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

TL;DR

This paper introduces a physics-informed neural network approach integrated with the quantum state framework to efficiently simulate open quantum system dynamics, especially effective at high temperatures with weak non-Markovian effects.

Contribution

It presents a novel PINN-based method for quantum dynamics simulation that reduces computational cost compared to traditional variational techniques.

Findings

High accuracy in simulating dissipative dynamics at high temperatures.

Challenges with error accumulation in strongly non-Markovian low-temperature regimes.

Abstract

This work integrates the physics-informed neural network (PINN) approach into the neural quantum state framework to simulate open quantum system dynamics, to circumvent the computationally expensive time-dependent variational principle required in conventional variational methods. The proposed PINN-DQME method employs time-encoded neural networks within a time-domain decomposition strategy to represent the evolution governed by the dissipaton-embedded quantum master equation (DQME). We implement and validate this approach in the single-impurity Anderson model, benchmarking the PINN-DQME results against the numerically exact hierarchical equations of motion. The PINN-DQME method demonstrates high accuracy in simulating quantum dissipative dynamics at high temperatures, where non-Markovian effects are weak. However, for strongly non-Markovian dynamics at low temperatures, it encounters challenges with error accumulation during time propagation, highlighting an area for future refinement in applying PINNs to complex quantum dynamical settings.