Quantum transformers for image classification: integrating variational quantum circuits and quantum wavelet KAN

A quantum Transformer framework is presented, a novel hybrid approach that integrates V-shaped Variational Quantum Circuits (VQC), Quantum Wavelet Kolmogorov-Arnold Networks (KAN), and classical Transformer architecture to address critical challenges in modern AI, including computational inefficiency, parameter bloat, and opacity. By leveraging quantum parallelism and entanglement, the framework optimizes deep learning tasks requiring significant computational resources. The modular design begins with a quantum encoding unit, mapping classical feature vectors into quantum initial states via amplitude or rotation-based encoding. These states are processed by a multi-head attention unit constructed from VQCs, where parameterized quantum operations generate quantum analogues of query (Q), key (K), and value (V) matrices, enabling entanglement-enhanced feature interactions across parallel attention modules to capture diverse contextual relationships. The outputs are aggregated and processed by a feed-forward unit powered by a Quantum Wavelet KAN. By replacing classical MLPs with quantum circuits using multi-scale wavelet basis functions, this unit achieves linear scaling with input dimensions and enhances feature resolution with significantly fewer parameters. A linear output unit transforms quantum results into classical probabilities for classification. Evaluated on Fashion MNIST and CIFAR-10 datasets, the framework demonstrates superior computational efficiency, transparency, and hardware compatibility, achieving accuracies of 94.42% and 90.57%, respectively. This cohesive architecture synergizes quantum computational principles with the Transformer’s global dependency modeling and KAN’s interpretability, marking significant advancements in classification precision and scalability for quantum-enhanced machine learning.