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Modern communication engineering has brought forward impractical requirements on powerful computation engines as well as simple implementations. Apparently, the two aspects are contradicted in most realistic applications. Because of the dispersive multipath propagation in underwater acoustic channels, traditional coherent and adaptive receivers are computationally intensive and, hence, inapplicable to the large-scale underwater sensor networks. Inspired by quantum computing and nature intelligence that are incorporated with the concept of culture evolution, in this paper, we suggest a novel quantum memetic algorithm (QMA) built with more qualified problem-solving ability. Instead of classical gene representations, the quantum bit structure is employed by chromosomes to enhance the population diversity of genetic searching. The quantum gate rotating is then explored to update chromosomes in an efficiently parallel way. As a hybridization strategy, quantum-rotation-based local search is integrated in the lifetime learning to further refine individuals' performance and accelerate their convergence toward the global optimality. As a significant real-world application, we develop a noncoherent underwater signal receiver that is based on a QMA framework. From a pattern recognition aspect, the suggested detection scheme includes two sequential phases: Features extraction and pattern classification. Finally, the highly computational optimization problem is elegantly addressed by QMA. Providing favorable robustness to various parameter configurations, QMA can considerably reinforce the search performance and improve the underwater signal detection. It is demonstrated from numerical experiments that QMA is much superior to genetic algorithm (GA) in this high-dimensional optimization. Meanwhile, QMA shows remarkable advantages in search performance, even to the current state-of-the-art quantum-inspired GA and memetic algorithm.