  Quantum computing holds promise for outperforming classical computing in
specialized applications such as optimization. With current Noisy Intermediate
Scale Quantum (NISQ) devices, only variational quantum algorithms like the
Quantum Alternating Operator Ansatz (QAOA) can be practically run. QAOA is
effective for solving Quadratic Unconstrained Binary Optimization (QUBO)
problems by approximating Quantum Annealing via Trotterization. Successful
implementation on NISQ devices requires shallow circuits, influenced by the
number of variables and the sparsity of the augmented interaction matrix. This
paper investigates the necessary sparsity levels for augmented interaction
matrices to ensure solvability with QAOA. By analyzing the Max-Cut problem with
varying sparsity, we provide insights into how the Hamiltonian density affects
the QAOA performance. Our findings highlight that, while denser matrices
complicate the energy landscape, the performance of QAOA remains largely
unaffected by sparsity variations. This study emphasizes the algorithm's
robustness and potential for optimization tasks on near-term quantum devices,
suggesting avenues for future research in enhancing QAOA for practical
applications.
