Quantum Algorithm for Continuous Global Optimization

Abstract

We investigate the entwined roles of information and quantum algorithms in reducing the complexity of the global optimization problem (GOP). We show that: (1) a modest amount of additional information is sufficient to map the general continuous GOP into the (discrete) Grover problem; (2) while this additional information is actually available in some classes of GOPs, it cannot be taken advantage of within classical optimization algorithms; (3) on the contrary, quantum algorithms over a natural framework for the efficient use of this information resulting in a speed-up of the solution of the GOP.