The paper studies the expressivity of Instantaneous Quantum Polynomial (IQP) feature‑map quantum kernels by deriving a Fourier representation of their associated Reproducing Kernel Hilbert Space (RKHS). It identifies three bandwidth regimes—localized, multimodal, and periodic—each with distinct expressive properties, and demonstrates these regimes on synthetic datasets for classification and anomaly detection, comparing against a classical Gaussian kernel. The work provides a clear link between the kernel’s accessible frequencies, its bandwidth hyperparameter, and the structure of the data, offering guidance for bandwidth selection when data exhibit known periodic or multimodal patterns.
arXiv:2511.10831v3 Announce Type: replace Abstract: Quantum kernel methods are a promising branch of quantum machine learning, but their per- formance across data types and encoding choices remains i...
arXiv:2503. 17020v2 Announce Type: replace-cross Abstract: Kernel methods compare inputs through feature maps.
arXiv:2510. 03389v2 Announce Type: replace-cross Abstract: Current quantum computers require algorithms that use limited resources economically.
arXiv:2508. 19437v2 Announce Type: replace-cross Abstract: The importance of analyzing nontrivial datasets when testing quantum machine learning (QML) models is becoming increasingly prominent in literature, yet a cohesive framework for understanding dataset characteristics remains elusive.
arXiv:2608. 03482v1 Announce Type: new Abstract: The performance of Support Vector Machines (SVMs) critically depends on the kernel function choice, which enables implicit mapping of data into high-dimensional feature spaces.
The paper introduces MMD-FUSE, a two-sample test that remains effective on small datasets by fusing classical and quantum kernels. By combining the inductive biases of classical kernels with the expressive power of quantum kernels, the hybrid approach achieves higher test power, especially for small, high‑dimensional data. Experiments on synthetic and real clinical datasets confirm that the method consistently outperforms purely classical counterparts and adapts robustly to varied data characteristics.
The paper derives a closed‑form expression for the reduced quantum channel of a single‑qubit Interactive Quantum Classifier (IQC), revealing that Hamiltonian parameters directly control the constant, sine, and cosine components of the classifier output. This Fourier interpretation motivates a generalized family of Hamiltonian encodings, including matrix‑parameterized environmental Hamiltonians that produce non‑separable Fourier structures. Numerical experiments on synthetic and real‑world datasets demonstrate that these generalized encodings improve classification performance on several nonlinear benchmarks, with a simpler four‑parameter extension achieving comparable results with fewer trainable parameters.
arXiv:2604. 26675v2 Announce Type: replace-cross Abstract: We investigate variational quantum classifiers (VQCs) for land-cover classification from multispectral satellite imagery, adopting a feature-map perspective in which the quantum circuit defines a nonlinear data embedding while the readout determines how this representation is exploited.
The paper introduces Neural Fourier Surrogates (NFS), a stochastic classical neural network that learns coefficients over a finite Fourier series support similar to quantum neural networks (QNNs). By testing on tabular benchmark datasets, NFS demonstrates competitive classification performance against established classical baselines and data‑reuploading QNNs. The authors also compare the learned Fourier spectra of QNNs and NFS on synthetic data, positioning NFS as a natural classical baseline for evaluating QNN performance.
arXiv:2608.24631v1 Announce Type: cross Abstract: Similarity in many decision systems is governed not by distance alone but by interactions among variables. In fraud and anomaly detection, small loca...
arXiv:2607. 11701v1 Announce Type: cross Abstract: Quantitative Structure-Activity Relationship ($\mathtt{QSAR}$) modeling is a foundational computational methodology in early-stage drug discovery, heavily relied upon for predicting compound toxicity, bioavailability, and therapeutic potential.
arXiv:2412. 09557v3 Announce Type: replace-cross Abstract: Quantum kernel learning (QKL) promises efficient machine learning by encoding feature maps onto exponentially large Hilbert spaces inherent in quantum systems.