  Several mathematical problems can be modeled as a search in a database. An
example is the problem of finding the minimum of a function. Quantum algorithms
for solving this problem have been proposed and all of them use the quantum
search algorithm as a subroutine and several intermediate measurements are
realized. In this work, it is proposed a new quantum algorithm for finding the
minimum of a function in which quantum search is not used as a subroutine and
only one measurement is needed. This is also named asymptotic quantum search.
As an example, we propose a quantum algorithm based on asymptotic quantum
search and quantum counting able to calculate a lower bound of the probability
of finding a Diophantine equation with integer solution.
