The Dynamics of Entanglement in the Adiabatic Search and Deutsch Algorithms

The goal of this paper is to study the effect of entanglement on the running time of a quantum computation. Adiabatic quantum computation is suited to this kind of study, since it allows us to explicitly calculate the time evolution of the entanglement throughout the calculation. On the other hand however, the adiabatic formalism makes it impossible to study the roles of entanglement and fidelity separately, which means that results have to be interpreted carefully. We study two algorithms: the search algorithm and the Deutsch-Jozsa algorithm. We find some evidence that entanglement can be considered a resource in quantum computation.