Deep learning nonlocal and scalable energy functionals for quantum Ising models

Costa, E.; Fazio, R.; Pilati, S.

doi:10.1103/physrevb.108.125113

Cited by 2 publications

(1 citation statement)

References 55 publications

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“…In recent years, machine learning (ML) techniques have been introduced in the framework of DFT [6], addressing continuous-space systems [7][8][9], as well as lattice [10,11] and spin models [12]. The main goal is to learn from data more reliable energy-density functionals, potentially adequate also for strongly correlated systems.…”

Section: Introductionmentioning

confidence: 99%

Solving deep-learning density functional theory via variational autoencoders

Costa,

Scriva,

Pilati

2024

Mach. Learn.: Sci. Technol.

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In recent years, machine learning models, chiefly deep neural networks, have revealed suited to learn accurate energy-density functionals from data. However, problematic instabilities have been shown to occur in the search of ground-state density profiles via energy minimization. Indeed, any small noise can lead astray from realistic profiles, causing the failure of the learned functional and, hence, strong violations of the variational property. In this article, we employ variational autoencoders (VAEs) to build a compressed, flexible, and regular representation of the ground-state density profiles of various quantum models. Performing energy minimization in this compressed space allows us to avoid both numerical instabilities and variational biases due to excessive constraints. Our tests are performed on one-dimensional single-particle models from the literature in the field and, notably, on a three-dimensional disordered potential. In all cases, the ground-state energies are estimated with errors below the chemical accuracy and the density profiles are accurately reproduced without numerical artifacts. Furthermore, we show that it is possible to perform transfer learning, applying pre-trained VAEs to different potentials.

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Section: Introductionmentioning

confidence: 99%

Solving deep-learning density functional theory via variational autoencoders

Costa,

Scriva,

Pilati

2024

Mach. Learn.: Sci. Technol.

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Dimensionality Reduction for Data Analysis With Quantum Feature Learning

Sihare

2024

WIREs Data Min & Knowl

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To improve data analysis and feature learning, this study compares the effectiveness of quantum dimensionality reduction (qDR) techniques to classical ones. In this study, we investigate several qDR techniques on a variety of datasets such as quantum Gaussian distribution adaptation (qGDA), quantum principal component analysis (qPCA), quantum linear discriminant analysis (qLDA), and quantum t‐SNE (qt‐SNE). The Olivetti Faces, Wine, Breast Cancer, Digits, and Iris are among the datasets used in this investigation. Through comparison evaluations against well‐established classical approaches, such as classical PCA (cPCA), classical LDA (cLDA), and classical GDA (cGDA), and using well‐established metrics like loss, fidelity, and processing time, the effectiveness of these techniques is assessed. The findings show that cPCA produced positive results with the lowest loss and highest fidelity when used on the Iris dataset. On the other hand, quantum uniform manifold approximation and projection (qUMAP) performs well and shows strong fidelity when tested against the Wine dataset, but ct‐SNE shows mediocre performance against the Digits dataset. Isomap and locally linear embedding (LLE) function differently depending on the dataset. Notably, LLE showed the largest loss and lowest fidelity on the Olivetti Faces dataset. The hypothesis testing findings showed that the qDR strategies did not significantly outperform the classical techniques in terms of maintaining pertinent information from quantum datasets. More specifically, the outcomes of paired t‐tests show that when it comes to the ability to capture complex patterns, there are no statistically significant differences between the cPCA and qPCA, the cLDA and qLDA, and the cGDA and qGDA. According to the findings of the assessments of mutual information (MI) and clustering accuracy, qPCA may be able to recognize patterns more clearly than standardized cPCA. Nevertheless, there is no discernible improvement between the qLDA and qGDA approaches and their classical counterparts.

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Deep learning nonlocal and scalable energy functionals for quantum Ising models

Cited by 2 publications

References 55 publications

Solving deep-learning density functional theory via variational autoencoders

Solving deep-learning density functional theory via variational autoencoders

Dimensionality Reduction for Data Analysis With Quantum Feature Learning

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