Transformer-based neural-network quantum states(NNQS)have shown great promise in representing quantum manybody ground states,offering high flexibility and accuracy.However,the interpretability of such models remains l...Transformer-based neural-network quantum states(NNQS)have shown great promise in representing quantum manybody ground states,offering high flexibility and accuracy.However,the interpretability of such models remains limited,especially in terms of connecting network components to physically meaningful quantities.We propose that the attention mechanism—a central module in transformer architectures—explicitly models the conditional information flow between orbitals.Intuitively,as the transformer learns to predict orbital configurations by optimizing an energy functional,it approximates the conditional probability distribution p(xn|x_(1),...,x_(n-1)),implicitly encoding conditional mutual information(CMI)among orbitals.This suggests a natural correspondence between attention maps and CMI structures in quantum systems.To probe this idea,we compare weighted attention scores from trained transformer wavefunction ansatze with CMI matrices across several representative small molecules.In most cases,we observe a positive rank-level correlation(Kendall's tau)between attention and CMI,suggesting that the learned attention can reflect physically relevant orbital dependencies.This study provides a quantitative link between transformer attention and conditional mutual information in the NNQS setting.Our results provide a step toward explainable deep learning in quantum chemistry,pointing to opportunities in interpreting attention as a proxy for physical correlations.展开更多
Quantum computing is a rapidly-emerging technology that is widely expected to solve valuable problems in physics and chemistry.After quantum computational advantage in the task of sampling has been demonstrated on bot...Quantum computing is a rapidly-emerging technology that is widely expected to solve valuable problems in physics and chemistry.After quantum computational advantage in the task of sampling has been demonstrated on both photonic and superconductor quantum platforms[1,2],quantum computing is urgently seeking to solve problems of practical interest that are often intractable or at least computationally demanding for classical computers[3].展开更多
The neural-network quantumstates(NNQS)method is rapidly emerging as a powerful tool in quantum mechanisms.While significant advancements have been achieved in simulating simple molecules using NNQS,the ab initio simul...The neural-network quantumstates(NNQS)method is rapidly emerging as a powerful tool in quantum mechanisms.While significant advancements have been achieved in simulating simple molecules using NNQS,the ab initio simulation of complex solid-state materials remains challenging.Here in this work,we have adopted the periodic density matrix embedding theory to extend the NNQS method to deal with complex solid-state systems.Our approach notably reduces thecomputational problem size while maintaining high accuracy.Wehave validated the accuracy and efficiency of our method against traditional methodologies and experimental data in extended systems,and have investigated the magnetic ordering and charge density wave state in transition metal compounds.The findings from our research indicate that the integration of quantum embedding with intuitive chemical fragmentation can significantly enhance the NNQS simulation of realistic materials.展开更多
基金partially supported by the National Natural Science Foundation of China(21825302)the Fundamental Research Funds for the Central Universities(WK20600-00018),the National Supercomputing Center in Jinan,and the USTC Supercomputing Center.
基金supported by the National Natural Science Foundation of China(Grant No.T2222026)the CAS Project for Young Scientists in Basic Research(Grant No.YSBR-034)the Robotic AIScientist Platform of the Chinese Academy of Sciences。
文摘Transformer-based neural-network quantum states(NNQS)have shown great promise in representing quantum manybody ground states,offering high flexibility and accuracy.However,the interpretability of such models remains limited,especially in terms of connecting network components to physically meaningful quantities.We propose that the attention mechanism—a central module in transformer architectures—explicitly models the conditional information flow between orbitals.Intuitively,as the transformer learns to predict orbital configurations by optimizing an energy functional,it approximates the conditional probability distribution p(xn|x_(1),...,x_(n-1)),implicitly encoding conditional mutual information(CMI)among orbitals.This suggests a natural correspondence between attention maps and CMI structures in quantum systems.To probe this idea,we compare weighted attention scores from trained transformer wavefunction ansatze with CMI matrices across several representative small molecules.In most cases,we observe a positive rank-level correlation(Kendall's tau)between attention and CMI,suggesting that the learned attention can reflect physically relevant orbital dependencies.This study provides a quantitative link between transformer attention and conditional mutual information in the NNQS setting.Our results provide a step toward explainable deep learning in quantum chemistry,pointing to opportunities in interpreting attention as a proxy for physical correlations.
基金supported by the National Natural Science Foundation of China(T2222026,22073086,21825302,and 22288201)Innovation Program for Quantum Science and Technology(2021ZD0303306)+1 种基金Anhui Initiative in Quantum Information Technologies(AHY090400)the Fundamental Research Funds for the Central Universities(WK2060000018)。
文摘Quantum computing is a rapidly-emerging technology that is widely expected to solve valuable problems in physics and chemistry.After quantum computational advantage in the task of sampling has been demonstrated on both photonic and superconductor quantum platforms[1,2],quantum computing is urgently seeking to solve problems of practical interest that are often intractable or at least computationally demanding for classical computers[3].
基金the National Natural Science Foundation of China(T2222026,22288201)Innovation Program for Quantum Science and Technology(2021ZD0303306).
文摘The neural-network quantumstates(NNQS)method is rapidly emerging as a powerful tool in quantum mechanisms.While significant advancements have been achieved in simulating simple molecules using NNQS,the ab initio simulation of complex solid-state materials remains challenging.Here in this work,we have adopted the periodic density matrix embedding theory to extend the NNQS method to deal with complex solid-state systems.Our approach notably reduces thecomputational problem size while maintaining high accuracy.Wehave validated the accuracy and efficiency of our method against traditional methodologies and experimental data in extended systems,and have investigated the magnetic ordering and charge density wave state in transition metal compounds.The findings from our research indicate that the integration of quantum embedding with intuitive chemical fragmentation can significantly enhance the NNQS simulation of realistic materials.
