Grover-like search via Frenkel exciton trapping mechanism

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.