QiT: Quantum-Inspired Transformer for Visual Recognition Task

A recurring weakness in quantum machine learning (QML) is that reported ``quantum advantages'' are seldom tested against a \emph{capacity-matched} classical control, leaving it unclear whether a gain comes from the quantum substrate or from the architectural change that accompanies it. Our primary contribution is methodological: a protocol for attributing such gains honestly -- a capacity-matched classical bottleneck of identical parameter budget, transparent reporting of where quantum does \emph{not} help, and validation on real quantum hardware -- which we develop and apply through a concrete case study. That case study is Quantum Adaptive Self-Attention (QASA), a hybrid Transformer that replaces the value projection of a \emph{single} encoder layer with a 36-parameter parameterized quantum circuit (PQC), keeping all other layers classical. Across nine synthetic benchmarks and the real-world ETTh1 dataset, QASA improves on a full-capacity classical Transformer for chaotic and trend-dominated signals. To ask whether this is a genuinely \emph{quantum} effect, we introduce a control rarely applied in quantum machine learning -- a capacity-matched classical bottleneck with the same parameter budget -- and find that it matches the PQC on the error metrics. The gain is therefore attributable to the low-rank value-projection \emph{bottleneck} (an \emph{architectural parsimony} principle), not to quantumness; adding further quantum layers only degrades performance and trainability. We accordingly position the quantum layer not as a source of accuracy advantage but as a \emph{competitive} instantiation of this principle: its low-rank compression onto the signal's intrinsic dimensionality is matched by a classical bottleneck, so the gain is architectural rather than quantum.

Variational quantum circuits (VQCs) are a leading approach to quantum machine learning on near-term devices, yet it remains unclear which circuit architecture yields the best accuracy-parameter trade-off on classical tabular data. We present a systematic empirical comparison of four VQC families -- multi-layer fully-connected (FC-VQC), residual (ResNet-VQC), hybrid quantum-classical transformer (QT), and fully quantum transformer (FQT) -- across five regression and classification benchmarks. Our key findings are: \textbf{(i)}~FC-VQCs achieve 90-96% of the $R^2$ of attention-based VQCs while using 40-50% fewer parameters, and consistently outperform equal-capacity MLPs (mean $R^2{=}0.829$ vs.\ MLP$_{720}$'s $0.753$ on Boston Housing, 3-seed average); \textbf{(ii)}FC-VQC's Type4 inter-block connectivity provides partial cross-token mixing that approximates the role of attention -- explicit quantum self-attention yields only marginal gains on most datasets while significantly increasing parameter count; \textbf{(iii)}expressibility saturates at circuit depth${\approx}\,3$, explaining why shallow VQCs already cover the Hilbert space effectively; \textbf{(iv)}~LayerNorm on the fully quantum transformer improves classification accuracy, suggesting normalization is important when all operations are quantum; \textbf{(v)}~in our noise study on Boston Housing, FQT degrades gracefully under depolarizing noise while QT collapses. All results are validated across three random seeds. These findings provide practical architectural guidance for deploying VQCs on near-term quantum hardware.

This work introduces quantum-inspired tensor-network circuits as trainable transforms for image inpainting. Among the proposed architectures, the diagonal quantum Fourier transform (QFT) relaxation is invertible with $O(N^2 \log N)$ computational cost for $N\times N$ images, inherently preserving minimum coherence throughout training via its circuit structure and eliminating the need for explicit coherence penalties. Unconstrained gradient-based phase optimization (Riemannian-optimization free) enables efficient learning from randomly sampled training data, allowing the learned transform to generalize to test images observed through fixed sampling masks. Numerical tests show that the learned models outperform fixed transforms and per-image optimization while matching the performance of much larger unitary architectures, yet with far fewer parameters.