Quantum walk on a comb with infinite teeth

TL;DR

This paper investigates the behavior of continuous time quantum random walks on an infinite comb structure, revealing unique decay rates and escape probabilities that differ from classical counterparts, with implications for quantum diffusion.

Contribution

It provides a detailed analysis of quantum walk dynamics on a comb with infinite teeth, highlighting differences from classical walks and characterizing escape and diffusion properties.

Findings

Return probability decays as t^{-1}

Finite probability of escape into teeth

Quantum walk behavior resembles a walk on a line

Abstract

We study continuous time quantum random walk on a comb with infinite teeth and show that the return probability to the starting point decays with time $t$ as $t^{-1}$. We analyse the diffusion along the spine and into the teeth and show that the walk can escape into the teeth with a finite probability and goes to infinity along the spine with a finite probability. The walk along the spine and into the teeth behaves qualitatively as a quantum random walk on a line. This behaviour is quite different from that of classical random walk on the comb.