Scaling limit of the time averaged distribution for continuous time quantum walk and Szegedy's walk on the path
Y Ide - arXiv preprint arXiv:2301.00283, 2022 - arxiv.org
arXiv preprint arXiv:2301.00283, 2022•arxiv.org
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.
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.
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 .
arxiv.org