Quantum walk on a comb with infinite teeth

• URL: http://arxiv.org/abs/2107.08866v2
• Date: Sun, 16 Jan 2022 17:44:45 GMT
• Title: Quantum walk on a comb with infinite teeth
• Abstract summary: We study continuous time quantum random walk on a comb with infinite teeth. The walk along the spine and into the teeth behaves qualitatively as a quantum random walk on a line.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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