Quantum and classical algorithms for graph classification and search problems

Brendan Douglas

    Research output: ThesisDoctoral Thesis

    203 Downloads (Pure)

    Abstract

    [Truncated abstract] This thesis is split into three parts, each addressing the overarching theme of applying graph theoretic techniques to classi cation and search problems. Part I explores this theme in the context of quantum algorithms, in particular involving quantum walks, coined by Aharonov et al. in 1993 [1]. As a quantum analogue to classical random walks, quantum walks represent a promising candidate for quantum algorithms providing speed-ups over known classical methods. I will discuss two categories of quantum walk algorithms; quantum search and graph isomorphism. In particular, the e ciency of quantum walk based search algorithms on various families of graphs will be investigated, linking both e ciency of quantum circuit implementation and the complexity of the search problem to the symmetry of the underlying graphs. Several families of graphs are presented that are amenable to efficient quantum walk based searching, together with explicit quantum circuit implementations. In the case of the n-cube, I show that O(p2n) steps of a quanum walk are suffcient to nd a marked sub-d-cube (where d
    Original languageEnglish
    QualificationDoctor of Philosophy
    Publication statusUnpublished - 2011

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