  This paper introduces a quantum-classical hybrid algorithm for generalized
pattern search (GPS) algorithms. We introduce a quantum search step algorithm
using amplitude amplification, which reduces the number of oracle calls needed
during the search step from O(N) classical calls to O(N^(1/2)) quantum calls.
This work addresses three fundamental issues with using a quantum search step
with GPS. First we address the need to mark an improved mesh point, a
requirement of the amplitude amplification algorithm. Second, we introduce a
modified version of the amplitude amplification algorithm QSearch, which is
guaranteed to terminate using a finite number of iterations. Third, we avoid
disrupting the GPS algorithm's convergence by limiting the quantum algorithm to
the search step.
