Toward Quantum-Aware Machine Learning: Improved Prediction of Quantum Dissipative Dynamics via Complex Valued Neural Networks

TL;DR

This paper introduces complex-valued neural networks (CVNNs) for modeling quantum dissipative dynamics, showing they outperform real-valued neural networks in accuracy, stability, and physical consistency across various quantum systems.

Contribution

The paper pioneers the use of CVNNs for quantum dynamics, maintaining quantum coherence and improving simulation fidelity over traditional real-valued neural networks.

Findings

CVNNs outperform RVNNs in convergence speed and stability

CVNNs better preserve physical properties like trace and Hermiticity

Performance gains increase with system size and complexity

Abstract

Accurately modeling quantum dissipative dynamics remains challenging due to environmental complexity and non-Markovian memory effects. Although machine learning provides a promising alternative to conventional simulation techniques, most existing models employ real-valued neural networks (RVNNs) that inherently mismatch the complex-valued nature of quantum mechanics. By decoupling the real and imaginary parts of the density matrix, RVNNs can obscure essential amplitude-phase correlations, compromising physical consistency. Here, we introduce complex-valued neural networks (CVNNs) as a physics-consistent framework for learning quantum dissipative dynamics. CVNNs operate directly on complex-valued inputs, preserve the algebraic structure of quantum states, and naturally encode quantum coherences. Through numerical benchmarks on the spin-boson model and several variants of the Fenna-Matthews-Olson complex, we demonstrate that CVNNs outperform RVNNs in convergence speed, training stability, and physical fidelity -- including significantly improved trace conservation and Hermiticity. These advantages increase with system size and coherence complexity, establishing CVNNs as a robust, scalable, quantum-aware classical approach for simulating open quantum systems in the pre-fault-tolerant quantum era.