A Quantum Global Optimization Algorithm: Application to the Knapsack Problem

Solving combinatorial optimization problems represents a challenge for researchers, especially hard NP-complete problems that are commonly handled through heuristic methods providing approximate solutions. The emergence of quantum computing, which enables performing parallel computation, raises hope for solving such problems within a reasonable time frame. This paper proposes a quantum global optimization algorithm to solve combinatorial optimization problems intended to provide an improved performance. The proposed algorithm aims to amplify the probability of selecting the global optimum of the objective function defining the addressed problem using a specific variant of Grover’s search based on simultaneously exploring all comparison cases of possible solutions to recognize the global optimum. The paper also includes the study of precision and runtime of the presented concept and introduces a version of the proposed algorithm addressing the knapsack problem, along with its execution results and a comparison with other competing algorithms