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IEEE Transactions on Network Science and Engineering

Quantum Fusion Learning for 6G Networks With Kolmogorov–Arnold Networks

Usama Inam Paracha, Uman Khalid, Syed Muhammad Abuzar Rizvi, Trung Q. Duong, Moe Z. Win, Hyundong Shin

Published Jan 1, 2026• 0 citations
Publisher
DOI
10.1109/tnse.2026.3725065

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We introduce quantum Kolmogorov-Arnold networks (QKAN), a quantum algorithmic framework inspired by the recently proposed Kolmogorov-Arnold Networks (KAN). QKAN inherits the compositional structure of KAN and is based on block-encodings, constructed recursively from a single layer using quantum singular value transformation. We demonstrate the algorithmic utility of QKAN in two applications. First, we introduce and analyze QKAN as a quantum learning model, treating the eigenvalues of block-encoded matrices as neurons and applying parametrized activation functions on the edges of the network. We show that QKAN is a wide-and-shallow neural architecture, where shallow depth is compensated by exponentially wide layers whenever efficient block-encodings of inputs are available. We further discuss how to parametrize and train QKAN using parametrized quantum circuits and quantum linear algebra subroutines. Second, we demonstrate that QKAN can serve as a multivariate quantum state-preparation protocol for functions with shallow compositional structure. We demonstrate this by efficiently preparing a multivariate Gaussian quantum state using a two-layer QKAN. Looking forward, we anticipate that QKAN's compositional and modular design will enable new applications in quantum machine learning and quantum state preparation.
Abstract We implemented a quantum version of the Kolmogorov-Arnold Network (KAN) on a quantum circuit. It optimizes the weight of each synaptic connection to enhance the overall performance of the neurons. This approach offers a significant boost in efficiency over traditional neural networks, as it can be optimized more accurately and requires only a few neurons to solve complex problems. The KAN is a multi-layer network, similar to a traditional neural network, with each layer represented as a matrix containing parameters and feedback. This structure is linear and mirrors the form of Variational Quantum Algorithms. Thus, we propose the Variational Quantum Kolmogorov-Arnold Network (VQKAN) as a quantum version of the Kolmogorov-Arnold Network. We demonstrated the optimization of VQKAN for the fitting of the given function in some ways, such as by using ansatzes and comparisons.
Variational quantum circuits (VQCs) are central to quantum machine learning, while recent progress in Kolmogorov-Arnold networks (KANs) highlights the power of learnable activation functions. We unify these directions by introducing the quantum variational activation function (QVAF), a general framework in which parameterized quantum circuits serve as learnable activation functions; in this work we study an efficient single-qubit instantiation called DatA Re-Uploading ActivatioN (DARUAN). We show that DARUAN with trainable data-preprocessing weights can realize an exponentially growing accessible frequency support with the number of re-uploading repetitions; for an explicit geometric choice of these weights, this gives a capacity-level exponential parameter reduction relative to independently parameterized Fourier activations. Embedding DARUAN into KAN yields the quantum-inspired Kolmogorov-Arnold Network (QKAN), which retains the interpretability of the KAN architecture while improving parameter efficiency, expressivity, and generalization. We further introduce layer extension and the hybrid QKAN (HQKAN) architecture to improve scalability and computational efficiency, enabling QKAN modules to act as compact replacements for multi-layer perceptrons (MLPs) in large-scale models. We provide theoretical analysis and extensive experiments on function regression, image classification, and autoregressive generative language modeling, demonstrating the efficiency and scalability of QKANs. Because the single-qubit circuits are efficiently simulable on classical quantum simulators, QKANs have quantum-inspired advantage in parameter efficiency and training stability; DARUANs and QKANs serve as present-day validation of the QVAF concept, and the trained DARUANs are directly executable and feasible on current noisy intermediate-scale quantum (NISQ) hardware for inference validation.