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

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.