Demonstrates the relationship between continuous and Szegedy’s quantum walks, indicating implications for their distributions.
In this paper, we consider Szegedy’s walk, a type of discrete time quantum walk, and corresponding continuous time quantum walk related to the birth and death chain. We show that the scaling limit of time averaged distribution for the continuous time quantum walk induces that of Szegedy’s walk if there exists the spectral gap on so-called the corresponding Jacobi matrix .
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Ide Yusuke (2023) studied this question.
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