Quantum search algorithms provide a quadratic speed-up over classical search for unstructured databases. While single-particle quantum search is well understood for a large set of graphs, considerably less is known about the behavior of multi-particle quantum search algorithms. In this thesis, we consider continuous-time quantum search of multiple bosons or fermions over arbitrary graphs and develop a method to identify the marked vertex after multiple measurements. We investigate the performance of bosonic search as compared to fermionic search by simulating this search algorithm and calculating the runtime numerically. It is found that, though bosonic search is substantially faster than fermionic search, the fermionic runtime may not scale as fast with the graph size $N$ as was shown in [6], if our method of post-measurement marked vertex identification is used. Furthermore, it is shown that the optimal hopping rate for a quantum search is different for bosons and fermions, and in general not equal to the optimal single particle hopping rate of [1].

https://github.com/TiTaTovenaar2004/QuantumSearch