Machine learning meets su(n) Lie algebra: Enhancing quantum dynamics learning with exact trace conservation.

Area of Science:

• Quantum mechanics
• Computational physics
• Machine learning

Background:

• Machine learning (ML) shows promise for simulating quantum dissipative dynamics.
• Existing ML methods struggle with physical constraints like trace conservation in reduced density matrices (RDMs).
• Physics-informed neural networks (PINNs) often lack full physical consistency.

Purpose of the Study:

• To develop a novel ML approach for simulating quantum dissipative dynamics that inherently enforces trace conservation.
• To improve the accuracy, robustness, and efficiency of ML models for quantum system simulations.
• To address limitations of existing PINNs in maintaining physical constraints.

Main Methods:

• Representing RDMs using the su(n) Lie algebra: an identity matrix plus traceless, orthogonal operators.
• Learning only the coefficients of these operators to ensure inherent trace conservation.
• Comparing four neural network architectures: PUNN, su(n)-PUNN, PINN, and su(n)-PINN on benchmark quantum systems.

Main Results:

• The su(n) Lie algebra-based approach guarantees exact trace conservation without penalty terms.
• This method simplifies optimization and enhances learning efficiency.
• The su(n)-PINN demonstrated superior accuracy, robustness, and efficiency compared to conventional methods.

Conclusions:

• The su(n) Lie algebra framework offers a physically consistent and efficient method for ML-based quantum dissipative dynamics.
• This approach overcomes key limitations of traditional PINNs in enforcing physical constraints.
• The developed method represents a significant advancement in applying ML to complex quantum simulations.