Quantum Search on Strongly Regular Graphs
Year: 2013
Type: dissertation
Abstract: In 1996, Farhi & Gutmann presented a continuous time analogue of Grover’s algorithm which was later interpreted as search by a quantum random walk on the complete graph. Similar work has since then been done on hypercubes and periodic lattices. We investigate the same search algorithm but for a new type of graphs called strongly regular graphs. The problem is solved by a, in this context, new technique involving degenerate perturbation theory. The result is that the search is optimal on all strongly regular graphs when the number of vertices N is large. However, different kinds of strongly regular graphs perform different when N is not large. Analyzing this provides some insight into what properties of graphs that are important for quantum search. Apart from the results, an important takeaway is the degenerate perturbation theory technique that was used to solve the problem and might be useful in solving other similar problems. In the thesis, an alternative solution to the complete graph case is given using this method. Also, the fact that strongly regular graphs proved to be convenient to analyze in these kinds of settings suggests that they can be used in other similar problems.
Author: Jonatan Janmark
Institution: KTH Royal Institute of Technology
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W605879172