Comparison of two types of quantum oracles based on Grover's adaptative search algorithm for multiobjective optimization problems

Quantum Computing is a field of study in computer science based on the laws of quantum physics. Quantum computing is an attractive subject considering that quantum algorithms proved to be more efficient than classical algorithms and the advent of large-scale quantum computation. In particular, Grover's search algorithm is a quantum algorithm that is asymptotically faster than any classical search algorithm and it is relevant for the design of fast optimization algorithms. This article proposes two algorithms based on Grover's adaptative search for biobjective optimization problems where access to the objective functions is given via two different quantum oracles. The proposed algorithms, considering both types of oracles, are compared against NSGA-II, a highly cited multiobjective optimization evolutionary algorithm. Experimental evidence suggests that the quantum optimization methods proposed in this work are at least as effective as NSGA-II in average, considering an equal number of executions. Experimental results showed which oracle required less iterations for similar effectiveness.