Characterizing Non-Markovian Dynamics of Open Quantum Systems

2025-03-28

AI Summary

To address the challenge of accurately characterizing non-Markovian dynamics in open quantum systems, this paper proposes a structure-preserving time-convolutionless (TCL) master equation modeling framework. The method innovatively integrates Karhunen–Loève (KL) expansion with neural networks for TCL parameterization: KL expansion enables low-dimensional, physically interpretable modeling in an optimal orthogonal basis—thereby preserving fundamental physical structures and overcoming the interpretability limitations of black-box data-driven approaches—while neural networks handle high-dimensional nonlinear dependencies. Evaluated on real experimental data from the LLNL QuDIT superconducting qubit platform, the KL-based approach achieves significantly higher predictive accuracy than purely data-driven models. This work delivers a high-fidelity, physically grounded, and interpretable dynamical model, advancing applications in quantum control, error mitigation, and other quantum information processing tasks.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Characterizing non-Markovian quantum dynamics is essential for accurately modeling open quantum systems, particularly in near-term quantum technologies. In this work, we develop a structure-preserving approach to characterizing non-Markovian evolution using the time-convolutionless (TCL) master equation, considering both linear and nonlinear formulations. To parameterize the master equation, we explore two distinct techniques: the Karhunen-Loeve (KL) expansion, which provides an optimal basis representation of the dynamics, and neural networks, which offer a data-driven approach to learning system-environment interactions. We demonstrate our methodology using experimental data from a superconducting qubit at the Quantum Device Integration Testbed (QuDIT) at Lawrence Livermore National Laboratory (LLNL). Our results show that while neural networks can capture complex dependencies, the KL expansion yields the most accurate predictions of the qubit's non-Markovian dynamics, highlighting its effectiveness in structure-preserving quantum system characterization. These findings provide valuable insights into efficient modeling strategies for open quantum systems, with implications for quantum control and error mitigation in near-term quantum processors.

Problem

• Characterizing non-Markovian dynamics in open quantum systems
• Developing structure-preserving methods for quantum evolution modeling
• Comparing KL expansion and neural networks for dynamics prediction

Innovation

• Structure-preserving TCL master equation approach
• KL expansion for optimal dynamics representation
• Neural networks for data-driven interaction learning