Solving a class of continuous global optimization problems using quantum algorithms

Abstract

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