Neuroscientists face challenges in analyzing high-dimensional neural recording data of dense functional networks. Without ground-truth reference data, finding the best algorithm for recovering neurologically relevant networks remains an open question. We implemented hybrid quantum algorithms to construct functional networks and compared them with the results of documented classical techniques. We demonstrated that our quantum state fidelity methods can provide competitive alternatives to classical metrics by revealing distinct functional networks. Our results suggest that quantum computing offers a viable and potentially advantageous alternative for data-driven modeling in neuroscience, underscoring its broader applicability in high-dimensional graph inference and complex system analysis.