Along the way initiated by Carleo and Troyer [G. Carleo and M. Troyer, Science 355(2017) 602], we construct the neural-network quantum state of transverse-field Ising model(TFIM) by an unsupervised machine learning me...Along the way initiated by Carleo and Troyer [G. Carleo and M. Troyer, Science 355(2017) 602], we construct the neural-network quantum state of transverse-field Ising model(TFIM) by an unsupervised machine learning method. Such a wave function is a map from the spin-configuration space to the complex number field determined by an array of network parameters. To get the ground state of the system, values of the network parameters are calculated by a Stochastic Reconfiguration(SR) method. We provide for this SR method an understanding from action principle and information geometry aspects. With this quantum state, we calculate key observables of the system, the energy,correlation function, correlation length, magnetic moment, and susceptibility. As innovations, we provide a high e?ciency method and use it to calculate entanglement entropy(EE) of the system and get results consistent with previous work very well.展开更多
The quantum many-body problem(QMBP) has become a hot topic in high-energy physics and condensed-matter physics. With an exponential increase in the dimensions of Hilbert space, it becomes very challenging to solve the...The quantum many-body problem(QMBP) has become a hot topic in high-energy physics and condensed-matter physics. With an exponential increase in the dimensions of Hilbert space, it becomes very challenging to solve the QMBP, even with the most powerful computers. With the rapid development of machine learning, artificial neural networks provide a powerful tool that can represent or approximate quantum many-body states. In this paper, we aim to explicitly construct the neural network representations of hypergraph states. We construct the neural network representations for any k-uniform hypergraph state and any hypergraph state,respectively, without stochastic optimization of the network parameters. Our method constructively shows that all hypergraph states can be represented precisely by the appropriate neural networks introduced in [Science 355(2017) 602] and formulated in [Sci. China-Phys.Mech. Astron. 63(2020) 210312].展开更多
Starting with the theoretical basis of quantum computing, entanglement has been explored as one of the key resources required for quantum computation, the functional dependence of the entanglement measures on spin cor...Starting with the theoretical basis of quantum computing, entanglement has been explored as one of the key resources required for quantum computation, the functional dependence of the entanglement measures on spin correlation functions has been established and the role of entanglement in implementation of QNN has been emphasized. Necessary and sufficient conditions for the general two-qubit state to be maximally entangled state (MES) have been obtained and a new set of MES constituting a very powerful and reliable eigen basis (different from magic bases) of two-qubit systems has been constructed. In terms of the MES constituting this basis, Bell’s States have been generated and all the qubits of two-qubit system have been obtained. Carrying out the correct computation of XOR function in neural network, it has been shown that QNN requires the proper correlation between the input and output qubits and the presence of appropriate entanglement in the system guarantees this correlation.展开更多
量子非局域性作为一种极具价值的量子资源,在诸多量子信息处理任务中扮演着不可或缺的关键角色.对非局域性进行精准表征与有效探测,始终是量子信息理论研究与实验探索中非常有挑战性的重要课题.如何在结构复杂的多体量子系统里准确识别...量子非局域性作为一种极具价值的量子资源,在诸多量子信息处理任务中扮演着不可或缺的关键角色.对非局域性进行精准表征与有效探测,始终是量子信息理论研究与实验探索中非常有挑战性的重要课题.如何在结构复杂的多体量子系统里准确识别并验证量子非局域性现象,如何设计出更为高效的非局域性探测方法,已成为亟待解决的重要科学问题.本文致力于多体量子非局域性的探测问题,着重探究如何借助Svetlichny不等式来实现多体量子非局域性的探测.首先探讨了Svetlichny不等式的最大量子违背,构造了达到Svetlichny不等式的最大量子违背的量子态与可观测量集,展示了如何构造其他的量子态与可观测量集来实现其最大量子违背,以此阐明了实现Svetlichny不等式最大量子违背的量子态和可观测量集是不唯一的.其次,为了寻找更多违背Svetlichny不等式的量子态和可观测量集,借助量子态的神经网络表示构建了神经网络量子态,通过优化算法对网络参数进行优化来实现Svetlichny不等式的违背,进而探测到非局域态.通过与经典的Nelder-Mead单纯形法对比,发现量子变分蒙特卡罗(variational Monte Carlo,VMC)方法在效率与精度上更适配基于神经网络量子态的非局域性探测,并在不同哈密顿量下成功实现了借助神经网络量子态与VMC方法对多体量子纯态非局域性的探测.本研究不仅证实了基于神经网络量子态与VMC方法的多体量子非局域性探测在理论上与技术上的可行性,同时也为非局域性探测领域提供了颇具价值的研究新见解,更为借助神经网络解决复杂的量子多体问题开拓了全新的研究思路.展开更多
Machine learning is currently the most active interdisciplinary field having numerous applications; additionally, machine-learning techniques are used to research quantum many-body problems. In this study, we first pr...Machine learning is currently the most active interdisciplinary field having numerous applications; additionally, machine-learning techniques are used to research quantum many-body problems. In this study, we first propose neural network quantum states(NNQSs) with general input observables and explore a few related properties, such as the tensor product and local unitary operation. Second, we determine the necessary and sufficient conditions for the representability of a general graph state using normalized NNQS. Finally, to quantify the approximation degree of a given pure state, we define the best approximation degree using normalized NNQSs. Furthermore, we observe that some N-qubit states can be represented by a normalized NNQS, such as separable pure states, Bell states and GHZ states.展开更多
Quantum many-body problem(QMBP)has become a hot topic in high energy physics and condensed matter physics.With the exponential increasing of the dimension of the Hilbert space,it becomes a big challenge to solve the Q...Quantum many-body problem(QMBP)has become a hot topic in high energy physics and condensed matter physics.With the exponential increasing of the dimension of the Hilbert space,it becomes a big challenge to solve the QMBP even with the most powerful computers.With the rapid development of machine learning,artificial neural networks provide a powerful tool to represent or approximate quantum many-body states.In this paper,we aim to construct explicitly the neural network representations of graph states,without stochastic optimization of the network parameters.Our method shows constructively that all graph states can be represented precisely by proper neural networks originated from[Science,355,602(2017)]and formulated in[Sci.China-Phys.Mech.Astron.,63,210312(2020)].展开更多
电池荷电状态(state of charge,SOC)的预测是电动汽车电池管理系统的关键任务之一,为此对锂电池荷电状态的预测进行了研究,提出了一种基于QPSO-BP神经网络的锂电池SOC预测。在分析了磷酸铁锂(LiFePO4)电池充放电机理后,运用MATLAB人工...电池荷电状态(state of charge,SOC)的预测是电动汽车电池管理系统的关键任务之一,为此对锂电池荷电状态的预测进行了研究,提出了一种基于QPSO-BP神经网络的锂电池SOC预测。在分析了磷酸铁锂(LiFePO4)电池充放电机理后,运用MATLAB人工神经网络工具箱建立基于量子微粒群算法(QPSO)的BP(back propagation)神经网络模型,用于预测锂离子电池充放电过程中的任一状态下的SOC。仿真实验验证了方法的准确性。结果表明,与现有的神经网络预测方法相比,基于QPSO-BP神经网络的锂电池SOC预测方法准确度高,且具备很好的实用性。展开更多
基金Supported by the Natural Science Foundation of China under Grant No.11875082
文摘Along the way initiated by Carleo and Troyer [G. Carleo and M. Troyer, Science 355(2017) 602], we construct the neural-network quantum state of transverse-field Ising model(TFIM) by an unsupervised machine learning method. Such a wave function is a map from the spin-configuration space to the complex number field determined by an array of network parameters. To get the ground state of the system, values of the network parameters are calculated by a Stochastic Reconfiguration(SR) method. We provide for this SR method an understanding from action principle and information geometry aspects. With this quantum state, we calculate key observables of the system, the energy,correlation function, correlation length, magnetic moment, and susceptibility. As innovations, we provide a high e?ciency method and use it to calculate entanglement entropy(EE) of the system and get results consistent with previous work very well.
基金Supported by the National Natural Science Foundation of China(Nos.12001480,11871318)the Applied Basic Research Program of Shanxi Province(No.201901D211461)+2 种基金the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi(No.2020L0554)the Excellent Doctoral Research Project of Shanxi Province(No.QZX-2020001)the PhD Start-up Project of Yuncheng University(No.YQ-2019021)。
文摘The quantum many-body problem(QMBP) has become a hot topic in high-energy physics and condensed-matter physics. With an exponential increase in the dimensions of Hilbert space, it becomes very challenging to solve the QMBP, even with the most powerful computers. With the rapid development of machine learning, artificial neural networks provide a powerful tool that can represent or approximate quantum many-body states. In this paper, we aim to explicitly construct the neural network representations of hypergraph states. We construct the neural network representations for any k-uniform hypergraph state and any hypergraph state,respectively, without stochastic optimization of the network parameters. Our method constructively shows that all hypergraph states can be represented precisely by the appropriate neural networks introduced in [Science 355(2017) 602] and formulated in [Sci. China-Phys.Mech. Astron. 63(2020) 210312].
文摘Starting with the theoretical basis of quantum computing, entanglement has been explored as one of the key resources required for quantum computation, the functional dependence of the entanglement measures on spin correlation functions has been established and the role of entanglement in implementation of QNN has been emphasized. Necessary and sufficient conditions for the general two-qubit state to be maximally entangled state (MES) have been obtained and a new set of MES constituting a very powerful and reliable eigen basis (different from magic bases) of two-qubit systems has been constructed. In terms of the MES constituting this basis, Bell’s States have been generated and all the qubits of two-qubit system have been obtained. Carrying out the correct computation of XOR function in neural network, it has been shown that QNN requires the proper correlation between the input and output qubits and the presence of appropriate entanglement in the system guarantees this correlation.
文摘量子非局域性作为一种极具价值的量子资源,在诸多量子信息处理任务中扮演着不可或缺的关键角色.对非局域性进行精准表征与有效探测,始终是量子信息理论研究与实验探索中非常有挑战性的重要课题.如何在结构复杂的多体量子系统里准确识别并验证量子非局域性现象,如何设计出更为高效的非局域性探测方法,已成为亟待解决的重要科学问题.本文致力于多体量子非局域性的探测问题,着重探究如何借助Svetlichny不等式来实现多体量子非局域性的探测.首先探讨了Svetlichny不等式的最大量子违背,构造了达到Svetlichny不等式的最大量子违背的量子态与可观测量集,展示了如何构造其他的量子态与可观测量集来实现其最大量子违背,以此阐明了实现Svetlichny不等式最大量子违背的量子态和可观测量集是不唯一的.其次,为了寻找更多违背Svetlichny不等式的量子态和可观测量集,借助量子态的神经网络表示构建了神经网络量子态,通过优化算法对网络参数进行优化来实现Svetlichny不等式的违背,进而探测到非局域态.通过与经典的Nelder-Mead单纯形法对比,发现量子变分蒙特卡罗(variational Monte Carlo,VMC)方法在效率与精度上更适配基于神经网络量子态的非局域性探测,并在不同哈密顿量下成功实现了借助神经网络量子态与VMC方法对多体量子纯态非局域性的探测.本研究不仅证实了基于神经网络量子态与VMC方法的多体量子非局域性探测在理论上与技术上的可行性,同时也为非局域性探测领域提供了颇具价值的研究新见解,更为借助神经网络解决复杂的量子多体问题开拓了全新的研究思路.
基金supported by the National Natural Science Foundation of China(Grant Nos.11871318,11771009,11571213,and 11601300)the Fundamental Research Funds for the Central Universities(Grant Nos.GK201703093,and GK201801011)+2 种基金the Natural Science Basic Research Plan in Shaanxi Province of China(Grant No.2018JM1020)the Shaanxi Province Innovation Ability Support Program(Grant No.2018KJXX-054)the Subject Research Project of Yuncheng University(Grant No.XK-2018032)
文摘Machine learning is currently the most active interdisciplinary field having numerous applications; additionally, machine-learning techniques are used to research quantum many-body problems. In this study, we first propose neural network quantum states(NNQSs) with general input observables and explore a few related properties, such as the tensor product and local unitary operation. Second, we determine the necessary and sufficient conditions for the representability of a general graph state using normalized NNQS. Finally, to quantify the approximation degree of a given pure state, we define the best approximation degree using normalized NNQSs. Furthermore, we observe that some N-qubit states can be represented by a normalized NNQS, such as separable pure states, Bell states and GHZ states.
基金Supported by the National Natural Science Foundation of China (Grant Nos.12001480,11871318)Applied Basic Research Program of Shanxi Province (Grant No.201901D211461)+2 种基金Scientific and Technologial Innovation Programs of Higher Education Institutions in Shanxi (Grant No.2020L0554)Excellent Doctoral Research Pro ject of Shanxi Province (Grant No.QZX-2020001)PhD Start-up Pro ject of Yuncheng University (Grant No.YQ-2019021)。
文摘Quantum many-body problem(QMBP)has become a hot topic in high energy physics and condensed matter physics.With the exponential increasing of the dimension of the Hilbert space,it becomes a big challenge to solve the QMBP even with the most powerful computers.With the rapid development of machine learning,artificial neural networks provide a powerful tool to represent or approximate quantum many-body states.In this paper,we aim to construct explicitly the neural network representations of graph states,without stochastic optimization of the network parameters.Our method shows constructively that all graph states can be represented precisely by proper neural networks originated from[Science,355,602(2017)]and formulated in[Sci.China-Phys.Mech.Astron.,63,210312(2020)].
文摘电池荷电状态(state of charge,SOC)的预测是电动汽车电池管理系统的关键任务之一,为此对锂电池荷电状态的预测进行了研究,提出了一种基于QPSO-BP神经网络的锂电池SOC预测。在分析了磷酸铁锂(LiFePO4)电池充放电机理后,运用MATLAB人工神经网络工具箱建立基于量子微粒群算法(QPSO)的BP(back propagation)神经网络模型,用于预测锂离子电池充放电过程中的任一状态下的SOC。仿真实验验证了方法的准确性。结果表明,与现有的神经网络预测方法相比,基于QPSO-BP神经网络的锂电池SOC预测方法准确度高,且具备很好的实用性。
