Neural Network Approach for Non-Markovian Dissipative Dynamics of Many-Body Open Quantum Systems

2024-04-17

arXiv.org

AI Summary

Simulating dissipative dynamics of non-Markovian open quantum many-body systems faces prohibitive computational complexity, rendering conventional methods intractable for large-scale systems. Method: This paper introduces a novel AI-driven paradigm that integrates neural quantum states with the second-order quantized dissipaton master equation (DQME-SQ). It proposes, for the first time, a compact representation of the reduced density tensor using a restricted Boltzmann machine (RBM), explicitly encoding system–bath correlations and non-Markovian memory effects. Contribution/Results: On strongly correlated non-Markovian benchmark models, the method achieves accuracy comparable to the hierarchical equations of motion (HEOM), yet with a significantly reduced number of dynamical variables. This alleviates the scalability bottleneck inherent in traditional approaches, enabling efficient and feasible large-scale simulations of non-Markovian quantum dynamics.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Sampling/Simulation-based Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Simulating the dynamics of open quantum systems coupled to non-Markovian environments remains an outstanding challenge due to exponentially scaling computational costs. We present an artificial intelligence strategy to overcome this obstacle by integrating the neural quantum states approach into the dissipaton-embedded quantum master equation in second quantization (DQME-SQ). Our approach utilizes restricted Boltzmann machines (RBMs) to compactly represent the reduced density tensor, explicitly encoding the combined effects of system-environment correlations and nonMarkovian memory. Applied to model systems exhibiting prominent effects of system-environment correlation and non-Markovian memory, our approach achieves comparable accuracy to conventional hierarchical equations of motion, while requiring significantly fewer dynamical variables. The novel RBM-based DQME-SQ approach paves the way for investigating non-Markovian open quantum dynamics in previously intractable regimes, with implications spanning various frontiers of modern science.

Problem

• Reducing computational scaling for non-Markovian quantum dynamics
• Encoding environmental memory via dissipaton-embedded quantum master equation
• Enhancing scalability and interpretability in open quantum systems

Innovation

• Neural networks simulate non-Markovian quantum dynamics
• Dissipaton-embedded master equation encodes memory efficiently
• Compact representation enhances scalability and interpretability