Energy and efficiency of adiabatic quantum search algorithms

We present the results of a detailed analysis of a general, unstructured adiabatic quantum search of a database of N items. In particular, we examine the effects on the computation time of adding energy to the system. We find that by increasing the lowest eigenvalue of the time-dependent Hamiltonian temporarily to a maximum of proportional torootN, it is possible to do the calculation in constant time. This leads us to derive the general theorem which provides the adiabatic analogue of the rootN bound of conventional quantum searches. The result suggests that the action associated with the oracle term in the time-dependent Hamiltonian is a direct measure of the resources required by the adiabatic quantum search.