# Dimerized Decomposition of Quantum Evolution on an Arbitrary Graph

## TL;DR

This paper introduces a systematic dimerized decomposition method to analyze quantum evolution on arbitrary graphs, enabling intuitive understanding of complex network dynamics by separating local properties from global structure.

## Contribution

The paper presents a novel dimerized decomposition approach that models quantum dynamics on any network topology using global flows, offering an intuitive alternative to spectral methods.

## Key findings

- Provides a new framework for analyzing quantum dynamics on complex networks.
- Separates local subsystem properties from global network structure.
- Enhances understanding of quantum evolution through flow-based interpretation.

## Abstract

The study of quantum evolution on graphs for diversified topologies is beneficial to modeling various realistic systems. A systematic method, the dimerized decomposition, is proposed to analyze the dynamics on an arbitrary network. By introducing global "flows" among interlinked dimerized subsystems, each of which locally consists of an input and a output port, the method provides an intuitive picture that the local properties of the subsystem are separated from the global structure of the network. The pictorial interpretation of quantum evolution as multiple flows through the graph allows for the analysis of the complex network dynamics supplementary to the conventional spectral method.