Quantum Attention by Overlap Interference: Predicting Classical and Many-Body Quantum Sequences

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.

Modeling long-range dependencies in sequential data remains a central challenge in machine learning. Transformers address this challenge through attention mechanisms, but their quadratic complexity with respect to sequence length limits scalability to long contexts. State-space models (SSMs) provide an efficient alternative with linear-time computation by evolving a latent state through recurrent updates, but their memory is typically formed via additive or linear transitions, which can limit their ability to capture complex global interactions across tokens. In this work, we introduce one of the first studies to leverage the superposition property of quantum systems to enhance state-based sequence modeling. In particular, we propose Quantum Long-Attention Memory (QLAM), a hybrid quantum-classical memory mechanism that can be viewed as a quantum extension of state-space models. Instead of maintaining a classical latent state updated through additive dynamics, QLAM represents the hidden state as a quantum state whose amplitudes encode a superposition of historical information. The state evolves through parameterized quantum circuits conditioned on the input, enabling a non-classical, globally update mechanism. In this way, QLAM preserves the recurrent and linear-time structure of SSMs while fundamentally enriching the memory representation through quantum superposition. Unlike attention mechanisms that explicitly compute pairwise interactions, QLAM implicitly captures global dependencies through the evolution of the quantum state, and retrieves task-relevant information via query-dependent measurements. We evaluate QLAM on sequential variants of standard image classification benchmarks, including sMNIST, sFashion-MNIST, and sCIFAR-10, where images are flattened into token sequences. Across all tasks, QLAM consistently improves over recurrent baselines and transformer-based models.

We propose a compact NISQ-compatible quantum transformer architecture for synthetic QNLP sequence modelling. The model preserves the autoregressive next-token interface of a classical transformer, but replaces attention and feed-forward sublayers with variational quantum encoder blocks, connector circuits, decoder blocks and a direct two-qubit measurement readout. Token contexts are angle-encoded into small quantum registers, processed by parallel variational heads and encoder integration circuits and conditioned through decoder ancillae to produce a distribution over a four-token vocabulary. We evaluate several architecture variants on deterministic and lexicographic grammar-generation tasks against a compact classical transformer baseline. The quantum models are trainable end-to-end and learn nontrivial grammar structure, including perfect deterministic generation in individual runs and high lexicographic validity in the strongest variant. The classical baseline remains more accurate and stable and the quantum models are sensitive to initialization. The contribution is therefore not a claim of quantum advantage, but a concrete architecture and evaluation of transformer-inspired QNLP sequence modelling under near-term quantum constraints.