Comfortability of quantum walks on embedded graphs on surfaces
- URL: http://arxiv.org/abs/2501.06765v1
- Date: Sun, 12 Jan 2025 10:23:01 GMT
- Title: Comfortability of quantum walks on embedded graphs on surfaces
- Authors: Yusuke Higuchi, Etsuo Segawa,
- Abstract summary: We find a detection of the orientablility of the underlying embedding by the scattering information.<n>We find that quantum walker feels more comfortable to a surface with small genus in some natural setting.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In this paper, a quantum walk model which reflects the underlying embedding on the surface is proposed. We obtain the scattering matrix of this quantum walk model characterized by the faces on the surface, and find a detection of the orientablility of the underlying embedding by the scattering information. The comfortability is the square norm of the stationary state restricted to the internal and reflected by the underlying embedding. We find that quantum walker feels more comfortable to a surface with small genus in some natural setting.
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