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

Hybrid Quantum Neural Networks (HQNNs), under the umbrella of Quantum Machine Learning (QML), have garnered significant attention due to their potential to enhance computational performance by integrating quantum layers within traditional neural network (NN) architectures. Despite numerous state-of-the-art applications, a fundamental question remains: Does the inclusion of quantum layers offer any computational advantage over purely classical models? If yes/no, how and why? In this paper, we analyze how classical and hybrid models adapt their architectural complexity in response to increasing problem complexity. To this end, we select a multiclass classification problem and perform comprehensive benchmarking of classical models for increasing problem complexity, identifying those that optimize both accuracy and computational efficiency to establish a robust baseline for comparison. These baseline models are then systematically compared with HQNNs by evaluating the rate of increase in floating-point operations (FLOPs) and number of parameters, providing insights into how architectural complexity scales with problem complexity in both classical and hybrid networks. We utilize classical machines to simulate the quantum layers in HQNNs, a common practice in Noisy Intermediate-Scale Quantum (NISQ) era. Our analysis reveals that, as problem complexity increases, the architectural complexity of HQNNs, and consequently their FLOPs consumption, despite the simulation overhead associated with quantum layer’s simulation on classical hardware, scales more efficiently $(53.1 \%$ increase in FLOPs from 10 features (low problem complexity) to 110 features (high problem complexity)), compared to classical networks (88.1%). Moreover, as the problem complexity increases, classical networks consistently exhibit a need for a larger number of parameters to accommodate the increasing problem complexity. Additionally, the rate of increase in number of parameters is also slower in HQNNs (81.4%) than classical NNs (88.5%). These findings suggest that HQNNs provide a more scalable and resource-efficient solution, positioning them as a promising alternative for tackling complex computational problems.