Bachelor Thesis at the Dept. of Physics, University of Milan, March-September 2020
- Full Title: Quantum Walks with time-dependent Hamiltonians and their application to the search problem on graphs
- Supervisors: Prof M. Paris, Prof S. Olivares, Dr C. Benedetti
In this thesis we studied the application of quantum walks with time-dependent Hamiltonian to the search problem on graphs. We compared the standard time-independent quantum walks search with the time-dependent one, with the goal of understanding if this implementation can lead to an improvement in performance for selected graphs. In particular, we studied its application to the cycle graph, where the search problem is not solved with the standard quantum walk approach of Farhi and Gutmann, and for completeness gave some results for the complete graph, in which the search may be accomplished exactly. In order to do so, we compared the two approaches in terms of search, localization, and a measure of robustness.
Here a long summary and the complete thesis can be found. As well as the dissertation slides.
The folder code currently contains various python code with lots of duplicates and quite messy. An overall tidy up is underway, with a consequent rewrite in Julia.