Abstract
Using a classical computer to search a database takes an amount of time that grows linearly with the number of items one wishes to search through. Quantum algorithms for the same task can provide up to a quadratic speedup, lessening the number of queries needed for a successful search. Previous work shows that nonlinear quantum walks, inspired by mean-field theories of the Bose-Hubbard model, could search databases faster than present (linear) quantum walk algorithms. This thesis analyzes a general case of these nonlinear quantum walks, showing that one model allows for search of a database in constant time, while also increasing the length of time during which the system can be measured relative to previous models. This model is then investigated using the Truncated Wigner Approximation to more accurately compute the dynamics of the Bose-Hubbard model corresponding to these nonlinear quantum walks. These calculations find that the performance of the algorithm is less than predicted by the mean-field theory.