Validating phase-space methods with tensor networks in two-dimensional spin models with power-law interactions

• URL: http://arxiv.org/abs/2305.17242v2
• Date: Tue, 30 May 2023 23:04:02 GMT
• Title: Validating phase-space methods with tensor networks in two-dimensional spin models with power-law interactions
• Authors: Sean R. Muleady, Mingru Yang, Steven R. White, Ana Maria Rey
• Abstract summary: We evaluate the dynamics of 2D power-law interacting XXZ models, implementable in a variety of state-of-the-art experimental platforms. We compute the spin squeezing as a measure of correlations in the system, and compare to semiclassical phase-space calculations utilizing the discrete truncated Wigner approximation (DTWA) We find the latter efficiently and accurately captures the scaling of entanglement with system size in these systems, despite the comparatively resource-intensive tensor network representation of the dynamics.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Using a recently developed extension of the time-dependent variational principle for matrix product states, we evaluate the dynamics of 2D power-law interacting XXZ models, implementable in a variety of state-of-the-art experimental platforms. We compute the spin squeezing as a measure of correlations in the system, and compare to semiclassical phase-space calculations utilizing the discrete truncated Wigner approximation (DTWA). We find the latter efficiently and accurately captures the scaling of entanglement with system size in these systems, despite the comparatively resource-intensive tensor network representation of the dynamics. We also compare the steady-state behavior of DTWA to thermal ensemble calculations with tensor networks. Our results open a way to benchmark dynamical calculations for two-dimensional quantum systems, and allow us to rigorously validate recent predictions for the generation of scalable entangled resources for metrology in these systems.

Related papers

• Latent Space Energy-based Neural ODEs [73.01344439786524]
  This paper introduces a novel family of deep dynamical models designed to represent continuous-time sequence data. We train the model using maximum likelihood estimation with Markov chain Monte Carlo. Experiments on oscillating systems, videos and real-world state sequences (MuJoCo) illustrate that ODEs with the learnable energy-based prior outperform existing counterparts.
  arXiv  Detail & Related papers  (2024-09-05T18:14:22Z)
• 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)
• Two-dimensional correlation propagation dynamics with a cluster discrete phase-space method [0.0]
  Nonequilibrium dynamics of highly-controlled quantum systems is a challenging issue in statistical physics. We develop a discrete phase-space approach for general SU($N$) spin systems that capture non-trivial quantum correlations inside each cluster. We demonstrate that the cluster discrete truncated Wigner approximation can reproduce key results in a recent experiment on the correlation propagation dynamics in a two dimensional Bose-Hubbard system.
  arXiv  Detail & Related papers  (2024-04-29T11:08:44Z)
• Online Variational Sequential Monte Carlo [49.97673761305336]
  We build upon the variational sequential Monte Carlo (VSMC) method, which provides computationally efficient and accurate model parameter estimation and Bayesian latent-state inference. Online VSMC is capable of performing efficiently, entirely on-the-fly, both parameter estimation and particle proposal adaptation.
  arXiv  Detail & Related papers  (2023-12-19T21:45:38Z)
• Capturing dynamical correlations using implicit neural representations [85.66456606776552]
  We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data. In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
  arXiv  Detail & Related papers  (2023-04-08T07:55:36Z)
• Modeling the space-time correlation of pulsed twin beams [68.8204255655161]
  Entangled twin-beams generated by parametric down-conversion are among the favorite sources for imaging-oriented applications. We propose a semi-analytic model which aims to bridge the gap between time-consuming numerical simulations and the unrealistic plane-wave pump theory.
  arXiv  Detail & Related papers  (2023-01-18T11:29:49Z)
• 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)
• Tensor-network study of correlation-spreading dynamics in the two-dimensional Bose-Hubbard model [0.0]
  We demonstrate that a tensor-network method running on classical computers is useful for this purpose. We specifically analyze real-time dynamics of the two-dimensional Bose-Hubbard model after a sudden quench. By estimating the phase and group velocities from the single-particle and density-density correlation functions, we predict how these velocities vary in the moderate interaction region.
  arXiv  Detail & Related papers  (2021-08-25T05:37:16Z)
• Dynamics of two-dimensional open quantum lattice models with tensor networks [0.0]
  We develop a tensor network method, based on an infinite Projected Entangled Pair Operator (iPEPO) ansatz, applicable directly in the thermodynamic limit. We consider dissipative transverse quantum Ising and driven-dissipative hard core boson models in non-mean field limits. Our method enables to study regimes which are accessible to current experiments but lie well beyond the applicability of existing techniques.
  arXiv  Detail & Related papers  (2020-12-22T18:24:20Z)
• Liquid Time-constant Networks [117.57116214802504]
  We introduce a new class of time-continuous recurrent neural network models. Instead of declaring a learning system's dynamics by implicit nonlinearities, we construct networks of linear first-order dynamical systems. These neural networks exhibit stable and bounded behavior, yield superior expressivity within the family of neural ordinary differential equations.
  arXiv  Detail & Related papers  (2020-06-08T09:53:35Z)
• Efficient variational contraction of two-dimensional tensor networks with a non-trivial unit cell [0.0]
  tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems. We generalize a recently proposed variational uniform matrix product state algorithm for capturing one-dimensional quantum lattices. A key property of the algorithm is a computational effort that scales linearly rather than exponentially in the size of the unit cell.
  arXiv  Detail & Related papers  (2020-03-02T19:01:06Z)

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.