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International Conference on Quantum Communications, Networking, and Computing (QCNC)

Hybrid Quantum Kolmogorov-Arnold Network Autoencoders for Anomaly Detection

Moe Hdaib, Sutharshan Rajasegarar, Lei Pan

Published Apr 6, 2026• 0 citations
Publisher

Abstract

A novel neural network architecture, KolmogorovArnold Networks (KAN), inspired by the compositional principles of the Kolmogorov-Arnold representation theorem, has recently emerged as an alternative to traditional multilayer perceptron (MLP) networks. In this work, we propose a Quantum-enhanced Kolmogorov-Arnold Network Autoencoder designed for anomaly detection in complex high-dimensional datasets. By integrating classical and quantum machine learning paradigms, our hybrid architecture combines the expressive capabilities of quantumaugmented nonlinear transformations with the robustness of classical networks. Our proposed approach employs parameterized quantum circuits to encode data into quantum states. These features are processed using quantum B-spline basis functions, enabling efficient function approximation while maintaining interpretability. We evaluate the performance of the proposed HQKAN Autoencoder on benchmark anomaly detection datasets, showcasing superior performance in terms of accuracy, generalization, and robustness against state-of-the-art classical baselines, which demonstrate promise for anomaly detection and complex data analysis.

DOI
10.1109/qcnc69040.2026.00112

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A novel neural network architecture, KolmogorovArnold Networks (KAN), inspired by the compositional principles of the Kolmogorov-Arnold representation theorem, has recently emerged as an alternative to traditional multilayer perceptron (MLP) networks. In this work, we propose a Quantum-enhanced Kolmogorov-Arnold Network Autoencoder designed for anomaly detection in complex high-dimensional datasets. By integrating classical and quantum machine learning paradigms, our hybrid architecture combines the expressive capabilities of quantumaugmented nonlinear transformations with the robustness of classical networks. Our proposed approach employs parameterized quantum circuits to encode data into quantum states. These features are processed using quantum B-spline basis functions, enabling efficient function approximation while maintaining interpretability. We evaluate the performance of the proposed HQKAN Autoencoder on benchmark anomaly detection datasets, showcasing superior performance in terms of accuracy, generalization, and robustness against state-of-the-art classical baselines, which demonstrate promise for anomaly detection and complex data analysis.
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There is a pressing need for anomaly detection algorithms that can handle large amounts of diverse traffic data due to the quick growth of networked systems and the sophistication of contemporary cyberattacks. Despite the widespread use of conventional machine learning techniques for network intrusion detection, feature representation constraints, dataset imbalance, and the computational expense of scaling to vast problem spaces sometimes restrict their efficacy. In the meantime, new developments in quantum-assisted computation have opened up exciting possibilities for using quantum state changes to improve the feature learning process. Using the NF-UNSWNB15-v2 benchmark, this research presents HybridQCNN, a unique quantum-classical computing framework for binary classification of network traffic.The proposed architecture combines standard preprocessing techniques with an 8-qubit Parameterized Quantum Circuit (PQC) featuring multiple variational layers, where IsingXX and IsingYY entangling operations are applied to encode interfeature correlations, and a subsequent fully connected classical layer handles the final binary decision. A rigorous leakage-free data partitioning protocol was enforced, ensuring that all preprocessing transformations—including feature encoding, normalization, and threshold computation—were derived exclusively from the training subset, thereby preventing any information leakage from held-out partitions during evaluation. Experimental validation on a class-balanced subset of 60,000 traffic records yielded a classification accuracy of 97.33%, an F1-score of 0.9730, and a malicious traffic detection precision of 98.38%. Furthermore, the model achieved an AUC-ROC of 0.9861, reflecting strong class-level discriminability. Despite this performance, the entire model contains only 489 trainable parameters, underscoring the parameter efficiency of hybrid architectures relative to conventional deep learning baselines. These results suggest that integrating variational quantum circuits with classical inference modules provides an effective and scalable solution for network anomaly detection.
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.
The integration of Quantum Computing and Machine Learning (QML) holds transformative potential for intelligent data analysis, especially in processing high-dimensional and complex datasets. This paper proposes a hybrid quantum-classical framework for proactive anomaly detection, combining Quantum Auto-Encoders (QAEs) for feature compression with Quantum k-Nearest Neighbors (QkNN) for classification. Tailored for high-stakes domains like cybersecurity and IoT analytics, the approach leverages quantum entanglement and exponential state-space properties to enhance anomaly identification accuracy and efficiency. QAEs capture latent representations of typical behavior, while QkNN applies quantum parallelism to classify deviations against known patterns. Evaluations on standard benchmark datasets demonstrate the proposed QAE+QkNN framework’s superiority in precision, scalability, and resilience, particularly under noisy and sparse data conditions. While current limitations in quantum hardware pose constraints, the results underscore the method’s practical viability and promise. This study contributes to the growing body of QML research and highlights the potential of quantum-augmented detection systems in enabling the next generation of real-time, intelligent monitoring solutions.