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arXiv:2610.31260

Can Entanglement-Induced Feature-Map Designs Improve Projected Quantum Kernels?

Ravi Kumar Jha, Hsuan-Yin Lin, Eirik Rosnes

quant-phcs.AIcs.LGSubmitted Oct 22, 2026• Announced Oct 23, 2026• 0 citations
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Abstract

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.

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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 algorithms have become a popular research domain in recent times for discovering quantum-enhanced solutions in machine learning applications. Quantum kernels are one of the directions that establish such quantum-enhanced solutions to some extent. This work presents a detailed analysis of the quantum kernel approach leveraging feature maps and relevant hyperparameters to develop enhanced quantum kernels. The study includes a new high-order feature map and assesses five existing state-of-the-art feature maps for enhanced quantum kernel classifiers. Additionally, the significance of the rotational factor as a hyperparameter is highlighted for improving kernel performance. Also, it is analyzed whether different hyperparameter-tuned feature maps can lead to enhanced decision boundaries, demonstrating kernel expressivity. The analysis is undertaken on classification tasks using four different nonlinear datasets of distinct complexity. Comparative evaluations are also made with traditional machine learning models-Support Vector Machines (Linear and RBF), Naïve Bayes, Linear Discriminant Analysis, Decision Tree, Random Forest, Adaptive Boosting, and MLP. Overall, the study demonstrates that a well-tuned quantum feature map can enhance the generalization ability of quantum kernels, making them more effective for broader quantum-enhanced machine learning applications.
Abstract Since the entry of kernel theory in the field of quantum machine learning, quantum kernel methods (QKMs) have gained increasing attention with regard to both probing promising applications and delivering intriguing research insights. Benchmarking these methods is crucial to gain robust insights and to understand their practical utility. In this work, we present a comprehensive large-scale study examining QKMs based on fidelity quantum kernels (FQKs) and projected quantum kernels (PQKs) across a manifold of design choices. Our investigation encompasses both classification and regression tasks for five dataset families and 64 datasets, systematically comparing the use of FQKs and PQKs quantum support vector machines and kernel ridge regression. This resulted in over 20,000 models that were trained and optimized using a state-of-the-art hyperparameter search to ensure robust and comprehensive insights. We delve into the importance of hyperparameters on model performance scores and support our findings through rigorous correlation analyses. Additionally, we provide an in-depth analysis addressing the design freedom of PQKs and explore the underlying principles responsible for learning. Our goal is not to identify the best-performing model for a specific task but to uncover the mechanisms that lead to effective QKMs and reveal universal patterns.
Quantum machine learning techniques are commonly considered one of the most promising candidates for demonstrating practical quantum advantage. In particular, quantum kernel methods have been demonstrated to be able to learn certain classically intractable functions efficiently if the kernel is well aligned with the target function. In the more general case, quantum kernels are known to suffer from exponential ``flattening'' of the spectrum as the number of qubits grows, preventing generalization and necessitating the control of the inductive bias by hyperparameters. We show that the general-purpose hyperparameter-tuning techniques proposed to improve the generalization of quantum kernels lead to the kernel becoming well approximated by a classical kernel, removing the possibility of quantum advantage. We provide extensive numerical evidence for this phenomenon utilizing multiple previously studied quantum feature maps and both synthetic and real data. Our results show that unless novel techniques are developed to control the inductive bias of quantum kernels, they are unlikely to provide a quantum advantage on classical data that lacks special structure.
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.
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.
Abstract Quantum kernels (QKs) are widely used in quantum machine learning applications; yet, their potential to surpass classical machine learning methods on classical datasets remains uncertain. This limitation can be attributed to the exponential concentration phenomenon, which can impair generalization. A common strategy to alleviate this is bandwidth tuning, which involves rescaling data points in the quantum model to improve generalization. In this work, we numerically demonstrate that optimal bandwidth tuning results in QKs that closely resemble radial basis function (RBF) kernels, leading to a lack of quantum advantage over classical methods. Moreover, we reveal that the size of optimal bandwidth tuning parameters further simplifies QKs, causing them to behave like polynomial kernels, corresponding to a low-order Taylor approximation of a RBF kernel. We thoroughly investigate this for fidelity quantum kernels and projected quantum kernels using various data encoding circuits across several classification datasets. We provide numerical evidence and derive a simple analytical model that elucidates how bandwidth tuning influences key quantities in classification tasks. Overall, our findings shed light on the mechanisms that render QK methods classically tractable.