Leveraging recurrence in neural network wavefunctions for large-scale simulations of Heisenberg antiferromagnets: the square lattice

• URL: http://arxiv.org/abs/2502.17144v1
• Date: Mon, 24 Feb 2025 13:35:23 GMT
• Title: Leveraging recurrence in neural network wavefunctions for large-scale simulations of Heisenberg antiferromagnets: the square lattice
• Authors: M. Schuyler Moss, Roeland Wiersema, Mohamed Hibat-Allah, Juan Carrasquilla, Roger G. Melko,
• Abstract summary: Machine-learning-based variational Monte Carlo simulations are a promising approach for targeting quantum many body ground states.<n>We employ recurrent neural networks (RNNs) as a variational ans"atze, and leverage their recurrent nature to simulate the ground states of progressively larger systems.<n>We show that we are able to systematically improve the accuracy of the results from our simulations by increasing the training time.
• Score: 1.9681634372790209
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Machine-learning-based variational Monte Carlo simulations are a promising approach for targeting quantum many body ground states, especially in two dimensions and in cases where the ground state is known to have a non-trivial sign structure. While many state-of-the-art variational energies have been reached with these methods for finite-size systems, little work has been done to use these results to extract information about the target state in the thermodynamic limit. In this work, we employ recurrent neural networks (RNNs) as a variational ans\"{a}tze, and leverage their recurrent nature to simulate the ground states of progressively larger systems through iterative retraining. This transfer learning technique allows us to simulate spin-$\frac{1}{2}$ systems on lattices with more than 1,000 spins without beginning optimization from scratch for each system size, thus reducing the demands for computational resources. In this study, we focus on the square-lattice antiferromagnetic Heisenberg model (SLAHM), where it is possible to carefully benchmark our results. We show that we are able to systematically improve the accuracy of the results from our simulations by increasing the training time, and obtain results for finite-sized lattices that are in good agreement with the literature values. Furthermore, we use these results to extract accurate estimates of the ground-state properties in the thermodynamic limit. This work demonstrates that RNN wavefunctions can be used to accurately study quantum many-body physics in the thermodynamic limit.

Related papers

• Machine learning force-field model for kinetic Monte Carlo simulations of itinerant Ising magnets [0.0]
  We present a scalable machine learning (ML) framework for large-scale kinetic Monte Carlo (kMC) simulations of electron Ising systems.<n>Our approach is reminiscent of the ML force-field models widely used in first-principles molecular dynamics simulations.
  arXiv  Detail & Related papers  (2024-11-29T15:35:37Z)
• Fourier Neural Operators for Learning Dynamics in Quantum Spin Systems [77.88054335119074]
  We use FNOs to model the evolution of random quantum spin systems. We apply FNOs to a compact set of Hamiltonian observables instead of the entire $2n$ quantum wavefunction.
  arXiv  Detail & Related papers  (2024-09-05T07:18:09Z)
• Robust Extraction of Thermal Observables from State Sampling and Real-Time Dynamics on Quantum Computers [49.1574468325115]
  We introduce a technique that imposes constraints on the density of states, most notably its non-negativity, and show that this way, we can reliably extract Boltzmann weights from noisy time series. Our work enables the implementation of the time-series algorithm on present-day quantum computers to study finite temperature properties of many-body quantum systems.
  arXiv  Detail & Related papers  (2023-05-30T18:00:05Z)
• Message-Passing Neural Quantum States for the Homogeneous Electron Gas [41.94295877935867]
  We introduce a message-passing-neural-network-based wave function Ansatz to simulate extended, strongly interacting fermions in continuous space. We demonstrate its accuracy by simulating the ground state of the homogeneous electron gas in three spatial dimensions.
  arXiv  Detail & Related papers  (2023-05-12T04:12:04Z)
• 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)
• Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics [62.997667081978825]
  We show how finite-temperature observables can be obtained with an algorithm motivated from the Jarzynski equality. We show that a finite temperature phase transition in the long-range transverse field Ising model can be characterized in trapped ion quantum simulators.
  arXiv  Detail & Related papers  (2022-06-03T18:00:02Z)
• Fermionic approach to variational quantum simulation of Kitaev spin models [50.92854230325576]
  Kitaev spin models are well known for being exactly solvable in a certain parameter regime via a mapping to free fermions. We use classical simulations to explore a novel variational ansatz that takes advantage of this fermionic representation. We also comment on the implications of our results for simulating non-Abelian anyons on quantum computers.
  arXiv  Detail & Related papers  (2022-04-11T18:00:01Z)
• Benchmarking a novel efficient numerical method for localized 1D Fermi-Hubbard systems on a quantum simulator [0.0]
  We show that a quantum simulator can be used to in-effect solve for the dynamics of a many-body system. We use a neutral-atom Fermi-Hubbard quantum simulator with $L_textexpsimeq290$ lattice sites to benchmark its performance. We derive a simple prediction of the behaviour of interacting Bloch oscillations for spin-imbalanced Fermi-Hubbard systems.
  arXiv  Detail & Related papers  (2021-05-13T16:03:11Z)

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.