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arXiv:2605.25365

Quantum Parameterized Self-Attention Network for Image Classification

Wenwei Zhang, Jintao Wang, Tianyu Ye, Changgeng Liao

quant-phSubmitted May 25, 2026• Announced May 26, 2026• 0 citations
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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.

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16 pages, 7 figures, 7 tables

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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.
This article proposes a quantum self-attention neural network (QSAN) model that is implementable on parameterized quantum circuits (PQCs), providing a novel avenue for addressing natural language processing (NLP) tasks via quantum computing. The QSAN architecture comprises four blocks: the data preprocessing block, the quantum encoding block, the model design block, and the network optimization block. Through these blocks, classical text data are initially preprocessed and encoded into quantum states. The rich semantic features and intricate relationships within these quantum states are then captured and learned by a quantum self-attention layer and a quantum fully connected layer. Finally, the model performance is enhanced by optimizing the network parameters. Simulation results on publicly available topic classification and sentiment analysis datasets demonstrate that the QSAN model outperforms state-of-the-art baselines. As a limitation of the current study, these evaluations are restricted to a maximum sentence length of eight words due to simulation and hardware constraints. Moreover, the effectiveness, scalability, trainability, and robustness of the proposed model are comprehensively evaluated, highlighting its superior performance and potential for advanced NLP tasks.
Quantum machine learning offers a compelling representational perspective: angle-encoded states inhabit Hilbert spaces in which periodic similarities and interactions can be expressed naturally. Realizing this perspective for visual recognition remains difficult, however, because present quantum neural networks are constrained by limited qubit counts, costly circuit simulation and measurement, noise, and unstable optimization on noisy intermediate-scale quantum devices. We investigate whether useful structural ideas from quantum models can instead be realized as scalable classical Transformer operations. We introduce QiT, a Quantum-inspired Transformer for vision tasks with three components: (i) angle-inspired encoding that maps image tokens to learned trigonometric Hilbert-space features analogous to quantum rotation-based state encoding; (ii) self-attention over these periodic features, inducing a classical cosine kernel approximated to quantum fidelity kernels; and (iii) gated multiplicative emulation, a trainable classical surrogate for interaction terms found in variational circuits. All components are differentiable tensor operations, so QiT claims neither quantum computation nor quantum speedup and retains the O(N2D)\mathcal{O}(N^2D)O(N2D) attention complexity of a standard Vision Transformer. Across image-classification benchmarks, QiT is competitive with a matched classical Transformer while avoiding the severe runtime cost observed for a small simulated quantum Transformer. QiT-B reaches 78.3\% ImageNet-1K top-1 accuracy with 45.7M parameters and 11.5 GFLOPs. These results position QiT as a scalable baseline for isolating and evaluating quantum-motivated inductive biases in visual recognition.
Image classification is a core task in the field of computer vision, with significant implications for applications such as medical imaging and autonomous driving. Classical neural network architectures face numerous challenges when dealing with high-dimensional and complex data, particularly in terms of feature extraction and data processing capabilities, limiting their performance in certain applications. Quantum computing offers promising new approaches to processing high-dimensional complex data, most notably through Parameterized Quantum Circuits (PQC) as quantum hybrid neural networks for image classification. In this paper, we propose a hybrid neural network featuring a specific PQC structure designed to generate entanglement in accordance with sample images. This PQC structure utilizes the adjacency matrix of the corresponding graph of the sample image, embedding adjacency relationships among nodes into the entanglement module, thereby generating entanglement aligned with the features of specific images. Numerical results validate the effectiveness of our PQC model across various image classification tasks, enhancing the efficiency of feature learning and representation. Our model demonstrates significant advantages in classification accuracy and learning efficiency on classical datasets. Our research not only advances the theoretical understanding of hybrid quantum networks but also paves the way for practical implementations in real-world scenarios.
Self-attention mechanism (SAM) is good at capturing the intrinsic connection between features to dramatically boost the performance of machine learning models. Nevertheless, the capability of SAM is not equipped with many current quantum machine learning (QML) models, thus confining their expansion on massive high-dimensional quantum data. To address the above problems, a quantum SAM (QSAM) consisting of a quantum logic similarity (QLS)-based quantum bit self-attention score matrix (QBSASM) is introduced to augment the data representation of SAM exponentially. According to QSAM, the framework and quantum circuits of a one-step achievable quantum self-attention network (QSAN) are designed to consider measurement times compression fully. Moreover, a prototype of quantum coordinates is presented during the design process to describe the mathematical relationship between the output bits and the control bits to facilitate the programming. Ultimately, MNIST binary classification experiments on the PennyLane platform and comparisons with cutting-edge QML models demonstrate QSAN converges about $1.7\times $ and $2.3\times $ faster than hardware-efficient ansatz and quantum approximate optimization algorithm (QAOA) ansatz, respectively, with similar parameter configurations and 100% prediction accuracy, which indicates that it has a better learning capability. In the CIFAR-10 classification experiments, QSAN achieves high prediction accuracy at a small scale relative to classical machine learning models. Predictably, QSAN elevates the efficiency of QML models and lays the foundation for future quantum computers to perform machine learning on massive amounts of data while promoting the advancement of quantum computer vision and other fields.
In this work, quantum transformers are designed and analysed in detail by extending the state-of-the-art classical transformer neural network architectures known to be very performant in natural language processing and image analysis. Building upon the previous work, which uses parametrised quantum circuits for data loading and orthogonal neural layers, we introduce three types of quantum transformers for training and inference, including a quantum transformer based on compound matrices, which guarantees a theoretical advantage of the quantum attention mechanism compared to their classical counterpart both in terms of asymptotic run time and the number of model parameters. These quantum architectures can be built using shallow quantum circuits and produce qualitatively different classification models. The three proposed quantum attention layers vary on the spectrum between closely following the classical transformers and exhibiting more quantum characteristics. As building blocks of the quantum transformer, we propose a novel method for loading a matrix as quantum states as well as two new trainable quantum orthogonal layers adaptable to different levels of connectivity and quality of quantum computers. We performed extensive simulations of the quantum transformers on standard medical image datasets that showed competitively, and at times better performance compared to the classical benchmarks, including the best-in-class classical vision transformers. The quantum transformers we trained on these small-scale datasets require fewer parameters compared to standard classical benchmarks. Finally, we implemented our quantum transformers on superconducting quantum computers and obtained encouraging results for up to six qubit experiments.
The automated design of parameterized quantum circuits for variational algorithms in the NISQ era faces a fundamental limitation, as conventional differentiable architecture search relies on classical models that fail to adequately represent quantum gate interactions under hardware noise. We introduce the Quantum-Based Self-Attention for Differentiable Quantum Architecture Search (QBSA-DQAS), a meta-learning framework featuring quantum-based self-attention and hardware-aware multi-objective search. The framework employs a two-stage quantum self-attention module that computes contextual dependencies by mapping architectural parameters through parameterized quantum circuits, replacing classical similarity metrics with quantum-derived attention scores, then applies position-wise quantum transformations for feature enrichment. Architecture search is guided by a task-agnostic multi-objective function jointly optimizing noisy expressibility and Probability of Successful Trials (PST). A post-search optimization stage applies gate commutation, fusion, and elimination to reduce circuit complexity. Experimental validation demonstrates superior performance on VQE tasks and large-scale Wireless Sensor Networks. For VQE on H2_22​, QBSA-DQAS achieves 0.9 accuracy compared to 0.89 for standard DQAS. Post-search optimization reduces discovered circuit complexity by up to 44% in gate count and 47% in depth without accuracy degradation. The framework maintains robust performance across three molecules and five IBM quantum hardware noise models. For WSN routing, discovered circuits achieve 8.6% energy reduction versus QAOA and 40.7% versus classical greedy methods, establishing the effectiveness of quantum-native architecture search for NISQ applications.