Simulating non-Markovian open quantum dynamics by exploiting physics-informed neural network

Area of Science:

• Quantum mechanics
• Computational physics
• Machine learning in physics

Background:

• Simulating open quantum systems is computationally demanding.
• Conventional variational methods often rely on the expensive time-dependent variational principle.
• Developing efficient numerical methods for quantum dynamics is crucial.

Purpose of the Study:

• To introduce a new computational framework for simulating open quantum system dynamics.
• To integrate physics-informed neural networks (PINNs) into the neural quantum state (NQS) approach.
• To bypass the computational cost associated with traditional variational methods.

Main Methods:

• The proposed PINN-DQME method utilizes time-encoded neural networks.
• A time-domain decomposition strategy is employed to represent system evolution.
• The method models dynamics governed by the dissipaton-embedded quantum master equation (DQME).

Main Results:

• The PINN-DQME method was implemented and validated using the single-impurity Anderson model.
• Results were benchmarked against the numerically exact hierarchical equations of motion.
• High accuracy was achieved for quantum dissipative dynamics at high temperatures (weak non-Markovian effects).

Conclusions:

• The PINN-DQME method provides an accurate approach for simulating quantum dissipative dynamics under specific conditions.
• Challenges with error accumulation were observed for strongly non-Markovian dynamics at low temperatures.
• Future work should focus on refining PINN applications for complex quantum dynamical systems.