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QUANTUM SEARCH ON RANDOM GRAPHS
Ahn, Alexander Song
Ahn, Alexander Song
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Thesis/Dissertation
Date
2021
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Mathematics
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Ahn_temple_0225M_14356.pdf
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http://dx.doi.org/10.34944/dspace/6471
Abstract
This project was motivated by the following question: what information do the properties of a random graph contain about the performance of a quantum search acting on it? To investigate this problem, we define a notion of search time to quantify the behavior of a quantum search, and find strong evidence of a relation between its distribution and the model of random graph on which the search was performed. Surprisingly, we also find strong evidence that the return time of a classical random walk initialized at the marked vertex is closely related to its search time, and that the distribution of degrees over the graph vertices may play a significant role in this relation.
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