FAQNAS: FLOPs-aware Hybrid Quantum Neural Architecture Search using Genetic Algorithm

TL;DR

This work tackles designing efficient hybrid quantum neural networks (HQNNs) in the NISQ era by treating design as a FLOPs-aware multi-objective optimization problem. It introduces FAQNAS, which uses NSGA-II to search a HQNN configuration space of $23{,}328$ architectures, explicitly minimizing quantum FLOPs $F^{\text{Q}}$ and maximizing accuracy (via $Acc_{val}$) while also considering model size. Evaluations on MNIST, Digits, Iris, Wine, and Breast Cancer show that accuracy improvements are primarily driven by quantum FLOPs, with classical FLOPs largely fixed, resulting in Pareto fronts that balance performance and efficiency across datasets. The results provide a practical blueprint for resource-efficient HQNNs today and scalable, hardware-aware guidelines for future quantum–classical computing systems.

Abstract

Hybrid Quantum Neural Networks (HQNNs), which combine parameterized quantum circuits with classical neural layers, are emerging as promising models in the noisy intermediate-scale quantum (NISQ) era. While quantum circuits are not naturally measured in floating point operations (FLOPs), most HQNNs (in NISQ era) are still trained on classical simulators where FLOPs directly dictate runtime and scalability. Hence, FLOPs represent a practical and viable metric to measure the computational complexity of HQNNs. In this work, we introduce FAQNAS, a FLOPs-aware neural architecture search (NAS) framework that formulates HQNN design as a multi-objective optimization problem balancing accuracy and FLOPs. Unlike traditional approaches, FAQNAS explicitly incorporates FLOPs into the optimization objective, enabling the discovery of architectures that achieve strong performance while minimizing computational cost. Experiments on five benchmark datasets (MNIST, Digits, Wine, Breast Cancer, and Iris) show that quantum FLOPs dominate accuracy improvements, while classical FLOPs remain largely fixed. Pareto-optimal solutions reveal that competitive accuracy can often be achieved with significantly reduced computational cost compared to FLOPs-agnostic baselines. Our results establish FLOPs-awareness as a practical criterion for HQNN design in the NISQ era and as a scalable principle for future HQNN systems.

Figures (7)

• Figure 1: An illustration Hybrid Quantum Neural Network Architecture. Typically Parametrized Quantum circuits are sandwiched between classical neuron layers with classical optimization loop.
• Figure 2: Our Methodology for FLOPs-aware Hybrid Quantum Neural Network (HQNN) architecture search. Candidate HQNNs are evaluated on accuracy and FLOPs across multiple datasets. The search evolves quantum layer configurations (encoding, qubits, gates, entanglement, depth) from a space of $23,328$ combinations using non-dominated sorting, crossover, and mutation. Pareto-optimal architectures are identified to balance performance and efficiency.
• Figure 4: Accuracy versus computational cost for candidate HQNN architectures on the MNIST dataset. Each panel shows accuracy as a function of (left) classical FLOPs, (middle) quantum FLOPs, and (right) total FLOPs. Purple dots represent all candidate architectures while gold stars denote Pareto-optimal solutions.
• Figure 5: Accuracy versus computational cost for candidate HQNN architectures on the Digits dataset. Each panel shows accuracy as a function of (left) classical FLOPs, (middle) quantum FLOPs, and (right) total FLOPs. Purple dots represent all candidate architectures while gold stars denote Pareto-optimal solutions.
• Figure 6: Accuracy versus computational cost for candidate HQNN architectures on the Iris dataset. Each panel shows accuracy as a function of (left) classical FLOPs, (middle) quantum FLOPs, and (right) total FLOPs. Purple dots represent all candidate architectures while gold stars denote Pareto-optimal solutions.