Quantum Parameterized Self-Attention Network for Image Classification

Abstract: Transformer now underpins modern AI as its core infrastructure. Its defining capability-dynamically focusing on the most relevant information in complex inputs-is bounded above by the self-attention scoring function. Quantum computing, with its superposition, entanglement, and probabilistic outputs, offers a fundamentally distinct computational framework for exploring beyond the design constraints of classical scoring functions. While quantum attention mechanisms have shown initial promise, existing works remain largely confined to redefining feature similarity measures, leaving the systematic use of parameterized quantum circuits (PQCs) as scoring functions largely unexplored; a substantial portion of existing schemes further rely on purely quantum architectures, precluding effective encoding of high-dimensional image inputs in the Noisy Intermediate-Scale Quantum era. We propose the Quantum Parameterized Self-Attention Network (QPSAN), implementing the self-attention scoring function via PQCs with only 5 trainable quantum parameters per layer. QPSAN computes query-key attention scores through quantum state encoding and joint measurement, yielding naturally bounded outputs without the explicit scaling of classical dot-product attention. We further establish a theoretical framework of the mathematical properties of this scoring function, demonstrating its potential to capture complex nonlinear query-key interactions, and quantifying the structural constraints of the encoding layer via effective degrees of freedom analysis. Experiments on four vision datasets show that QPSAN significantly outperforms the Vision Transformer (ViT) baseline, with the quantum representational advantage amplifying as data complexity increases. Ablation studies indicate that the performance gains may stem from the structural inductive bias of the quantum circuit rather than from parameter scale.