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Title: Quantum stochastic walks: A generalization of classical random walks and quantum walks

Abstract

We introduce the quantum stochastic walk (QSW), which determines the evolution of a generalized quantum-mechanical walk on a graph that obeys a quantum stochastic equation of motion. Using an axiomatic approach, we specify the rules for all possible quantum, classical, and quantum-stochastic transitions from a vertex as defined by its connectivity. We show how the family of possible QSWs encompasses both the classical random walk (CRW) and the quantum walk (QW) as special cases but also includes more general probability distributions. As an example, we study the QSW on a line and the glued tree of depth three to observe the behavior of the QW-to-CRW transition.

Authors:
; ;  [1]
  1. Department of Chemistry and Chemical Biology and Center for Excitonics, Harvard University, Cambridge, Massachusetts 02138 (United States)
Publication Date:
OSTI Identifier:
21408212
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 81; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.81.022323; (c) 2010 The American Physical Society; Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EQUATIONS OF MOTION; EVOLUTION; GRAPH THEORY; PROBABILITY; QUANTUM MECHANICS; RANDOMNESS; STOCHASTIC PROCESSES; DIFFERENTIAL EQUATIONS; EQUATIONS; MATHEMATICS; MECHANICS; PARTIAL DIFFERENTIAL EQUATIONS

Citation Formats

Whitfield, James D, Rodriguez-Rosario, Cesar A, and Aspuru-Guzik, Alan. Quantum stochastic walks: A generalization of classical random walks and quantum walks. United States: N. p., 2010. Web. doi:10.1103/PHYSREVA.81.022323.
Whitfield, James D, Rodriguez-Rosario, Cesar A, & Aspuru-Guzik, Alan. Quantum stochastic walks: A generalization of classical random walks and quantum walks. United States. https://doi.org/10.1103/PHYSREVA.81.022323
Whitfield, James D, Rodriguez-Rosario, Cesar A, and Aspuru-Guzik, Alan. 2010. "Quantum stochastic walks: A generalization of classical random walks and quantum walks". United States. https://doi.org/10.1103/PHYSREVA.81.022323.
@article{osti_21408212,
title = {Quantum stochastic walks: A generalization of classical random walks and quantum walks},
author = {Whitfield, James D and Rodriguez-Rosario, Cesar A and Aspuru-Guzik, Alan},
abstractNote = {We introduce the quantum stochastic walk (QSW), which determines the evolution of a generalized quantum-mechanical walk on a graph that obeys a quantum stochastic equation of motion. Using an axiomatic approach, we specify the rules for all possible quantum, classical, and quantum-stochastic transitions from a vertex as defined by its connectivity. We show how the family of possible QSWs encompasses both the classical random walk (CRW) and the quantum walk (QW) as special cases but also includes more general probability distributions. As an example, we study the QSW on a line and the glued tree of depth three to observe the behavior of the QW-to-CRW transition.},
doi = {10.1103/PHYSREVA.81.022323},
url = {https://www.osti.gov/biblio/21408212}, journal = {Physical Review. A},
issn = {1050-2947},
number = 2,
volume = 81,
place = {United States},
year = {Mon Feb 15 00:00:00 EST 2010},
month = {Mon Feb 15 00:00:00 EST 2010}
}