Quantum machine learning (QML) is a promising application of quantum computing, yet when and how practical learning models can achieve quantum advantage remains poorly understood. Even a polynomial improvement in the resources needed to attain a given predictive performance would be significant. In this work, we investigate empirical scaling laws of quantum vision transformers (QViTs), which connect QML to the transformer architecture underlying modern large language models. We ask whether QViTs exhibit scaling behavior analogous to classical models and how this behavior changes when qubit number is included alongside dataset size and model parameters. The validation losses in our numerical image-classification experiments are well described by a joint shifted power-law model in qubit number, transformer depth, and training dataset size. Expressing this fit in terms of the classical encoder parameter budget identifies a regime in which increasing the number of qubits can compensate for fewer classical encoder parameters at comparable predicted performance. This finding is consistent with earlier observations of parameter efficiency in quantum learning models and suggests a direction for exploring possible resource savings in QML.
Quantum machine learning (QML) is a promising application of quantum computing, yet when and how practical learning models can achieve quantum advantage remains poorly understood. Even a polynomial improvement in the resources needed to attain a given predictive performance would be significant. In this work, we investigate empirical scaling laws of quantum vision transformers (QViTs), which connect QML to the transformer architecture underlying modern large language models. We ask whether QViTs exhibit scaling behavior analogous to classical models and how this behavior changes when qubit number is included alongside dataset size and model parameters. The validation losses in our numerical image-classification experiments are well described by a joint shifted power-law model in qubit number, transformer depth, and training dataset size. Expressing this fit in terms of the classical encoder parameter budget identifies a regime in which increasing the number of qubits can compensate for fewer classical encoder parameters at comparable predicted performance. This finding is consistent with earlier observations of parameter efficiency in quantum learning models and suggests a direction for exploring possible resource savings in QML.
Transformers excel in various domains but often demand massive computational resources. Quantum Neural Networks (QNNs) combine classical and quantum computing to mitigate these costs. However, QNNs typically fix the number of qubits, forcing complete retraining whenever the qubit count changes and leading to substantial inefficiency. We propose an Adaptive Quantum Transformer (AQT) to resolve this limitation by introducing an adapter module — originally designed for large language models (LLMs) — into a quantum vision Transformer. This module reuses parameters when the qubit count expands or contracts, preserving learned states. We validate AQT in an autoscaling cloud environment, demonstrating dynamic qubit scaling without sacrificing accuracy or retraining from scratch. Results on vision tasks reveal that AQT achieves higher accuracy than a conventional quantum vision Transformer while converging faster and requiring fewer computational resources. Notably, AQT provides over triple the efficiency in training time and better stability under fluctuating qubit availability, suggesting a promising avenue for practical, cost-effective quantum–classical hybrid intelligence.
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 emergence of deep vision models such as convolutional neural networks and vision transformers has revolutionized computer vision, enabling significant advancements in image classification, object detection, and segmentation. In parallel, the rapid development of quantum computing has spurred interest in quantum machine learning (QML), which integrates the strengths of quantum computation with the representational power of deep learning. In QML, parameterized quantum circuits offer the potential to capture complex image features, define complex decision boundaries, and provide other computational advantages. This paper investigates hybrid quantum-classical vision architectures, with a focus on hybrid quantum-classical convolutional neural networks and hybrid quantum-classical vision transformers. These hybrid models explore both quantum pre-processing and post-processing of data, respectively, where quantum circuits are strategically integrated into the data pipeline to enhance model performance. Our results suggest that these hybrid models can enhance accuracy and computational efficiency in vision-related tasks, even with the constraints of current noisy intermediate-scale quantum devices.
In mainstream machine learning, transformers are gaining widespread usage. As Vision Transformers rise in popularity in computer vision, they now aim to tackle a wide variety of machine learning applications. In particular, transformers for High Energy Physics (HEP) experiments continue to be investigated for tasks including jet tagging, particle reconstruction, and pile-up mitigation. An improved Quantum Vision Transformer (QViT) with a quantum-enhanced self-attention mechanism is introduced and discussed. A shallow circuit is proposed for each component of self-attention to leverage current Noisy Intermediate Scale Quantum (NISQ) devices. Variations of the hybrid architecture/model are explored and analyzed. The results demonstrate a successful proof of concept for the QViT, and establish a competitive performance benchmark for the proposed design and implementation. The findings also provide strong motivation to experiment with different architectures, hyperparameters, and datasets, setting the stage for implementation in HEP environments where transformers are increasingly used in state of the art machine learning solutions.
Quantum deep learning (QDL) for image classification has emerged as a rapidly growing research area at the intersection of quantum computing and computer vision. However, the literature remains fragmented across diverse model architectures, datasets, and evaluation settings, making it difficult to obtain a focused understanding of the field. This study presents a systematic review of QDL models for image classification published between 2020 and 2025. The review was conducted using a Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA)-based selection process supported by a mapping perspective. Relevant studies were identified from major academic databases, screened using predefined inclusion and exclusion criteria, and analyzed through a taxonomy-based framework. A total of 47 studies were included and organized into four main architectural categories: Quantum Neural Networks (QNNs), Quantum Convolutional Neural Networks (QCNNs), Quantum Vision Transformers (QViT), and Quantum Attention Mechanisms. The findings show that most existing approaches rely on hybrid quantum-classical designs, where quantum components are integrated selectively into specific stages of the learning pipeline rather than replacing the full classical architecture. Several studies report encouraging results, such as improved parameter efficiency, competitive ACC (accuracy), and robustness in specific settings. Current progress remains constrained by hardware noise, limited qubit availability, encoding overhead, scalability challenges, and inconsistent benchmarking practices. It remains a promising but still emerging direction, with future progress expected to depend on more scalable architectures, fairer evaluation protocols, and broader validation on realistic application.
Models based on vision transformer architectures are considered state-of-the-art when it comes to image classification tasks. However, they require extensive computational resources both for training and deployment. The problem is exacerbated as the amount and complexity of the data increases. Quantum-based vision transformer models could potentially alleviate this issue by reducing the training and operating time while maintaining the same predictive power. Although current quantum computers are not yet able to perform high-dimensional tasks, they do offer one of the most efficient solutions for the future. In this work, we construct several variations of a quantum hybrid vision transformer for a classification problem in high-energy physics (distinguishing photons and electrons in the electromagnetic calorimeter). We test them against classical vision transformer architectures. Our findings indicate that the hybrid models can achieve comparable performance to their classical analogs with a similar number of parameters.