Computational Advantage in Hybrid Quantum Neural Networks: Myth or Reality?

Hybrid Quantum Neural Networks (HQNNs) have gained attention for their potential to enhance computational performance by incorporating quantum layers into classical neural network (NN) architectures. However, a key question remains: Do quantum layers offer computational advantages over purely classical models? This paper explores how classical and hybrid models adapt their architectural complexity to increasing problem complexity. Using a multiclass classification problem, we benchmark classical models to identify optimal configurations for accuracy and efficiency, establishing a baseline for comparison. HQNNs, simulated on classical hardware (as common in the Noisy Intermediate-Scale Quantum (NISQ) era), are evaluated for their scaling of floating-point operations (FLOPs) and parameter growth. Our findings reveal that as problem complexity increases, HQNNs exhibit more efficient scaling of architectural complexity and computational resources. For example, from 10 to 110 features, HQNNs show an 53.1% increase in FLOPs compared to 88.1% for classical models, despite simulation overheads. Additionally, the parameter growth rate is slower in HQNNs (81.4%) than in classical models (88.5%). These results highlight HQNNs' scalability and resource efficiency, positioning them as a promising alternative for solving complex computational problems.