Energy and efficiency of adiabatic quantum search algorithms
Saurya Das, Randy Kobes, G. Kunstatter · Journal of Physics A Mathematical and General · 2003
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 ∝√ N , 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 √ N 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.