Natural and Quantum Walks on Graphs

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Khanteimouri, Payam | 2010

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 40652 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Daneshgar, Amir
Abstract:
A Markov chain on a base graph is a stochatic process that can be visualized as a particle movement such that the probability of moving from a vertex i to a vertex j is specified by the corresponding transition kernel Ka. In this thesis, based on the result of A.Daneahgar and H.Hajiabolhassa, we recall some general necessary conditions for the existence of graph homomorphism, which holds on both directed and undirected cases. A discrete-time quantum walk on a graph is the repeated application of a unitary evolution operator. In this regard, also, we explain the quantum search algorithm on the result of Grover and the algorithms that is based on the quantum walk approach of A.Ambainis, E.Bach, A.Nayak, A.Vishwanath and J.Watrous
Keywords:
Random Walk ; Graph Homomorphism ; Quantum Bit ; Quotient Walk ; Quantum Walk

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