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

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.

arXiv commentThis paper reviews the technical details of calculating spin-1/2 J1-J2 model using convolutional neural network ansatz on Sunway Supercomputer

References in corpus (18)

• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Large Batch Training of Convolutional Networks
• Optimizing Neural Networks with Kronecker-factored Approximate Curvature
• Green Function Monte Carlo with Stochastic Reconfiguration
• Study of the Two-Dimensional Frustrated J1-J2 Model with Neural Network Quantum States
• Weak binding between two aromatic rings: feeling the van der Waals attraction by quantum Monte Carlo methods
• Neural Quantum States of frustrated magnets: generalization and sign structure
• Dirac-type nodal spin liquid revealed by refined quantum many-body solver using neural-network wave function, correlation ratio, and level spectroscopy
• Optimizing large parameter sets in variational quantum Monte Carlo
• Diffusion Monte Carlo with lattice regularization
• Solving frustrated quantum many-particle models with convolutional neural networks
• Neural network wave functions and the sign problem
• Shampoo: Preconditioned Stochastic Tensor Optimization
• Hybrid convolutional neural network and PEPS wave functions for quantum many-particle states
• Chiral spin states in the pyrochlore Heisenberg magnet: Fermionic mean-field theory and variational Monte Carlo calculations
• Scalable Second Order Optimization for Deep Learning
• Adaptive Neural Network-Based Approximation to Accelerate Eulerian Fluid Simulation
• Marshall-Peierls sign rule in frustrated Heisenberg chains