  We analyze the possibility of modifying the original Farhi-Gutmann
Hamiltonian algorithm in order to speed up the procedure for producing a
suitably distributed unknown normalized quantum mechanical state. Such a
modification is feasible provided only a nearly optimal fidelity is sought. We
propose to select the lower bounds of the nearly optimal fidelity values such
that their deviations from unit fidelity are less than the minimum error
probability characterizing the optimum ambiguous discrimination scheme between
the two nonorthogonal quantum states yielding the chosen nearly optimal
fidelity values. Departing from the working assumptions of perfect state
overlap and uniform distribution of the target state on the unit sphere in
N-dimensional complex Hilbert space, we determine that the modified algorithm
can indeed outperform the original analog counterpart of a quantum search
algorithm. This performance enhancement occurs in terms of speed for a
convenient choice of both the ratio E'/E between the energy eigenvalues E' and
E of the modified search Hamiltonian and the quantum mechanical overlap x
between the source and the target states. Finally, we briefly discuss possible
analytical improvements of our investigation together with its potential
relevance in practical quantum engineering applications.
