  We show that by a suitable choice of time-dependent Hamiltonian, the search
for a marked item in an unstructured database can be achieved in unit time,
using Adiabatic Quantum Computation. This is a considerable improvement over
the O(sqrt(N)) time required in previous algorithms. The trade-off is that in
the intermediate stages of the computation process, the ground state energy of
the computer increases to a maximum of O(sqrt(N)), before returning to zero at
the end of the process.
