  We propose a scalable implementation of Grover's quantum search algorithm in
a trapped-ion quantum information processor. The system is initialized in an
entangled Dicke state by using simple adiabatic techniques. The
inversion-about-average and the oracle operators take the form of single
off-resonant laser pulses, addressing, respectively, all and half of the ions
in the trap. This is made possible by utilizing the physical symmetrie of the
trapped-ion linear crystal. The physical realization of the algorithm
represents a dramatic simplification: each logical iteration (oracle and
inversion about average) requires only two physical interaction steps, in
contrast to the large number of concatenated gates required by previous
approaches. This does not only facilitate the implementation, but also
increases the overall fidelity of the algorithm.
