  We propose the physical implementation of a Grover-like search problem by
means of Frenkel exciton trapping at a shallow isotopic impurity against a
background of competing mechanisms. The search culminating at the impurity
molecule, designated the "winner" site, is marked by its enhanced interaction
with acoustic phonons at low temperatures. The quantum search proceeds with the
assistance of an Oracle-like exciton-phonon interaction which addresses only
the impurity site, via the Dyson propagator within the Green's function
formalism. The optimum parameters of a graph lattice with long-range intersite
interactions required to trap the exciton in the fastest time are determined,
and estimates of error rates for the naphthalene doped organic system are
evaluated. We extend analysis of quantum search to a fluctuating long-range
interacting cycle (LRIC) graph lattice system.
