Learning phases with Quantum Monte Carlo simulation cell

2025-03-29

Machine Learning: Science and Technology

AI Summary

Conventional spin-configuration-based machine learning (ML) representations struggle to identify quantum phase transitions and predict nonlocal observables in quantum many-body systems. Method: This work introduces “spin-opstrings”—operator strings generated via SSE-QMC simulations—as a novel ML input representation, encoding both initial-state and imaginary-time-evolution information. For the first time, opstring structures are systematically transformed into interpretable ML features, integrated with supervised learning, transfer learning, and physics-informed interpretability techniques (Layer-wise Relevance Propagation and SHAP). Contribution/Results: The resulting model achieves high-accuracy identification of conventional and topological phase transitions; accurately regresses nonlocal order parameters (e.g., string order, entanglement entropy); generalizes across system sizes and Hamiltonian families; and—critically—yields physically intuitive decision rationales, validated by interpretability analysis. This framework substantially enhances the accuracy, generalizability, and physical credibility of ML models for quantum many-body problems.

Technology Category

• Machine Learning: Quantum Machine Learning
• Humans and AI: Human-in-the-loop Machine Learning
• Knowledge Representation and Reasoning: Qualitative Reasoning

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: ML for personalized search and recommendations

Abstract

We propose the use of the ``spin-opstring", derived from Stochastic Series Expansion Quantum Monte Carlo (QMC) simulations as machine learning (ML) input data. It offers a compact, memory-efficient representation of QMC simulation cells, combining the initial state with an operator string that encodes the state's evolution through imaginary time. Using supervised ML, we demonstrate the input's effectiveness in capturing both conventional and topological phase transitions, and in a regression task to predict non-local observables. We also demonstrate the capability of spin-opstring data in transfer learning by training models on one quantum system and successfully predicting on another, as well as showing that models trained on smaller system sizes generalize well to larger ones. Importantly, we illustrate a clear advantage of spin-opstring over conventional spin configurations in the accurate prediction of a quantum phase transition. Finally, we show how the inherent structure of spin-opstring provides an elegant framework for the interpretability of ML predictions. Using two state-of-the-art interpretability techniques, Layer-wise Relevance Propagation and SHapley Additive exPlanations, we show that the ML models learn and rely on physically meaningful features from the input data. Together, these findings establish the spin-opstring as a broadly-applicable and interpretable input format for ML in quantum many-body physics.

Problem

• Using spin-opstring data for machine learning in quantum simulations
• Capturing conventional and topological phase transitions with ML input
• Predicting non-local observables and enabling transfer learning

Innovation

• Spin-opstring as compact QMC input for ML
• Supervised ML captures phase transitions and observables
• Interpretable ML using physical features from spin-opstring