1/2 J_(1)-J_(2)Heisenberg model on a square lattice has been debated in the past three decades,and it remains one of the fundamental problems unsettled in the study of quantum many-body theory.By using the state-of-the-art tensor network method,specifically,the finite projected entangled pair state(PEPS)algorithm,to simulate the global phase diagram of the J_(1)-J_(2)Heisenberg model up to 24×24 sites,we provide very solid evidences to show that the nature of the intermediate nonmagnetic phase is a gapless quantum spin liquid(QSL),whose spin-spin and dimer-dimer correlations both decay with a power law behavior.There also exists a valence-bond solid(VBS)phase in a very narrow region 0.56■J_(2)/J_(1)≤0.61 before the system enters the well known collinear antiferromagnetic phase.We stress that we make the first detailed comparison between the results of PEPS and the well-established density matrix renormalization group(DMRG)method through one-to-one direct benchmark for small system sizes,and thus give rise to a very solid PEPS calculation beyond DMRG.Our numerical evidences explicitly demonstrate the huge power of PEPS for highly frustrated spin systems.Finally,an effective field theory is also proposed to understand the physical nature of the discovered gapless QSL and its relation to deconfined quantum critical point(DQCP).
基金supported by the National Key R&D Program of China(2022YFA1403700)the National Natural Science Foundation of China(NSFC)and the Research Grants Council(RGC)Joint Research Scheme of the Hong Kong Research Grants Council(N-CUHK427/18)+4 种基金the National Natural Science Foundation of China(12141402)supported by the Science,Technology and Innovation Commission of Shenzhen Municipality(ZDSYS20190902092905285)Guangdong Basic and Applied Basic Research Foundation(2020B1515120100)Center for Computational Science and Engineering at Southern University of Science and Technology.S.S.G.was supported by the National Natural Science Foundation of China(11874078 and 11834014)the Dongguan Key Laboratory of Artificial Intelligence Design for Advanced Materials.
文摘The emergence of exotic quantum phenomena in frustrated magnets is rapidly driving the development of quantum many-body physics,raising fundamental questions on the nature of quantum phase transitions.Here we unveil the behaviour of emergent symmetry involving two extraordinarily representative phenomena,i.e.,the deconfined quantum critical point(DQCP)and the quantum spin liquid(QSL)state.Via large-scale tensor network simulations,we study a spatially anisotropic spin-1/2 square-lattice frustrated antiferromagnetic(AFM)model,namely the J1x-J1y-J2 model,which contains anisotropic nearestneighbor couplings J1x,J1y and the next nearest neighbor coupling J2.For small J1y/J1x,by tuning J2,a direct continuous transition between the AFM and valence bond solid phase is observed.With growing J1y/J1x,a gapless QSL phase gradually emerges between the AFM and VBS phases.We observe an emergent O(4)symmetry along the AFM–VBS transition line,which is consistent with the prediction of DQCP theory.Most surprisingly,we find that such an emergent O(4)symmetry holds for the whole QSL–VBS transition line as well.These findings reveal the intrinsic relationship between the QSL and DQCP from categorical symmetry point of view,and strongly constrain the quantum field theory description of the QSL phase.The phase diagram and critical exponents presented in this paper are of direct relevance to future experiments on frustrated magnets and cold atom systems.
基金supported by the National Science Foundation of U.S.(2011845,2315596 and 2244219).
文摘Graph de-anonymization is a technique used to reveal connections between entities in anonymized graphs,which is crucial in detecting malicious activities,network analysis,social network analysis,and more.Despite its paramount importance,conventional methods often grapple with inefficiencies and challenges tied to obtaining accurate query graph data.This paper introduces a neural-based inexact graph de-anonymization,which comprises an embedding phase,a comparison phase,and a matching procedure.The embedding phase uses a graph convolutional network to generate embedding vectors for both the query and anonymized graphs.The comparison phase uses a neural tensor network to ascertain node resemblances.The matching procedure employs a refined greedy algorithm to discern optimal node pairings.Additionally,we comprehensively evaluate its performance via well-conducted experiments on various real datasets.The results demonstrate the effectiveness of our proposed approach in enhancing the efficiency and performance of graph de-anonymization through the use of graph embedding vectors.
