Dimension truncation for open quantum systems in terms of tensor networks

TL;DR

This paper introduces a tensor network-based method called reservoir network to estimate the minimal effective reservoir dimension in open quantum systems, aiding understanding of memory effects and enabling new computational approaches.

Contribution

It presents a novel tensor network formalism for modeling open quantum systems and introduces the reservoir network as a tool for analyzing memory effects and system-environment interactions.

Findings

Reservoir network efficiently encodes open system dynamics.

Method facilitates estimation of minimal reservoir dimension.

Potential applications in numerical simulations and machine learning.

Abstract

We present novel and simple estimation of a minimal dimension required for an effective reservoir in open quantum systems. Using a tensor network formalism we introduce a new object called a reservoir network (RN). The reservoir network is the tensor network in the form of a Matrix Product State, which contains all effects of open dynamics. This object is especially useful for understanding memory effects. We discuss possible applications of the reservoir network and the estimation of dimension to develop new numerical and machine learning based methods for open quantum systems.