A note on adapting methods for continuous global optimization to the discrete case
Annals of Operations Research
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Quantum computation and quantum information
Quantum computation and quantum information
On Uniform Covering, Adaptive Random Search and Raspberries
Journal of Global Optimization
A Simple Finite Cone Covering Algorithm for Concave Minimization
Journal of Global Optimization
Quantum Database Search by a Single Query
QCQC '98 Selected papers from the First NASA International Conference on Quantum Computing and Quantum Communications
Grover's Quantum Algorithm Applied to Global Optimization
SIAM Journal on Optimization
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
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This paper gives a quantum algorithm for global optimization. The heart of such approaches employ Grover's database search (1996; Phys Rev Lett 79(23):4709---4712, 1997a; 79(2):325---328, 1997b). Chi and Kim (1998) show that when the phases of the generalized Grover database search operator are optimally chosen, it is capable of finding a solution by a single query. To apply this method to global optimization requires knowledge of the number of marked points m to calculate the optimal phases, but this value is seldom known. This paper focuses on overcoming this hurdle by showing that an estimate of the optimal phases can be found and used to replace the optimal phases while maintaining a high probability of finding a solution. Merging this finding with a recently discovered dynamic quantum global optimization algorithm (BBW2D) that reduces the problem to finding successively improving regions using Grover's search, we present a hybrid method that improves the efficiency and reduces the variance of the search algorithm when empirically compared to other existing quantum search algorithms.