Optimizing design choices for neural quantum states

Reh, Moritz; Schmitt, Markus; Gärttner, Martin

doi:10.1103/physrevb.107.195115

Cited by 18 publications

(7 citation statements)

References 54 publications

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“…Unfortunately, the performance depends on the symmetrization technique (see, e.g. [21]); therefore, careful consideration of the symmetrization is necessary to obtain a good performance 6 . • Combination.…”

Section: 321mentioning

confidence: 99%

“…Since then, extensions and improvements of the artificial neural network method have been continuously pursued all over the world. Currently, its applications have been extended to simulations of quantum spin systems with geometrical frustration [9][10][11][12][13][14][15][16][17][18][19][20][21][22], itinerant boson systems [23,24], fermion systems [9,[25][26][27][28][29][30][31][32][33][34][35], fermion-boson coupled systems [36], topologically nontrivial quantum states [5,6,[37][38][39][40][41], excited states [15,32,36,[42][43][44], real-time evolution [7,45,46], open quantum systems [47][48]…”

Section: Introductionmentioning

confidence: 99%

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Boltzmann machines and quantum many-body problems

Nomura

2023

J. Phys.: Condens. Matter

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Analyzing quantum many-body problems and elucidating the entangled structure of quantum states is a significant challenge common to a wide range of fields. Recently, a novel approach using machine learning was introduced to address this challenge. The idea is to ‘embed’ nontrivial quantum correlations (quantum entanglement) into artificial neural networks. Through intensive developments, artificial neural network methods are becoming new powerful tools for analyzing quantum many-body problems. Among various artificial neural networks, this topical review focuses on Boltzmann machines and provides an overview of recent developments and applications.

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Section: 321mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Boltzmann machines and quantum many-body problems

Nomura

2023

J. Phys.: Condens. Matter

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“…years, machine learning methods [29,30] have provided a complementary strategy to rationalize phases of matter, often in combination with conventional quantum many-body methods. The demonstrations of these roles played by machine learning methods in tackling many-body problems results in characterizing different phases of matter [31][32][33][34][35][36][37][38][39][40], deep learning of the quantum dynamics [41][42][43][44], obtaining many-body wave functions [45][46][47][48][49], and optimizing the performance of computational simulations [50].…”

Section: Introductionmentioning

confidence: 99%

Transfer learning from Hermitian to non-Hermitian quantum many-body physics

Sayyad,

Lado

2024

J. Phys.: Condens. Matter

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Identifying phase boundaries of interacting systems is one of the key steps to understanding quantum many-body models. The development of various numerical and analytical methods has allowed exploring the phase diagrams of many Hermitian interacting systems. However, numerical challenges and scarcity of analytical solutions hinder obtaining phase boundaries in non-Hermitian many-body models. Recent machine learning methods have emerged as a potential strategy to learn phase boundaries from various observables without having access to the full many-body wavefunction. Here, we show that a machine learning methodology trained solely on Hermitian correlation functions allows identifying phase boundaries of non-Hermitian interacting models. These results demonstrate that Hermitian machine learning algorithms can be redeployed to non-Hermitian models without requiring further training to reveal non-Hermitian phase diagrams. Our findings establish transfer learning as a versatile strategy to leverage Hermitian physics to machine learning non-Hermitian phenomena.

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“…To consider an architecture scalable, both the number of its parameters and the network evaluation cost should at most grow mildly with the system size 𝑁 . [32] The RBMs and its variants violate the first requirement because of a given constant ratio 𝛼 between the number of hidden and visible neurons, the number of parameters grows quadratically. [30] RNNs violate the second requirement with its quadratic scaling computing cost, as the cost of evaluating an unsymmetrized configuration grows linearly with the system size 𝑁 , and the symmetrization gives another factor 𝑁 .…”

mentioning

confidence: 99%

“…[30] RNNs violate the second requirement with its quadratic scaling computing cost, as the cost of evaluating an unsymmetrized configuration grows linearly with the system size 𝑁 , and the symmetrization gives another factor 𝑁 . [32] Meanwhile, the autoregressive property imposes specific constraints on the architecture of RNNs, thereby restricting their expressiveness. [33] Recently proposed transformer-based wavefunctions also come at a significant computational cost due to their quadratic complexity with respect to the input sequence length.…”

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confidence: 99%

Solving Quantum Many-Particle Models with Graph Attention Network

Yu 于,

Lin 林

2024

Chinese Phys. Lett.

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Deep learning methods have been shown to be effective in representing ground-state wavefunctions of quantum many-body systems, but the existing approaches cannot be easily used for non-square like or large systems. Here, we propose a variational ansatz based on the graph attention network (GAT) which learns distributed latent representations and can be used on non-square lattices. The GAT-based ansatz has a computational complexity that grows linearly with the system size and can be extended to large systems naturally. Numerical results show that our method achieves the state-of-the-art results on spin-1/2 J 1-J 2 Heisenberg models over the square, honeycomb, triangular, and kagome lattices with different interaction strengths and lattice sizes (up to 24 × 24 for square lattice). The method also provides excellent results for the ground states of transverse field Ising models on square lattices. The GAT-based techniques are effcient and versatile and hold promise for studying large quantum many-body systems with exponentially-sized objects.

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Optimizing design choices for neural quantum states

Cited by 18 publications

References 54 publications

Boltzmann machines and quantum many-body problems

Boltzmann machines and quantum many-body problems

Transfer learning from Hermitian to non-Hermitian quantum many-body physics

Solving Quantum Many-Particle Models with Graph Attention Network

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