Quantum resource-performance balance in quantum convolutional neural networks: a study of hierarchical Ansatz-based QCNN

Abstract Quantum Convolutional Neural Networks (QCNNs) are a significant quantum machine learning architecture. However, most current designs still mimic the ‘convolution-pooling’ structure of classical CNNs, facing dual challenges of limited feature extraction and inefficient quantum resource usage. To address this, we propose a QCNN based on a hierarchical Ansatz design. Its core is an alternating ‘convolution-entanglement’ structure, which replaces abrupt qubit discarding in traditional pooling with sequential global entanglement layers. This enables non-destructive directional information aggregation, aiming to preserve quantum correlations in data more comprehensively. In the encoding layer, we integrate Principal Component Analysis (PCA) with Instantaneous Quantum Polynomial (IQP) encoding to mitigate the dimensionality mismatch between high-dimensional classical data and limited quantum resources. To systematically evaluate the performance of the proposed architecture, we conducted extensive experiments on the MNIST and Fashion-MNIST datasets. The results demonstrate that: 1) Under various convolutional kernel configurations, our model achieves excellent classification performance, peaking at 99.39% accuracy on MNIST; 2) Even with minimalistic single-qubit rotation gates as the convolutional layer, the model attains 99.14% accuracy using only 16 parameters, demonstrating high parameter efficiency; 3) Crucially, experiments reveal a nonlinear relationship between quantum resources and performance. When qubits exceed a task-specific optimal number, performance declines significantly due to feature space dilution and exacerbated Barren Plateaus. This suggests that, under current quantum hardware conditions, matching resource allocation to task complexity may be more critical than simply scaling up the system. This study offers one potential direction for exploring QCNN architectures. The findings still require further validation across more diverse tasks and in quantum hardware environments closer to practical conditions. We hope this work can provide some useful insights and inform subsequent research.