Learning Volterra Kernels for Non-Markovian Open Quantum Systems
Quantum Physics
2026-01-15 v1 Optimization and Control
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
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Cite
@article{arxiv.2601.09075,
title = {Learning Volterra Kernels for Non-Markovian Open Quantum Systems},
author = {Jimmie Adriazola and Katarzyna Roszak},
journal= {arXiv preprint arXiv:2601.09075},
year = {2026}
}