Neural-Network Quantum State of Transverse-Field Ising Model

Shi, Han-qing; Sun, Xiaoyue; Zeng, Ding-fang

doi:10.1088/0253-6102/71/11/1379

Cited by 6 publications

(4 citation statements)

References 41 publications

(84 reference statements)

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“…The recent state-of-the-art neural networks have been shown to provide high efficient representations of such complex states, making the overwhelming complexity computationally tractable [6,7]. Except for the success in the industrial applications, such as the image and speech recognitions [8], the autonomous driving, and the game of Go [9], neural networks have been widely adopted to study a broad spectrum of areas in physics, ranging from statistical and quantum physics to high energy and cosmology [10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Learning topological defects formation with neural networks in a quantum phase transition

Shi,

Zhang

2024

Commun. Theor. Phys.

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Neural networks possess formidable representational power, rendering them invaluable in solving complex quantum many-body systems. While they excel at analyzing static solutions, nonequilibrium processes, including critical dynamics during a quantum phase transition, pose a greater challenge for neural networks. To address this, we utilize neural networks and machine learning algorithms to investigate the time evolutions, universal statistics, and correlations of topological defects in a one-dimensional transverse-field quantum Ising model. Specifically, our analysis involves computing the energy of the system during a quantum phase transition following a linear quench of the transverse magnetic field strength. The excitation energies satisfy a power-law relation to the quench rate, indicating a proportional relationship between the excitation energy and the kink numbers. Moreover, we establish a universal power-law relationship between the first three cumulants of the kink numbers and the quench rate, indicating a binomial distribution of the kinks. Finally, the normalized kink-kink correlations are also investigated and it is found that the numerical values are consistent with the analytic formula.

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Section: Introductionmentioning

confidence: 99%

Learning topological defects formation with neural networks in a quantum phase transition

Shi,

Zhang

2024

Commun. Theor. Phys.

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“…The NGD has also been used in solving quantum many-body problems [15] where the model can be transformed to a statistical one, and the metric is called Fubini-Study metric tensor [14,16]. In the field of variational Monte Carlo method in neural network [17,18], NGD (also called Stochastic Reconfiguration [19][20][21]) method is also widely used, and the FI matrix is called S matrix. Although the NGD has shown its efficiency in various realm, there comes a question whether the FI matrix is the only choice for the metric in the NGD?…”

Section: Introductionmentioning

confidence: 99%

Generalization to the Natural Gradient Descent

Dong¹,

Le²,

Zhang³

et al. 2022

Preprint

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Optimization problem, which is aimed at finding the global minimal value of a given cost function, is one of the central problem in science and engineering. Various numerical methods have been proposed to solve this problem, among which the Gradient Descent (GD) method is the most popular one due to its simplicity and efficiency. However, the GD method suffers from two main issues: the local minima and the slow convergence especially near the minima point. The Natural Gradient Descent(NGD), which has been proved as one of the most powerful method for various optimization problems in machine learning, tensor network, variational quantum algorithms and so on, supplies an efficient way to accelerate the convergence. Here, we give a unified method to extend the NGD method to a more general situation which keeps the fast convergence by looking for a more suitable metric through introducing a 'proper' reference Riemannian manifold. Our method generalizes the NDG, and may give more insight of the optimization methods.

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“…This neural network formalism, originally inspired by ideas from statistical mechanics, represents a class of energy-based models that found numerous uses in physics describing spin glasses, Ising model [2] and multiple machine-learning applications [20]. In recent years, it has been extended to describe quantum systems by quantum neural network states [9], leading to a flurry of results in condensed matter physics [22], quantum error correction [17,24], quantum computing and beyond [12]. There exist several variations of Boltzmann machines, depending on the underlying graph structure [20].…”

Section: Introductionmentioning

confidence: 99%

Stoquastic ground states are classical thermal distributions

King,

Strelchuk

2020

Preprint

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We study the structure of the ground states of local stoquastic Hamiltonians and show that under mild assumptions the following distributions can efficiently approximate one another: (a) distributions arising from ground states of stoquastic Hamiltonians, (b) distributions arising from ground states of stoquastic frustration-free Hamiltonians, (c) Gibbs distributions of local classical Hamiltonian, and (d) distributions represented by real-valued Deep Boltzmann machines. In addition, we highlight regimes where it is possible to efficiently classically sample from the above distributions.

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Neural-Network Quantum State of Transverse-Field Ising Model

Cited by 6 publications

References 41 publications

Learning topological defects formation with neural networks in a quantum phase transition

Learning topological defects formation with neural networks in a quantum phase transition

Generalization to the Natural Gradient Descent

Stoquastic ground states are classical thermal distributions

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