Quantum computing can solve in some cases optimization problems faster than classical one, since quantum mechanics phenomena could speed up the optimum search; in particular, it suits the formulation of Quadratic Unconstrained Binary Optimization (QUBO) problems, which can model many scenarios, such as finance and machine learning. The problem to be solved is mapped onto a cost function over binary variables, with weights involving at most couples of bits. QUBO problems can be solved with both quantum annealers and general-purpose gate-array-based quantum computers. The former mimics the behaviour of simulated annealing in a quantum framework; the latter exploits quantum superposition to explore the solution space concurrently, as the Grover Adaptive Search (GAS) algorithm, which is the object of this thesis, does through Grover Search (GS) algorithm.