Positive-definite parametrization of mixed quantum states with deep neural networks

• URL: http://arxiv.org/abs/2206.13488v1
• Date: Mon, 27 Jun 2022 17:51:38 GMT
• Title: Positive-definite parametrization of mixed quantum states with deep neural networks
• Authors: Filippo Vicentini, Riccardo Rossi, Giuseppe Carleo
• Abstract summary: We show how to embed an autoregressive structure in the GHDO to allow direct sampling of the probability distribution. We benchmark this architecture by the steady state of the dissipative transverse-field Ising model.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce the Gram-Hadamard Density Operator (GHDO), a new deep neural-network architecture that can encode positive semi-definite density operators of exponential rank with polynomial resources. We then show how to embed an autoregressive structure in the GHDO to allow direct sampling of the probability distribution. These properties are especially important when representing and variationally optimizing the mixed quantum state of a system interacting with an environment. Finally, we benchmark this architecture by simulating the steady state of the dissipative transverse-field Ising model. Estimating local observables and the R\'enyi entropy, we show significant improvements over previous state-of-the-art variational approaches.

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)
• Deep Neural Networks as Variational Solutions for Correlated Open Quantum Systems [0.0]
  We show that parametrizing the density matrix directly with more powerful models can yield better variational ansatz functions. We present results for the dissipative one-dimensional transverse-field Ising model and a two-dimensional dissipative Heisenberg model.
  arXiv  Detail & Related papers  (2024-01-25T13:41:34Z)
• Subsurface Characterization using Ensemble-based Approaches with Deep Generative Models [2.184775414778289]
  Inverse modeling is limited for ill-posed, high-dimensional applications due to computational costs and poor prediction accuracy with sparse datasets. We combine Wasserstein Geneversarative Adrial Network with Gradient Penalty (WGAN-GP) and Ensemble Smoother with Multiple Data Assimilation (ES-MDA) WGAN-GP is trained to generate high-dimensional K fields from a low-dimensional latent space and ES-MDA updates the latent variables by assimilating available measurements.
  arXiv  Detail & Related papers  (2023-10-02T01:27:10Z)
• Dynamic Kernel-Based Adaptive Spatial Aggregation for Learned Image Compression [63.56922682378755]
  We focus on extending spatial aggregation capability and propose a dynamic kernel-based transform coding. The proposed adaptive aggregation generates kernel offsets to capture valid information in the content-conditioned range to help transform. Experimental results demonstrate that our method achieves superior rate-distortion performance on three benchmarks compared to the state-of-the-art learning-based methods.
  arXiv  Detail & Related papers  (2023-08-17T01:34:51Z)
• Differentiating Metropolis-Hastings to Optimize Intractable Densities [51.16801956665228]
  We develop an algorithm for automatic differentiation of Metropolis-Hastings samplers. We apply gradient-based optimization to objectives expressed as expectations over intractable target densities.
  arXiv  Detail & Related papers  (2023-06-13T17:56:02Z)
• Machine learning in and out of equilibrium [58.88325379746631]
  Our study uses a Fokker-Planck approach, adapted from statistical physics, to explore these parallels. We focus in particular on the stationary state of the system in the long-time limit, which in conventional SGD is out of equilibrium. We propose a new variation of Langevin dynamics (SGLD) that harnesses without replacement minibatching.
  arXiv  Detail & Related papers  (2023-06-06T09:12:49Z)
• Distributed Bayesian Learning of Dynamic States [65.7870637855531]
  The proposed algorithm is a distributed Bayesian filtering task for finite-state hidden Markov models. It can be used for sequential state estimation, as well as for modeling opinion formation over social networks under dynamic environments.
  arXiv  Detail & Related papers  (2022-12-05T19:40:17Z)
• Structured Optimal Variational Inference for Dynamic Latent Space Models [16.531262817315696]
  We consider a latent space model for dynamic networks, where our objective is to estimate the pairwise inner products plus the intercept of the latent positions. To balance posterior inference and computational scalability, we consider a structured mean-field variational inference framework.
  arXiv  Detail & Related papers  (2022-09-29T22:10:42Z)
• Ground state search by local and sequential updates of neural network quantum states [3.3711670942444023]
  We propose a local optimization procedure for neural network quantum states. We analyze both the ground state energy and the correlations for the non-integrable tilted Ising model with restricted Boltzmann machines. We find that sequential local updates can lead to faster convergence to states which have energy and correlations closer to those of the ground state. To show the generality of the approach we apply it to both 1D and 2D non-integrable spin systems.
  arXiv  Detail & Related papers  (2022-07-22T05:24:19Z)
• An Energy-Based Prior for Generative Saliency [62.79775297611203]
  We propose a novel generative saliency prediction framework that adopts an informative energy-based model as a prior distribution. With the generative saliency model, we can obtain a pixel-wise uncertainty map from an image, indicating model confidence in the saliency prediction. Experimental results show that our generative saliency model with an energy-based prior can achieve not only accurate saliency predictions but also reliable uncertainty maps consistent with human perception.
  arXiv  Detail & Related papers  (2022-04-19T10:51:00Z)
• Probabilistic partition of unity networks: clustering based deep approximation [0.0]
  Partition of unity networks (POU-Nets) have been shown capable of realizing algebraic convergence rates for regression and solution of PDEs. We enrich POU-Nets with a Gaussian noise model to obtain a probabilistic generalization amenable to gradient-based generalizations of a maximum likelihood loss. We provide benchmarks quantifying performance in high/low-dimensions, demonstrating that convergence rates depend only on the latent dimension of data within high-dimensional space.
  arXiv  Detail & Related papers  (2021-07-07T08:02:00Z)

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.