Learning Volterra Kernels for Non-Markovian Open Quantum Systems

TL;DR

This paper introduces a data-driven method to identify non-Markovian quantum dynamics by modeling the memory effects with Volterra kernels, enabling better understanding of complex open quantum systems.

Contribution

The paper presents a novel framework combining the Nakajima--Zwanzig formalism with rational function approximation to learn operator-valued memory kernels in quantum systems.

Findings

Successfully models non-Markovian dynamics using Volterra kernels.

Demonstrates the effectiveness of Padé approximants in approximating correlation functions.

Provides a well-posed optimization approach for kernel learning.

Abstract

We develop a data-driven framework for identifying non-Markovian dynamical equations of motion for open quantum systems. Starting from the Nakajima--Zwanzig formalism, we vectorize the reduced density matrix into a four-dimensional state vector and cast the dynamics as a Volterra integro-differential equation with an operator-valued memory kernel. The learning task is then formulated as a constrained optimization problem over the admissible operator space, where correlation functions are approximated by rational functions using Pad\'e approximants. We establish well-posedness of the learnin