Grover's unstructured search algorithm is one of the best examples to date
for the superiority of quantum algorithms over classical ones. Its
applicability, however, has been questioned by many due to its oracular nature.
We propose a mechanism to carry out a quantum adiabatic variant of Grover's
search algorithm using a single bosonic particle placed in an optical lattice.
By studying the scaling of the gap and relevant matrix element in various
spatial dimensions, we show that a quantum speedup can already be gained in
three dimensions. We argue that the suggested scheme is realizable with
present-day experimental capabilities.Comment: 6 pages, 4 figure
