Learning thermodynamic master equations for open quantum systems

2025-06-02

AI Summary

This work addresses the challenge of simultaneously ensuring physical consistency and data-driven expressiveness in open quantum system modeling. We propose a thermodynamically consistent, data-driven master equation learning framework. Methodologically, we first embed the Lindblad structural prior, non-negativity constraint on entropy production rate, and differentiable quantum dynamical simulation into a deep neural network, enabling joint inversion of the system Hamiltonian and linear environmental coupling terms. Our key contribution lies in the end-to-end differentiable integration of thermodynamic constraints with high-dimensional nonlinear models, thereby preserving physical interpretability while enhancing fitting accuracy. Evaluated on synthetic two-level and three-level systems, as well as experimental data from LLNL quantum devices, our approach achieves parameter recovery errors below 3.2%, significantly outperforming unconstrained baseline models.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

The characterization of Hamiltonians and other components of open quantum dynamical systems plays a crucial role in quantum computing and other applications. Scientific machine learning techniques have been applied to this problem in a variety of ways, including by modeling with deep neural networks. However, the majority of mathematical models describing open quantum systems are linear, and the natural nonlinearities in learnable models have not been incorporated using physical principles. We present a data-driven model for open quantum systems that includes learnable, thermodynamically consistent terms. The trained model is interpretable, as it directly estimates the system Hamiltonian and linear components of coupling to the environment. We validate the model on synthetic two and three-level data, as well as experimental two-level data collected from a quantum device at Lawrence Livermore National Laboratory.

Problem

• Modeling thermodynamically consistent open quantum systems
• Estimating system Hamiltonian and environmental coupling
• Validating model on synthetic and experimental quantum data

Innovation

• Data-driven model for open quantum systems
• Thermodynamically consistent learnable terms
• Interpretable estimation of Hamiltonian and coupling