Machine learning time-local generators of open quantum dynamics

TL;DR

This paper explores how neural networks can learn and predict open quantum system dynamics from unitary evolution, demonstrating their ability to approximate time-local generators and extrapolate long-term behavior.

Contribution

It shows that neural networks can effectively learn time-local generators of open quantum dynamics from unitary evolution data, including cases with time-independent generators.

Findings

Neural networks can learn time-local generators from unitary dynamics.

Time-independent generators can be extrapolated to unseen times.

This approach aids in studying long-time quantum dynamics and thermalization.

Abstract

In the study of closed many-body quantum systems one is often interested in the evolution of a subset of degrees of freedom. On many occasions it is possible to approach the problem by performing an appropriate decomposition into a bath and a system. In the simplest case the evolution of the reduced state of the system is governed by a quantum master equation with a time-independent, i.e. Markovian, generator. Such evolution is typically emerging under the assumption of a weak coupling between the system and an infinitely large bath. Here, we are interested in understanding to which extent a neural network function approximator can predict open quantum dynamics - described by time-local generators - from an underlying unitary dynamics. We investigate this question using a class of spin models, which is inspired by recent experimental setups. We find that indeed time-local generators can be learned. In certain situations they are even time-independent and allow to extrapolate the dynamics to unseen times. This might be useful for situations in which experiments or numerical simulations do not allow to capture long-time dynamics and for exploring thermalization occurring in closed quantum systems.