Probing non-Markovian dynamics of noisy intermediate-scale quantum (NISQ) systems

A precise understanding of the influence of an environment on quantum dynamics, which is at the heart of the theory of open quantum systems, is crucial for further progress in the development of controllable large-scale quantum systems. However, existing approaches to account for complex system environment interaction in the presence of memory effects are either based on heuristic and oversimplified principles or give rise to computational difficulties. In practice, one can take advantage of available experimental data and replace the first-principles simulation with a data-driven analysis that is often much simpler. Inspired by recent advances in data analysis and machine learning, we suggest a data-driven approach to the analysis of the non-Markovian dynamics of open quantum systems. Our method allows capturing the most important properties of open quantum systems, such as the effective dimension of the environment, eigenfrequencies of the joint system-environment quantum dynamics, as well as reconstructing the minimal Markovian embedding, predicting dynamics, and denoising of measured quantum trajectories. We demonstrate the performance of the suggested approach on various models of open quantum systems, including a qubit coupled with a finite environment, a spin-boson model, and the damped Jaynes-Cummings model.