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arXiv:2505.14593 · Array

Assessing projected quantum kernels for the classification of IoT data

Francesco D’Amore, Luca Mariani, Carlo Mastroianni, Francesco Plastina, Luca Salatino, Jacopo Settino, Andrea Vinci

Published Jan 27, 2026• 2 citations
arXivHTMLPDF

Abstract

The use of quantum computing for machine learning is among the most promising applications of quantum technologies. Quantum models inspired by classical algorithms are developed to explore some possible advantages over classical approaches. A primary challenge in the development and testing of Quantum Machine Learning (QML) algorithms is the scarcity of datasets designed specifically for a quantum approach. Existing datasets, often borrowed from classical machine learning, need modifications to be compatible with current quantum hardware. In this work, we utilize a dataset generated by Internet-of-Things (IoT) devices in a format directly compatible with the proposed quantum data process, eliminating the need for feature reduction. Among quantum-inspired machine learning algorithms, the Projected Quantum Kernel (PQK) stands out for its elegant solution of projecting the data encoded in the Hilbert space into a classical space. For a prediction task concerning office room occupancy, we compare PQK with the standard Quantum Kernel (QK) and their classical counterparts to investigate how different feature maps affect the encoding of IoT data. Our findings show that the PQK demonstrates comparable effectiveness to classical methods when the proposed shallow circuit is used for quantum encoding.

DOI
10.1016/j.array.2026.100695

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The use of quantum computing for machine learning is among the most exciting applications of quantum technologies. Researchers are developing quantum models inspired by classical ones to find some possible quantum advantages over classical approaches. Although such a clear quantum advantage has not yet been achieved, the need for rigorous methodologies to test quantum machine learning (QML) algorithms is an evident requirement. A major challenge in QML development and testing is the lack of datasets specifically designed for quantum algorithms. Existing datasets, often borrowed from classical machine learning, need modifications to be compatible with current noisy quantum hardware. In this work, we use a dataset produced by internet-of-things (IoT) devices in a form usable for quantum algorithms without the need for feature reductions. Among quantum-inspired machine learning algorithms, the Projected Quantum Kernel (PQK) stands out for its elegant solution of projecting the data encoded in Hilbert space into classical space. In this paper, we detail how a PQK approach can be used to develop a prediction model on IoT data using quantum machine learning.
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Convolutional Neural Networks (CNNs) have shown promising results in efficiency and accuracy in image classification. However, their efficacy often relies on large, labeled datasets, posing challenges for applications with limited data availability. Our research addresses these challenges by introducing an innovative approach that leverages projected quantum kernels (PQK) to enhance feature extraction for CNNs, specifically tailored for small datasets. Projected quantum kernels, derived from quantum computing principles, offer a promising avenue for capturing complex patterns and intricate data structures that traditional CNNs might miss. By incorporating these kernels into the feature extraction process, we improved the representational ability of CNNs. Our experiments demonstrated that, with 1000 training samples, the PQK-enhanced CNN achieved 95% accuracy on the MNIST dataset and 90% on the CIFAR-10 dataset, significantly outperforming the classical CNN, which achieved only 60% and 12% accuracy on the respective datasets. This research reveals the potential of quantum computing in overcoming data scarcity issues in machine learning and paves the way for future exploration of quantum-assisted neural networks, suggesting that projected quantum kernels can serve as a powerful approach for enhancing CNN-based classification in data-constrained environments.
Projected quantum kernels (PQKs) have emerged as a notable approach to circumvent the hardness of machine learning tasks arising from the exponential dimensionality of the quantum Hilbert space. However, recent PQK studies often rely heavily on extensive classical hyperparameter tuning of the radial basis function (RBF) kernel parameter and the support vector machine regularization parameter. The extensive tuning can mask the true representational power of the underlying PQKs induced by quantum feature maps, which has not been explored in detail. Thus, this work aims to expose the structural capabilities of PQKs by isolating and evaluating their native inductive bias through comparisons between untuned and tuned PQKs against the RBF baseline. Furthermore, we propose novel quantum feature maps that leverage two-qubit entanglement to capture multivariate correlations in IoT data. The results show that extensive tuning can lead to competitive performance architectures, while our proposed entanglement topologies exhibit a significantly stronger native inductive bias. This reveals that superior quantum architectural design can yield structurally better PQKs with improvements arising from quantum-mechanical properties rather than from classical hyperparameter tuning.
Quantum and classical machine learning have been naturally connected through kernel methods, which have also served as proof-of-concept for quantum advantage. Quantum embeddings encode classical data into quantum feature states, enabling the construction of embedding quantum kernels (EQKs) by measuring vector similarities and projected quantum kernels (PQKs) through projections of these states. However, in both approaches, the model is influenced by the choice of the embedding. In this work, we propose using the training of a quantum neural network (QNN) to construct neural quantum kernels, specifically neural EQKs and neural PQKs—problem-inspired kernel functions. Unlike previous approaches, our method requires the kernel matrix to be constructed only once, significantly reducing computational overhead. To achieve this, we introduce a scalable training method for an n -qubit data reuploading QNN. Furthermore, we demonstrate neural quantum kernels can alleviate exponential concentration and enhance generalization capabilities compared to problem-agnostic kernels, positioning them as a scalable and robust solution for quantum machine learning applications.
Quantum computing is the application of Quantum mechanical resources to solve computational problems more precisely, quickly, and effectively than classical computers. Machine learning is all about discovering patterns and relationships in data. Quantum Machine Learning (QML) blends Machine Learning (ML) and Quantum Computing (QC) technologies. QML approaches may be utilized efficiently for data classification problems. Quantum Feature Maps (QFMs) are used for transferring non-linear classical data from lower input space to higher dimensional Hilbert space. Calculating the inner product between data points for classification purposes is exceedingly costly when Hilbert Space is vast. Quantum Kernel Techniques, which are immediate results of QFMs, are used to overcome this problem. In general, we cannot claim that QFMs are superior than Classical Feature Maps (CFMs); yet, there are datasets for which QFMs perform better while CFMs are less effective. It gives us the motivation behind using QFM for classification. In this paper, we proposed two new non-linear encoding functions based quantum kernels for data classification in the range [0, 2π]. The make_moons and make_circles datasets are utilized in this article to perform binary classifications using Qiskit and Sklearn. Construction of quantum kernels is performed, and Support Vector Machines (SVM) are then applied for classification. We have compared the results of our two newly proposed non-linear encoding functions to those mentioned in the literature. Our classifier's performance is approximately comparable or in some cases better to that of existing classifiers in literature.