Supplementing Recurrent Neural Network Wave Functions with Symmetry and Annealing to Improve Accuracy

• URL: http://arxiv.org/abs/2207.14314v2
• Date: Fri, 12 Jan 2024 22:59:47 GMT
• Title: Supplementing Recurrent Neural Network Wave Functions with Symmetry and Annealing to Improve Accuracy
• Authors: Mohamed Hibat-Allah, Roger G. Melko, Juan Carrasquilla
• Abstract summary: Recurrent neural networks (RNNs) are a class of neural networks that have emerged from the paradigm of artificial intelligence. We show that our method is superior to Density Matrix Renormalisation Group (DMRG) for system sizes larger than or equal to $14 times 14$ on the triangular lattice.
• Score: 0.7234862895932991
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recurrent neural networks (RNNs) are a class of neural networks that have emerged from the paradigm of artificial intelligence and has enabled lots of interesting advances in the field of natural language processing. Interestingly, these architectures were shown to be powerful ansatze to approximate the ground state of quantum systems. Here, we build over the results of [Phys. Rev. Research 2, 023358 (2020)] and construct a more powerful RNN wave function ansatz in two dimensions. We use symmetry and annealing to obtain accurate estimates of ground state energies of the two-dimensional (2D) Heisenberg model, on the square lattice and on the triangular lattice. We show that our method is superior to Density Matrix Renormalisation Group (DMRG) for system sizes larger than or equal to $14 \times 14$ on the triangular lattice.

Related papers

• Enhancing lattice kinetic schemes for fluid dynamics with Lattice-Equivariant Neural Networks [79.16635054977068]
  We present a new class of equivariant neural networks, dubbed Lattice-Equivariant Neural Networks (LENNs) Our approach develops within a recently introduced framework aimed at learning neural network-based surrogate models Lattice Boltzmann collision operators. Our work opens towards practical utilization of machine learning-augmented Lattice Boltzmann CFD in real-world simulations.
  arXiv  Detail & Related papers  (2024-05-22T17:23:15Z)
• Neural network approach to quasiparticle dispersions in doped antiferromagnets [0.0]
  We study the ability of neural quantum states to represent the bosonic and fermionic $t-J$ model on different 1D and 2D lattices. We present a method to calculate dispersion relations from the neural network state representation.
  arXiv  Detail & Related papers  (2023-10-12T17:59:33Z)
• NeuRBF: A Neural Fields Representation with Adaptive Radial Basis Functions [93.02515761070201]
  We present a novel type of neural fields that uses general radial bases for signal representation. Our method builds upon general radial bases with flexible kernel position and shape, which have higher spatial adaptivity and can more closely fit target signals. When applied to neural radiance field reconstruction, our method achieves state-of-the-art rendering quality, with small model size and comparable training speed.
  arXiv  Detail & Related papers  (2023-09-27T06:32:05Z)
• Towards Neural Variational Monte Carlo That Scales Linearly with System Size [67.09349921751341]
  Quantum many-body problems are central to demystifying some exotic quantum phenomena, e.g., high-temperature superconductors. The combination of neural networks (NN) for representing quantum states, and the Variational Monte Carlo (VMC) algorithm, has been shown to be a promising method for solving such problems. We propose a NN architecture called Vector-Quantized Neural Quantum States (VQ-NQS) that utilizes vector-quantization techniques to leverage redundancies in the local-energy calculations of the VMC algorithm.
  arXiv  Detail & Related papers  (2022-12-21T19:00:04Z)
• Neural network enhanced measurement efficiency for molecular groundstates [63.36515347329037]
  We adapt common neural network models to learn complex groundstate wavefunctions for several molecular qubit Hamiltonians. We find that using a neural network model provides a robust improvement over using single-copy measurement outcomes alone to reconstruct observables.
  arXiv  Detail & Related papers  (2022-06-30T17:45:05Z)
• Efficient Simulation of Dynamics in Two-Dimensional Quantum Spin Systems with Isometric Tensor Networks [0.0]
  We investigate the computational power of the recently introduced class of isometric tensor network states (isoTNSs) We discuss several technical details regarding the implementation of isoTNSs-based algorithms and compare different disentanglers. We compute the dynamical spin structure factor of 2D quantum spin systems for two paradigmatic models.
  arXiv  Detail & Related papers  (2021-12-15T19:00:05Z)
• Physics Validation of Novel Convolutional 2D Architectures for Speeding Up High Energy Physics Simulations [0.0]
  We apply Geneversarative Adrial Networks (GANs), a deep learning technique, to replace the calorimeter detector simulations. We develop new two-dimensional convolutional networks to solve the same 3D image generation problem faster. Our results demonstrate a high physics accuracy and further consolidate the use of GANs for fast detector simulations.
  arXiv  Detail & Related papers  (2021-05-19T07:24:23Z)
• Group Convolutional Neural Networks Improve Quantum State Accuracy [1.52292571922932]
  We show how to create maximally expressive models for quantum states with specific symmetry properties. We implement group equivariant convolutional networks (G-CNN) citecohen2016group, and demonstrate that performance improvements can be achieved without increasing memory use.
  arXiv  Detail & Related papers  (2021-04-11T19:45:10Z)
• Efficient Tensor Network ansatz for high-dimensional quantum many-body problems [0.0]
  We introduce a novel tensor network structure augmenting the well-established Tree Network representation of a quantum many-body wave function. We benchmark this novel approach against paradigmatic two-dimensional spin models demonstrating unprecedented precision and system sizes.
  arXiv  Detail & Related papers  (2020-11-16T19:00:04Z)
• Variational Monte Carlo calculations of $\mathbf{A\leq 4}$ nuclei with an artificial neural-network correlator ansatz [62.997667081978825]
  We introduce a neural-network quantum state ansatz to model the ground-state wave function of light nuclei. We compute the binding energies and point-nucleon densities of $Aleq 4$ nuclei as emerging from a leading-order pionless effective field theory Hamiltonian.
  arXiv  Detail & Related papers  (2020-07-28T14:52:28Z)
• Binarized Graph Neural Network [65.20589262811677]
  We develop a binarized graph neural network to learn the binary representations of the nodes with binary network parameters. Our proposed method can be seamlessly integrated into the existing GNN-based embedding approaches. Experiments indicate that the proposed binarized graph neural network, namely BGN, is orders of magnitude more efficient in terms of both time and space.
  arXiv  Detail & Related papers  (2020-04-19T09:43:14Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.