Explorative Curriculum Learning for Strongly Correlated Electron Systems

2025-05-01

AI Summary

Neural quantum states (NQS) face prohibitive computational costs and poor generalization across parameter regimes when applied to strongly correlated electron systems. Method: We propose a physics-informed transferable curriculum learning framework that integrates perturbation theory with curriculum learning to embed prior physical knowledge; we further design Pairing-Net, a novel graph neural network architecture that overcomes key limitations of conventional NQS in generalizability and scalability. Contributions/Results: Our framework achieves ~200× speedup in computation while significantly enhancing numerical stability. It enables efficient and robust exploration of many-body phase space on large lattices (≥32 sites) and across broad parameter ranges (U/t ∈ [0, 12]). This work establishes a new paradigm for automated phase diagram discovery in strongly correlated systems.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

Recent advances in neural network quantum states (NQS) have enabled high-accuracy predictions for complex quantum many-body systems such as strongly correlated electron systems. However, the computational cost remains prohibitive, making exploration of the diverse parameters of interaction strengths and other physical parameters inefficient. While transfer learning has been proposed to mitigate this challenge, achieving generalization to large-scale systems and diverse parameter regimes remains difficult. To address this limitation, we propose a novel curriculum learning framework based on transfer learning for NQS. This facilitates efficient and stable exploration across a vast parameter space of quantum many-body systems. In addition, by interpreting NQS transfer learning through a perturbative lens, we demonstrate how prior physical knowledge can be flexibly incorporated into the curriculum learning process. We also propose Pairing-Net, an architecture to practically implement this strategy for strongly correlated electron systems, and empirically verify its effectiveness. Our results show an approximately 200-fold speedup in computation and a marked improvement in optimization stability compared to conventional methods.

Problem

• High computational cost in neural network quantum states for correlated systems
• Difficulty generalizing transfer learning to large-scale quantum systems
• Inefficient exploration of diverse parameter spaces in many-body systems

Innovation

• Curriculum learning framework for NQS transfer
• Pairing-Net architecture for electron systems
• Perturbative lens integrates prior physical knowledge