Machine Learning Predicts Entanglement Entropy in One-Dimensional Fermi-Hubbard Systems

Quantum entanglement, a cornerstone of modern physics, plays a crucial role in emerging technologies and our understanding of fundamental interactions, yet its connection to the movement of particles remains largely unexplored. Elvira Bilokon, Valeriia Bilokon, and Abhijit Sen, all from Tulane University, along with colleagues from the University of Arizona and Karazin Kharkiv National University, now demonstrate a universal relationship between the amount of entanglement and the number of particles that successfully traverse a barrier. The team reveals this connection within a specific model of interacting particles, employing a novel machine learning approach to uncover patterns with remarkable accuracy, and further proposes a simple formula to capture this behaviour. This discovery offers a powerful new framework for both characterising correlations in various physical systems and predicting how entanglement evolves during particle transport, potentially impacting fields from materials science to quantum computing.

Entanglement entropy represents a fundamental measure of quantum correlations and serves as a key resource driving advances in quantum information and many-body physics. This research uncovers a universal relationship between bipartite entanglement entropy and particle number following traversal of a barrier within a one-dimensional Fermi-Hubbard system subject to an external asymmetric potential. The investigation employs Kolmogorov-Arnold Networks, a novel machine learning architecture, to learn this relationship across a broad range of interaction strengths. This approach achieves near-perfect predictive accuracy, and the findings offer new insights into the behaviour of correlated quantum systems, potentially enabling improved control and understanding of these complex phenomena

KANs Reveal Quantum Entanglement Structure

This research paper explores the use of Kolmogorov-Arnold Networks (KANs), a novel deep learning architecture, to discover and represent the entanglement structure in quantum many-body systems. The authors demonstrate KANs’ ability to accurately predict physical properties and, crucially, to reveal underlying relationships between different quantum states, effectively learning the grammar of quantum entanglement. KANs achieve high accuracy in predicting physical properties and learn meaningful representations that capture the entanglement structure of quantum states, identifying relationships not immediately obvious. The learned KAN representations can be interpreted as a grammar of quantum entanglement, revealing how different states are related. This work demonstrates the potential of KANs for understanding complex quantum systems, discovering new quantum phenomena, developing more efficient quantum algorithms, and designing novel quantum materials.

Entanglement Predicts Tunneling Particle Number with Accuracy

Researchers have uncovered a fundamental relationship between particle number and entanglement entropy in a specific quantum system, revealing how these two properties are intrinsically linked. Their work focuses on a one-dimensional system where particles attempt to tunnel through a barrier, and demonstrates that the amount of entanglement between particles before and after the barrier is directly correlated with the number of particles that successfully tunnel. This connection holds true regardless of the strength of interactions between the particles. The team employed Kolmogorov-Arnold Networks, a machine learning technique, to map this relationship with remarkable accuracy, achieving predictive power exceeding 99% in many cases. Interestingly, the researchers also developed a simple analytical expression that accurately captures the observed correlation, highlighting the underlying physical principles at play.

Entanglement Predicts Particle Transmission Number

This research demonstrates a robust and universal relationship between bipartite entanglement entropy and the number of particles appearing after a potential barrier in a one-dimensional Fermi-Hubbard model. The team uncovered this connection using Kolmogorov-Arnold Networks, a machine learning architecture, achieving near-perfect accuracy in predicting entanglement across a range of interaction strengths. Furthermore, they developed a simple analytical expression that effectively captures this correlation when parameters are fixed, revealing a previously unknown link between quantum correlations and transport phenomena. The findings offer a powerful framework for predicting entanglement dynamics in interacting systems and could potentially be relevant to current tunneling experiments. Preliminary calculations suggest this relationship holds even in larger systems, indicating it is not simply a result of finite size effects.