Optimization of Bottlenecks in Quantum Graphs Guided by Fiedler Vector-Based Spectral Derivatives

TL;DR

This paper investigates how spectral properties, especially the Fiedler vector, can be used to identify and optimize bottlenecks in quantum networks modeled as QDAGs, improving entanglement distribution.

Contribution

It introduces eigenvalue-based rewiring techniques leveraging the Fiedler vector to optimize quantum network routing and entanglement distribution.

Findings

Fiedler vector correlates with network bottlenecks.

Rewiring based on spectral derivatives enhances entanglement flow.

Spectral methods improve quantum network optimization.

Abstract

This paper discusses the relationships between the Fiedler vector, the Cheeger constant, and threshold behaviors in networks of quantum resource nodes represented as Quantum Directed Acyclic Graphs (QDAGs). We explore how these mathematical constructs can be applied to understand the dynamics of quantum information flow in QDAGs, especially in the context of routing problems with bottlenecks in graph signal processing, and how new eigenvalue-based rewiring techniques can optimize entanglement distribution between nodes in a QDAG.