Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2409.18480

Autoencoder-based learning of Quantum phase transitions in the two-component Bose-Hubbard model

Iftekher S. Chowdhury, Binay Prakash Akhouri, Haque, Shah, Eric M. Howard

Published Sep 27, 2024• 0 citations
arXivHTMLPDF

Abstract

This paper investigates the use of autoencoders and machine learning methods for detecting and analyzing quantum phase transitions in the Two-Component Bose-Hubbard Model. By leveraging deep learning models such as autoencoders, we investigate latent space representations, reconstruction error analysis, and cluster distance calculations to identify phase boundaries and critical points. The study is supplemented by dimensionality reduction techniques such as PCA and t-SNE for latent space visualization. The results demonstrate the potential of autoencoders to describe the dynamics of quantum phase transitions.

DOI
10.48550/arxiv.2409.18480

Related papers

Unsupervised Latent-Space Discovery of Quantum Phases in the Bose–Hubbard Model

ming Cheng

We demonstrate that a variational autoencoder (VAE) can autonomously learn the quantum phase structure of the Bose–Hubbard model using only local observables. Based on data generated from the Gutzwiller mean-field approximation, the VAE organizes the system into a low-dimensional latent space that cleanly separates superfluid and Mott-insulating regimes and reconstructs the conventional (U/t, μ/t) phase diagram without supervision. Extending the input to finite temperature, the latent geometry captures the thermal suppression of superfluidity and the smooth deformation of phase boundaries. These results establish latent-space learning as a scalable, prior-free framework for identifying phase structure in high-dimensional quantum systems.

•Feb 10, 2026•0 citations

The critical temperature of the 2D-Ising model through deep learning autoencoders

Constantia Alexandrou, Andreas Athenodorou, Charalambos Chrysostomou +1 more

Abstract We investigate deep learning autoencoders for the unsupervised recognition of phase transitions in physical systems formulated on a lattice. We focus our investigation on the 2-dimensional ferromagnetic Ising model and then test the application of the autoencoder on the anti-ferromagnetic Ising model. We use spin configurations produced for the 2-dimensional ferromagnetic and anti-ferromagnetic Ising model in zero external magnetic field. For the ferromagnetic Ising model, we study numerically the relation between one latent variable extracted from the autoencoder to the critical temperature T c . The proposed autoencoder reveals the two phases, one for which the spins are ordered and the other for which spins are disordered, reflecting the restoration of the ℤ 2 symmetry as the temperature increases. We provide a finite volume analysis for a sequence of increasing lattice sizes. For the largest volume studied, the transition between the two phases occurs very close to the theoretically extracted critical temperature. We define as a quasi-order parameter the absolute average latent variable z ̃ , which enables us to predict the critical temperature. One can define a latent susceptibility and use it to quantify the value of the critical temperature T c ( L ) at different lattice sizes and that these values suffer from only small finite scaling effects. We demonstrate that T c ( L ) extrapolates to the known theoretical value as L → ∞ suggesting that the autoencoder can also be used to extract the critical temperature of the phase transition to an adequate precision. Subsequently, we test the application of the autoencoder on the anti-ferromagnetic Ising model, demonstrating that the proposed network can detect the phase transition successfully in a similar way. Graphical abstract

arXiv:1903.03506•The European Physical Journal B•Dec 1, 2020•51 citations

Detecting the phase transition in a strongly interacting Fermi gas by unsupervised machine learning

D. Eberz, M. Link, A. Kell +3 more

We study the critical temperature of the superfluid phase transition of strongly interacting fermions in the crossover regime between a Bardeen-Cooper-Schrieffer superconductor and a Bose-Einstein condensate of dimers. To this end, we employ the technique of unsupervised machine learning using an autoencoder neural network, which we directly apply to time-of-flight images of the fermions. We extract the critical temperature of the phase transition from trend changes in the data distribution revealed in the latent space of the autoencoder bottleneck.

Physical Review A•Dec 4, 2023•4 citations

Phase determination with and without deep learning

Burak Çivitcioğlu, Rudolf A. Römer, A. Honecker

Detection of phase transitions is a critical task in statistical physics, traditionally pursued through analytic methods and direct numerical simulations. Recently, machine-learning techniques have emerged as promising tools in this context, with a particular focus on supervised and unsupervised learning methods, along with nonlearning approaches. In this paper, we study the performance of unsupervised learning in detecting phase transitions in the J_{1}-J_{2} Ising model on the square lattice. The model is chosen due to its simplicity and complexity, thus providing an understanding of the application of machine-learning techniques in both straightforward and challenging scenarios. We propose a simple method based on a direct comparison of configurations. The reconstruction error, defined as the mean-squared distance between two configurations, is used to determine the critical temperatures. The results from the comparison of configurations are contrasted with those of the configurations generated by variational autoencoders. Our findings highlight that for certain systems a simpler method can yield results comparable to more complex neural networks. This paper contributes to the broader understanding of machine-learning applications in statistical physics and introduces an efficient approach to the detection of phase transitions using machine determination techniques.

arXiv:2403.09786•Physical review. E•Feb 18, 2025•7 citations

Semi-supervised learning of order parameter in 2D Ising and XY models using Conditional Variational Autoencoders

adwait naravane, Nilmani Mathur A

We investigate the application of deep learning techniques employing the conditional variational autoencoders for semi-supervised learning of latent parameters to describe phase transition in the two-dimensional (2D) ferromagnetic Ising model and the two-dimensional XY model. For both models, we utilize spin configurations generated using the Wolff algorithms below and above the critical temperatures. For the 2D Ising model we find the latent parameter of conditional variational autoencoders is correlated to the known order parameter of magnetization more efficiently than their correspondence in variational autoencoders used previously. It can also clearly identify the restoration of the $\mathbb{Z}_2$ symmetry beyond the critical point. The critical temperature extracted from the latent parameter at larger lattices are found to be approaching its correct value. Similarly, for the 2D XY model, we find our chosen network with the latent representation of conditional variational autoencoders is equally capable of separating the two phases between the high and low temperatures, again at the correct critical temperature with reasonable accuracy. Together these results show that the latent representation of conditional variational autoencoders can be employed efficiently to identify the phases of condensed matter systems, without their prior knowledge.

arXiv:2306.16822•Jun 29, 2023•0 citations

Unsupervised machine learning account of magnetic transitions in the Hubbard model

Kelvin Ch’ng, Nick Vazquez, Ehsan Khatami

We employ several unsupervised machine learning techniques, including autoencoders, random trees embedding, and t-distributed stochastic neighboring ensemble (t-SNE), to reduce the dimensionality of, and therefore classify, raw (auxiliary) spin configurations generated, through Monte Carlo simulations of small clusters, for the Ising and Fermi-Hubbard models at finite temperatures. Results from a convolutional autoencoder for the three-dimensional Ising model can be shown to produce the magnetization and the susceptibility as a function of temperature with a high degree of accuracy. Quantum fluctuations distort this picture and prevent us from making such connections between the output of the autoencoder and physical observables for the Hubbard model. However, we are able to define an indicator based on the output of the t-SNE algorithm that shows a near perfect agreement with the antiferromagnetic structure factor of the model in two and three spatial dimensions in the weak-coupling regime. t-SNE also predicts a transition to the canted antiferromagnetic phase for the three-dimensional model when a strong magnetic field is present. We show that these techniques cannot be expected to work away from half filling when the "sign problem" in quantum Monte Carlo simulations is present.

arXiv:1708.03350•Physical review. E•Jan 16, 2018•147 citations
This paper investigates the use of autoencoders and machine learning methods for detecting and analyzing quantum phase transitions in the Two-Component Bose-Hubbard Model. By leveraging deep learning models such as autoencoders, we investigate latent space representations, reconstruction error analysis, and cluster distance calculations to identify phase boundaries and critical points. The study is supplemented by dimensionality reduction techniques such as PCA and t-SNE for latent space visualization. The results demonstrate the potential of autoencoders to describe the dynamics of quantum phase transitions.
We demonstrate that a variational autoencoder (VAE) can autonomously learn the quantum phase structure of the Bose–Hubbard model using only local observables. Based on data generated from the Gutzwiller mean-field approximation, the VAE organizes the system into a low-dimensional latent space that cleanly separates superfluid and Mott-insulating regimes and reconstructs the conventional (U/t, μ/t) phase diagram without supervision. Extending the input to finite temperature, the latent geometry captures the thermal suppression of superfluidity and the smooth deformation of phase boundaries. These results establish latent-space learning as a scalable, prior-free framework for identifying phase structure in high-dimensional quantum systems.
Abstract We investigate deep learning autoencoders for the unsupervised recognition of phase transitions in physical systems formulated on a lattice. We focus our investigation on the 2-dimensional ferromagnetic Ising model and then test the application of the autoencoder on the anti-ferromagnetic Ising model. We use spin configurations produced for the 2-dimensional ferromagnetic and anti-ferromagnetic Ising model in zero external magnetic field. For the ferromagnetic Ising model, we study numerically the relation between one latent variable extracted from the autoencoder to the critical temperature T c . The proposed autoencoder reveals the two phases, one for which the spins are ordered and the other for which spins are disordered, reflecting the restoration of the ℤ 2 symmetry as the temperature increases. We provide a finite volume analysis for a sequence of increasing lattice sizes. For the largest volume studied, the transition between the two phases occurs very close to the theoretically extracted critical temperature. We define as a quasi-order parameter the absolute average latent variable z ̃ , which enables us to predict the critical temperature. One can define a latent susceptibility and use it to quantify the value of the critical temperature T c ( L ) at different lattice sizes and that these values suffer from only small finite scaling effects. We demonstrate that T c ( L ) extrapolates to the known theoretical value as L → ∞ suggesting that the autoencoder can also be used to extract the critical temperature of the phase transition to an adequate precision. Subsequently, we test the application of the autoencoder on the anti-ferromagnetic Ising model, demonstrating that the proposed network can detect the phase transition successfully in a similar way. Graphical abstract
We study the critical temperature of the superfluid phase transition of strongly interacting fermions in the crossover regime between a Bardeen-Cooper-Schrieffer superconductor and a Bose-Einstein condensate of dimers. To this end, we employ the technique of unsupervised machine learning using an autoencoder neural network, which we directly apply to time-of-flight images of the fermions. We extract the critical temperature of the phase transition from trend changes in the data distribution revealed in the latent space of the autoencoder bottleneck.
Detection of phase transitions is a critical task in statistical physics, traditionally pursued through analytic methods and direct numerical simulations. Recently, machine-learning techniques have emerged as promising tools in this context, with a particular focus on supervised and unsupervised learning methods, along with nonlearning approaches. In this paper, we study the performance of unsupervised learning in detecting phase transitions in the J_{1}-J_{2} Ising model on the square lattice. The model is chosen due to its simplicity and complexity, thus providing an understanding of the application of machine-learning techniques in both straightforward and challenging scenarios. We propose a simple method based on a direct comparison of configurations. The reconstruction error, defined as the mean-squared distance between two configurations, is used to determine the critical temperatures. The results from the comparison of configurations are contrasted with those of the configurations generated by variational autoencoders. Our findings highlight that for certain systems a simpler method can yield results comparable to more complex neural networks. This paper contributes to the broader understanding of machine-learning applications in statistical physics and introduces an efficient approach to the detection of phase transitions using machine determination techniques.
We investigate the application of deep learning techniques employing the conditional variational autoencoders for semi-supervised learning of latent parameters to describe phase transition in the two-dimensional (2D) ferromagnetic Ising model and the two-dimensional XY model. For both models, we utilize spin configurations generated using the Wolff algorithms below and above the critical temperatures. For the 2D Ising model we find the latent parameter of conditional variational autoencoders is correlated to the known order parameter of magnetization more efficiently than their correspondence in variational autoencoders used previously. It can also clearly identify the restoration of the Z2\mathbb{Z}_2Z2​ symmetry beyond the critical point. The critical temperature extracted from the latent parameter at larger lattices are found to be approaching its correct value. Similarly, for the 2D XY model, we find our chosen network with the latent representation of conditional variational autoencoders is equally capable of separating the two phases between the high and low temperatures, again at the correct critical temperature with reasonable accuracy. Together these results show that the latent representation of conditional variational autoencoders can be employed efficiently to identify the phases of condensed matter systems, without their prior knowledge.
We employ several unsupervised machine learning techniques, including autoencoders, random trees embedding, and t-distributed stochastic neighboring ensemble (t-SNE), to reduce the dimensionality of, and therefore classify, raw (auxiliary) spin configurations generated, through Monte Carlo simulations of small clusters, for the Ising and Fermi-Hubbard models at finite temperatures. Results from a convolutional autoencoder for the three-dimensional Ising model can be shown to produce the magnetization and the susceptibility as a function of temperature with a high degree of accuracy. Quantum fluctuations distort this picture and prevent us from making such connections between the output of the autoencoder and physical observables for the Hubbard model. However, we are able to define an indicator based on the output of the t-SNE algorithm that shows a near perfect agreement with the antiferromagnetic structure factor of the model in two and three spatial dimensions in the weak-coupling regime. t-SNE also predicts a transition to the canted antiferromagnetic phase for the three-dimensional model when a strong magnetic field is present. We show that these techniques cannot be expected to work away from half filling when the "sign problem" in quantum Monte Carlo simulations is present.