Quantum Stochastic Walks: A Generalization of Classical Random Walks and Quantum Walks
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Quantum Stochastic Walks: A Generalization of Classical Random Walks and Quantum Walks
| Title: | Quantum Stochastic Walks: A Generalization of Classical Random Walks and Quantum Walks |
| Author: |
Rodríguez-Rosario, César A.; Aspuru-Guzik, Alan; Whitfield, James D.
Note: Order does not necessarily reflect citation order of authors. |
| Citation: | Whitfield, James D., César A. Rodríguez-Rosario, and Alán Aspuru-Guzik. 2010. Quantum stochastic walks: A generalization of classical random walks and quantum walks. Physical Review A 81(2): 022323. |
| Full Text & Related Files: |
0905.2942v2.pdf (256.3Kb; PDF) 
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| 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. |
| Published Version: | doi: 10.1103/PhysRevA.81.022323 |
| Terms of Use: | This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP |
| Citable link to this page: | http://nrs.harvard.edu/urn-3:HUL.InstRepos:4685234 |
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Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University
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