Path-filtering in path-integral simulations of open quantum systems using GFlowNets.

Area of Science:

• Quantum mechanics
• Computational physics
• Machine learning

Background:

• Modeling open quantum systems often uses the influence functional (IF) approach for path-integral equations.
• Path-filtering schemes reduce computational cost by removing low-threshold IF elements, but may compromise physical accuracy.
• Ensuring mathematical stability does not guarantee the preservation of the simulated quantum process's physics.

Purpose of the Study:

• To explore training Generative Flow Networks (GFlowNets) for creating filtering protocols in quantum dynamics simulations.
• To optimize filtering protocols for both mathematical stability and physical accuracy.
• To investigate GFlowNets' ability to generate effective filtering strategies for open quantum systems.

Main Methods:

• Generative Flow Networks (GFlowNets) were trained using the trajectory balance objective.
• The model generated sets of paths to augment truncated initial sets.
• Reward functions were designed to ensure conservation of the density matrix trace, real populations, and accurate dynamics compared to a reference.

Main Results:

• GFlowNets successfully learned to produce filtering protocols for quantum dynamics simulations.
• The trained model demonstrated the ability to maintain mathematical stability and physical accuracy.
• Proof-of-concept simulations on a two-level system coupled to a dissipative reservoir showcased the effectiveness of GFlowNet-generated filtering solutions.

Conclusions:

• GFlowNets offer an elegant and effective approach to optimizing filtering protocols for open quantum system simulations.
• This method enhances the feasibility of complex quantum dynamics modeling by balancing computational efficiency with physical fidelity.
• The study highlights the potential of machine learning, specifically GFlowNets, in advancing quantum computational methods.