Quantum walk on a comb with infinite teeth

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.

65 pages, 46 figures

References in corpus (2)

• Exponential algorithmic speedup by quantum walk
• On the relationship between continuous- and discrete-time quantum walk