Quantum Walks in the Normalized Laplacian

TL;DR

This paper characterizes perfect state transfer in quantum walks based on the normalized Laplacian, highlighting unique classical-quantum walk connections and excluding certain trees as potential hosts.

Contribution

It introduces a novel analysis of perfect state transfer in normalized Laplacian quantum walks and explores their relationship with classical random walks.

Findings

Identifies conditions for perfect state transfer in normalized Laplacian quantum walks

Establishes a link between classical random walks and quantum walks in this model

Rules out specific trees as candidates for perfect state transfer

Abstract

We provide a characterization of perfect state transfer in a quantum walk whose Hamiltonian is given by the normalized Laplacian. We discuss a connection between classical random walks and quantum walks only present in this model, and we also rule out several trees as candidates to host perfect state transfer.