Quantum Adaptive Self-Attention for Quantum Transformer Models

Integrating quantum computing into deep learning architectures is a promising but poorly understood endeavor: when does a quantum layer actually help, and how much quantum is enough? We address both questions through Quantum Adaptive Self-Attention (QASA), a hybrid Transformer that replaces the value projection in a single encoder layer with a parameterized quantum circuit (PQC), while keeping all other layers classical. This minimal quantum integration strategy uses only 36 trainable quantum parameters-fewer than any competing quantum model-yet achieves the best MSE on 4 of 9 synthetic benchmarks and a 6.0% MAE reduction on the real-world ETTh1 dataset. An ablation study reveals that quantum layer position matters more than count: adding more quantum layers degrades performance, while a single layer at the optimal position consistently outperforms multi-layer quantum configurations. Comparison with two recent quantum time-series baselines-QLSTM and QnnFormer-confirms that QASA matches or exceeds models with 2-4× more quantum parameters, significantly outperforming QLSTM on the seasonal trend task (p=0.009, Cohen's d>6). Crucially, the benefit is task-conditional : QASA excels on chaotic, noisy, and trend-dominated signals, while classical Transformers remain superior for clean periodic waveforms-providing a practical taxonomy for when quantum enhancement is warranted. These findings establish an architectural parsimony principle for hybrid quantum-classical design: maximal quantum benefit is achieved not by maximizing quantum resources, but by strategically placing minimal quantum computation where it matters most.