Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2108.13830 · IEEE Transactions on Parallel and Distributed Systems

Bridging the Gap between Deep Learning and Frustrated Quantum Spin System for Extreme-Scale Simulations on New Generation of Sunway Supercomputer

Mingfan Li, Junshi Chen, Qian Xiao, Fei Wang, Qingcai Jiang, Xuncheng Zhao, Rongfen Lin, Hong An, Xiao Liang, Lixin He

Published Jan 25, 2022• 21 citations
arXivHTMLPDF

Abstract

Efficient numerical methods are promising tools for delivering unique insights into the fascinating properties of physics, such as the highly frustrated quantum many-body systems. However, the computational complexity of obtaining the wave functions for accurately describing the quantum states increases exponentially with respect to particle number. Here we present a novel convolutional neural network (CNN) for simulating the two-dimensional highly frustrated spin-$1/2$$J_1-J_2$Heisenberg model, meanwhile the simulation is performed at an extreme scale system with low cost and high scalability. By ingenious employment of transfer learning and CNN’s translational invariance, we successfully investigate the quantum system with the lattice size up to$24\times 24$, within 30 million cores of the new generation of sunway supercomputer. The final achievement demonstrates the effectiveness of CNN-based representation of quantum-state and brings the state-of-the-art record up to a brand-new level from both aspects of remarkable accuracy and unprecedented scales.

DOI
10.1109/tpds.2022.3145163

Related papers

Two-dimensional frustrated J1−J2 model studied with neural network quantum states

Kenny Choo, Titus Neupert, Giuseppe Carleo

The use of artificial neural networks to represent quantum wave functions has recently attracted interest as a way to solve complex many-body problems. The potential of these variational parametrizations has been supported by analytical and numerical evidence in controlled benchmarks. While approaching the end of the early research phase in this field, it becomes increasingly important to show how neural-network states perform for models and physical problems that constitute a clear open challenge for other many-body computational methods. In this paper, we start addressing this aspect, concentrating on a presently unsolved model describing two-dimensional frustrated magnets. Using a fully convolutional neural network model as a variational ans\"atz, we study the frustrated spin-1/$2{J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model on the square lattice. We demonstrate that the resulting predictions for both ground-state energies and properties are competitive with, and often improve upon, existing state-of-the-art methods. In a relatively small region in the parameter space, corresponding to the maximally frustrated regime, our ans\"atz exhibits comparatively good but not the best performance. The gap between the complexity of the models adopted here and those routinely adopted in deep-learning applications is, however, still substantial, such that further improvements in future generations of neural-network quantum states are likely to be expected.

arXiv:1903.06713•Physical review. B./Physical review. B•Sep 11, 2019•237 citations

Solving frustrated quantum many-particle models with convolutional neural networks

Xiao Liang, Wen-Yuan Liu, Peize Lin +3 more

Recently, there has been significant progress in solving quantum many-particle problems via machine learning based on the restricted Boltzmann machine. However, it is still highly challenging to solve frustrated models via machine learning, which has not been demonstrated so far. In this paper, we design a brand new convolutional neural network (CNN) to solve such quantum many-particle problems. We demonstrate, for the first time, solving the highly frustrated spin-1/2 ${J}_{1}\ensuremath{-}{J}_{2}$ antiferromagnetic Heisenberg model on square lattices via CNN. The energy per site achieved by the CNN is even better than previous string-bond-state calculations. Our work therefore opens up a new routine to solve challenging frustrated quantum many-particle problems using machine learning.

arXiv:1807.09422•Physical review. B./Physical review. B•Sep 24, 2018•103 citations

Interpreting convolutional neural networks' low-dimensional approximation to quantum spin systems

Yilong Ju, Shah Saad Alam, Jonathan Minoff +3 more

Convolutional neural networks (CNNs) have been employed along with variational Monte Carlo methods for finding the ground state of quantum many-body spin systems with great success. However, it remains uncertain how CNNs, with a model complexity that scales at most linearly with the number of particles, solve the “curse of dimensionality” and efficiently represent wavefunctions in exponentially large Hilbert spaces. In this work, we use methodologies from information theory, group theory and machine learning, to elucidate how CNN captures relevant physics of quantum systems. We connect CNNs to a class of restricted maximum entropy (MaxEnt) and entangled plaquette correlator product state (EP-CPS) models that approximate symmetry constrained classical correlations between subsystems. For the final part of the puzzle, inspired by similar analyses for matrix product states and tensor networks, we show that the CNNs rely on the spectrum of each subsystem's entanglement Hamiltonians as captured by the size of the convolutional filter. All put together, these allow CNNs to simulate exponential quantum wave functions using a model that scales at most linear in system size as well as provide clues into when CNNs might fail to simulate Hamiltonians. We incorporate our insights into a new training algorithm and demonstrate its improved efficiency, accuracy, and robustness. Finally, we use regression analysis to show how the CNNs solutions can be used to identify salient physical features of the system that are the most relevant to an efficient approximation. Our integrated approach can be extended to similarly analyzing other neural network architectures and quantum spin systems.

arXiv:2210.00692•Physical Review Research•Jan 23, 2025•0 citations

AI for Quantum Mechanics: High Performance Quantum Many-Body Simulations via Deep Learning

Xuncheng Zhao, Mingfan Li, Qian Xiao +8 more

Solving quantum many-body problems is one of the most fascinating research fields in condensed matter physics. An efficient numerical method is crucial to understand the mechanism of novel physics, such as the high Tc superconductivity, as one has to find the optimal solution in the exponentially large Hilbert space. The development of Artificial Intelligence (AI) provides a unique opportunity to solve the quantum many-body problems, but there is still a large gap from the goal. In this work, we present a novel computational framework, and adapt it to the Sunway supercomputer. With highly efficient scalability up to 40 million heterogeneous cores, we can drastically increase the number of variational parameters, which greatly improves the accuracy of the solutions. The investigations of the spin-1/2 J1-J2 model and the t-J model achieve unprecedented accuracy and time-to-solution far beyond the previous state of the art.

International Conference for High Performance Computing, Networking, Storage and Analysis (SC)•Nov 1, 2022•14 citations

Disentangling Tensor Network States with Deep Neural Network

Chaohui Fan, Bo Zhan, Yuntian Gu +5 more

We introduce Neural Tensor Network States ($ν$TNS), a variational many-body wave-function ansatz that integrates deep neural networks with tensor-network architectures. In the $ν$TNS framework, a neural network serves as a disentangler of the wave-function, transforming the physical degrees of freedom into renormalized variables with much less entanglement. The renormalized state is then efficiently encoded by a back-flow tensor network. This construction yields a compact yet highly expressive representation of strongly correlated quantum states. Using convolutional neural networks combined with matrix product states as a concrete implementation, we obtain state-of-the-art variational energies for the spin-$1/2$ $J_1$-$J_2$ Heisenberg model on the square lattice at the highly frustrated point $J_2/J_1=0.5$, for systems up to $20\times 20$ with periodic boundary conditions. Finite-size scaling of spin, dimer, and plaquette correlations exhibits power-law decay without magnetic or valence-bond long-range order, consistent with a gapless quantum spin-liquid ground state at that point.This $ν$TNS framework is flexible and naturally extensible to other neural and tensor-network structures, offering a general platform for investigating strongly correlated quantum many-body systems.

cond-mat.str-elCross-listedarXiv:2603.14425•Mar 17, 2026•0 citations

Deep learning representations for quantum many-body systems on heterogeneous hardware

Xiao Liang, Mingfan Li, Qian Xiao +4 more

Abstract The quantum many-body problems are important for condensed matter physics, however solving the problems are challenging because the Hilbert space grows exponentially with the size of the problem. The recently developed deep learning methods provide a promising new route to solve long-standing quantum many-body problems. We report that a deep learning based simulation can achieve solutions with competitive precision for the spin J 1 – J 2 model and fermionic t-J model, on rectangular lattices within periodic boundary conditions. The optimizations of the deep neural networks are performed on the heterogeneous platforms, such as the new generation Sunway supercomputer and the multi graphical-processing-unit clusters. Both high scalability and high performance are achieved within an AI-HPC hybrid framework. The accomplishment of this work opens the door to simulate spin and fermionic lattice models with state-of-the-art lattice size and precision.

arXiv:2204.07816•Machine Learning Science and Technology•Mar 1, 2023•15 citations
Efficient numerical methods are promising tools for delivering unique insights into the fascinating properties of physics, such as the highly frustrated quantum many-body systems. However, the computational complexity of obtaining the wave functions for accurately describing the quantum states increases exponentially with respect to particle number. Here we present a novel convolutional neural network (CNN) for simulating the two-dimensional highly frustrated spin-1/2$$J_1-J_2Heisenberg model, meanwhile the simulation is performed at an extreme scale system with low cost and high scalability. By ingenious employment of transfer learning and CNN’s translational invariance, we successfully investigate the quantum system with the lattice size up to24×2424\times 2424×24, within 30 million cores of the new generation of sunway supercomputer. The final achievement demonstrates the effectiveness of CNN-based representation of quantum-state and brings the state-of-the-art record up to a brand-new level from both aspects of remarkable accuracy and unprecedented scales.
The use of artificial neural networks to represent quantum wave functions has recently attracted interest as a way to solve complex many-body problems. The potential of these variational parametrizations has been supported by analytical and numerical evidence in controlled benchmarks. While approaching the end of the early research phase in this field, it becomes increasingly important to show how neural-network states perform for models and physical problems that constitute a clear open challenge for other many-body computational methods. In this paper, we start addressing this aspect, concentrating on a presently unsolved model describing two-dimensional frustrated magnets. Using a fully convolutional neural network model as a variational ans\"atz, we study the frustrated spin-1/$2{J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model on the square lattice. We demonstrate that the resulting predictions for both ground-state energies and properties are competitive with, and often improve upon, existing state-of-the-art methods. In a relatively small region in the parameter space, corresponding to the maximally frustrated regime, our ans\"atz exhibits comparatively good but not the best performance. The gap between the complexity of the models adopted here and those routinely adopted in deep-learning applications is, however, still substantial, such that further improvements in future generations of neural-network quantum states are likely to be expected.
Recently, there has been significant progress in solving quantum many-particle problems via machine learning based on the restricted Boltzmann machine. However, it is still highly challenging to solve frustrated models via machine learning, which has not been demonstrated so far. In this paper, we design a brand new convolutional neural network (CNN) to solve such quantum many-particle problems. We demonstrate, for the first time, solving the highly frustrated spin-1/2 ${J}_{1}\ensuremath{-}{J}_{2}$ antiferromagnetic Heisenberg model on square lattices via CNN. The energy per site achieved by the CNN is even better than previous string-bond-state calculations. Our work therefore opens up a new routine to solve challenging frustrated quantum many-particle problems using machine learning.
Convolutional neural networks (CNNs) have been employed along with variational Monte Carlo methods for finding the ground state of quantum many-body spin systems with great success. However, it remains uncertain how CNNs, with a model complexity that scales at most linearly with the number of particles, solve the “curse of dimensionality” and efficiently represent wavefunctions in exponentially large Hilbert spaces. In this work, we use methodologies from information theory, group theory and machine learning, to elucidate how CNN captures relevant physics of quantum systems. We connect CNNs to a class of restricted maximum entropy (MaxEnt) and entangled plaquette correlator product state (EP-CPS) models that approximate symmetry constrained classical correlations between subsystems. For the final part of the puzzle, inspired by similar analyses for matrix product states and tensor networks, we show that the CNNs rely on the spectrum of each subsystem's entanglement Hamiltonians as captured by the size of the convolutional filter. All put together, these allow CNNs to simulate exponential quantum wave functions using a model that scales at most linear in system size as well as provide clues into when CNNs might fail to simulate Hamiltonians. We incorporate our insights into a new training algorithm and demonstrate its improved efficiency, accuracy, and robustness. Finally, we use regression analysis to show how the CNNs solutions can be used to identify salient physical features of the system that are the most relevant to an efficient approximation. Our integrated approach can be extended to similarly analyzing other neural network architectures and quantum spin systems.
Solving quantum many-body problems is one of the most fascinating research fields in condensed matter physics. An efficient numerical method is crucial to understand the mechanism of novel physics, such as the high Tc superconductivity, as one has to find the optimal solution in the exponentially large Hilbert space. The development of Artificial Intelligence (AI) provides a unique opportunity to solve the quantum many-body problems, but there is still a large gap from the goal. In this work, we present a novel computational framework, and adapt it to the Sunway supercomputer. With highly efficient scalability up to 40 million heterogeneous cores, we can drastically increase the number of variational parameters, which greatly improves the accuracy of the solutions. The investigations of the spin-1/2 J1-J2 model and the t-J model achieve unprecedented accuracy and time-to-solution far beyond the previous state of the art.
We introduce Neural Tensor Network States (νννTNS), a variational many-body wave-function ansatz that integrates deep neural networks with tensor-network architectures. In the νννTNS framework, a neural network serves as a disentangler of the wave-function, transforming the physical degrees of freedom into renormalized variables with much less entanglement. The renormalized state is then efficiently encoded by a back-flow tensor network. This construction yields a compact yet highly expressive representation of strongly correlated quantum states. Using convolutional neural networks combined with matrix product states as a concrete implementation, we obtain state-of-the-art variational energies for the spin-1/21/21/2 J1J_1J1​-J2J_2J2​ Heisenberg model on the square lattice at the highly frustrated point J2/J1=0.5J_2/J_1=0.5J2​/J1​=0.5, for systems up to 20×2020\times 2020×20 with periodic boundary conditions. Finite-size scaling of spin, dimer, and plaquette correlations exhibits power-law decay without magnetic or valence-bond long-range order, consistent with a gapless quantum spin-liquid ground state at that point.This νννTNS framework is flexible and naturally extensible to other neural and tensor-network structures, offering a general platform for investigating strongly correlated quantum many-body systems.
Abstract The quantum many-body problems are important for condensed matter physics, however solving the problems are challenging because the Hilbert space grows exponentially with the size of the problem. The recently developed deep learning methods provide a promising new route to solve long-standing quantum many-body problems. We report that a deep learning based simulation can achieve solutions with competitive precision for the spin J 1 – J 2 model and fermionic t-J model, on rectangular lattices within periodic boundary conditions. The optimizations of the deep neural networks are performed on the heterogeneous platforms, such as the new generation Sunway supercomputer and the multi graphical-processing-unit clusters. Both high scalability and high performance are achieved within an AI-HPC hybrid framework. The accomplishment of this work opens the door to simulate spin and fermionic lattice models with state-of-the-art lattice size and precision.