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    Quantum Walks and Structured Searches on Free Groups and Networks

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    Genre
    Thesis/Dissertation
    Date
    2017
    Author
    Ratner, Michael
    Advisor
    Yang, Wei-shih, 1954-
    Committee member
    Walton, Chelsea
    Klapper, Isaac
    Shi, Justin Y.
    Department
    Mathematics
    Subject
    Mathematics
    Computer Science
    Quantum Physics
    Cayley Graphs
    Green's Functions
    Quantum Walks
    Random Graphs
    Spatial Search
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/2215
    
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    DOI
    http://dx.doi.org/10.34944/dspace/2197
    Abstract
    Quantum walks have been utilized by many quantum algorithms which provide improved performance over their classical counterparts. Quantum search algorithms, the quantum analogues of spatial search algorithms, have been studied on a wide variety of structures. We study quantum walks and searches on the Cayley graphs of finitely-generated free groups. Return properties are analyzed via Green’s functions, and quantum searches are examined. Additionally, the stopping times and success rates of quantum searches on random networks are experimentally estimated.
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