Quantum Enhanced Pattern Search Optimization

Abstract: 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.