From classical to quantum walks with stochastic resetting on networks

Sascha Wald; Lucas Böttcher

doi:10.1103/PhysRevE.103.012122

From classical to quantum walks with stochastic resetting on networks

Sascha Wald, Lucas Böttcher

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Abstract

Random walks are fundamental models of stochastic processes with applications in various fields including physics, biology, and computer science. We study classical and quantum random walks under the influence of stochastic resetting on arbitrary networks. Based on the mathematical formalism of quantum stochastic walks, we provide a framework of classical and quantum walks whose evolution is determined by graph Laplacians. We study the influence of quantum effects on the stationary and long-time average probability distribution by interpolating between the classical and quantum regime. We compare our analytical results on stationary and long-time average probability distributions with numerical simulations on different networks, revealing differences in the way resets affect the sampling properties of classical and quantum walks.

Original language	English
Article number	012122
Number of pages	12
Journal	Phys. Rev. E
Volume	103
Issue number	1
DOIs	https://doi.org/10.1103/PhysRevE.103.012122
Publication status	Published - 19 Jan 2021
Externally published	Yes

Bibliographical note

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

Keywords

cond-mat.stat-mech
quant-ph

ASJC Scopus subject areas

Condensed Matter Physics
Statistical and Nonlinear Physics
Statistics and Probability

Access to Document

10.1103/PhysRevE.103.012122Licence: CC BY

PublishedFinal published version, 1.54 MBLicence: CC BY

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