  In this work we investigate the capabilities of a hybrid quantum-classical
procedure to explore the solution space using the D-Wave $2000Q^{TM}$ Quantum
Annealer device. Here we study the ability of the Quantum hardware to solve the
Number Partitioning Problem, a well-known NP-Hard optimization model that poses
some challenges typical of those encountered in real-world applications. This
represents one of the most complex scenario in terms of qubits connectivity
and, by increasing the input problem size, we analyse the scaling properties of
the quantum-classical workflow. We find remarkable results in most instances of
the model; for the most complex ones, we investigate further the D-Wave Hybrid
suite. Specifically, we were able to find the optimal solutions even in the
worst cases by fine-tuning the parameters that schedule the annealing time and
allowing a pause in the annealing cycle.
