Kernel methods are powerful tools in machine learning but commonly used full-Gram kernels face three key limitations: (1) quadratic scaling with training set size; (2) the use of fixed, non-trainable kernels; and (3) the absence of an intrinsic formulation for multiclass classification. We present McQuack, a trainable quantum kernel method for multiclass problems that achieves linear scaling in the number of training samples. This is accomplished by replacing the full training-set Gram matrix with a trainable sample-to-(class-centroid) fidelity matrix. We evaluate the model in simulation and on 124 qubits of two IBM devices, across more than 150 datasets. In simulation, McQuack outperforms existing "pure" quantum baselines, while results from hardware inference -- obtained without training -- achieve performance similar to an RBF kernel. Finally, we study the trainability of the model and observe no evidence of barren plateaus in our experiments with up to 13 qubits, and highlight the importance of parameter initialization for successful optimization.
Kernel methods are powerful tools in machine learning but commonly used full-Gram kernels face three key limitations: (1) quadratic scaling with training set size; (2) the use of fixed, non-trainable kernels; and (3) the absence of an intrinsic formulation for multiclass classification. We present McQuack, a trainable quantum kernel method for multiclass problems that achieves linear scaling in the number of training samples. This is accomplished by replacing the full training-set Gram matrix with a trainable sample-to-(class-centroid) fidelity matrix. We evaluate the model in simulation and on 124 qubits of two IBM devices, across more than 150 datasets. In simulation, McQuack outperforms existing "pure" quantum baselines, while results from hardware inference -- obtained without training -- achieve performance similar to an RBF kernel. Finally, we study the trainability of the model and observe no evidence of barren plateaus in our experiments with up to 13 qubits, and highlight the importance of parameter initialization for successful optimization.
Quantum computing (QC) seems to show potential for application in machine learning (ML). In particular quantum kernel methods (QKM) exhibit promising properties for use in supervised ML tasks. However, a major disadvantage of kernel methods is their unfavorable quadratic scaling with the number of training samples. Together with the limits imposed by currently available quantum hardware (NISQ devices) with their low qubit coherence times, small number of qubits, and high error rates, the use of QC in ML at an industrially relevant scale is currently impossible. As a small step in improving the potential applications of QKMs, we introduce QUACK, a quantum kernel algorithm whose time complexity scales linear with the number of samples during training, and independent of the number of training samples in the inference stage. In the training process, only the kernel entries for the samples and the centers of the classes are calculated, i.e. the maximum shape of the kernel for n samples and c classes is (n, c). During training, the parameters of the quantum kernel and the positions of the centroids are optimized iteratively. In the inference stage, for every new sample the circuit is only evaluated for every centroid, i.e. c times. We show that the QUACK algorithm nevertheless provides satisfactory results and can perform at a similar level as classical kernel methods with quadratic scaling during training. In addition, our (simulated) algorithm is able to handle high-dimensional datasets such as MNIST with 784 features without any dimensionality reduction.
Quantum kernel methods have emerged as a promising approach for leveraging high-dimensional feature spaces in machine learning, particularly in domains where classical kernel methods face scalability limitations. In this work, we present the first large-scale study of fidelity-quantum-kernel support vector machines for hyperspectral data classification without requiring heavy prior feature selection or dimensionality reduction. By simulating quantum kernels using tensor network contraction techniques and GPU acceleration, we overcome the computational bottlenecks traditionally associated with quantum models, achieving quadratic scaling O(n^2) in the number of qubits. Our approach enables the evaluation of quantum kernels on hyperspectral data with hundreds of spectral bands, aligning quantum feature spaces with real-world remote sensing applications. We provide an in-depth analysis of kernel bandwidth optimization, demonstrating its crucial role in mitigating exponential concentration effects and ensuring the model's ability to generalize. Experimental results on binary classification (Indian Pines and Methane Detection) and multiclass classification (Indian Pines) demonstrate that quantum kernels achieve competitive performance compared to a broad range of state-of-the-art classical baselines. As illustrative cases, on four 50-band splits selected from Indian Pines, the quantum model achieved a 78.0 pm6.2% accuracy for a binary classification task compared to 72.0 pm5.0% for the standard radial basis function (RBF) kernel. For a four-class classification task, the quantum kernel reached 83.3 pm3.1% accuracy, outperforming several state-of-the-art baselines. On five 75-band splits selected from the Methane Detection dataset, the quantum approach yielded 58.5\pm5.0% accuracy versus 55.1\pm2.5% for the classical counterpart...
Quantum kernel methods have emerged as a promising approach for leveraging high-dimensional feature spaces in machine learning, particularly in domains where classical kernel methods face scalability limitations. In this work, we present the first large-scale study of fidelity-quantum-kernel support vector machines for hyperspectral data classification without requiring heavy prior feature selection or dimensionality reduction. By simulating quantum kernels using tensor network contraction techniques and graphics processing unit acceleration, we overcome the computational bottlenecks traditionally associated with quantum models, achieving quadratic scaling O(n2) in the number of qubits. Our approach enables the evaluation of quantum kernels on hyperspectral data with hundreds of spectral bands, aligning quantum feature spaces with real-world remote sensing applications. We provide an in-depth analysis of kernel bandwidth optimization, demonstrating its crucial role in mitigating exponential concentration effects and ensuring the model's ability to generalize. Experimental results on binary classification (Indian Pines and methane detection) and multiclass classification (Indian Pines) demonstrate that quantum kernels achieve competitive performance compared to a broad range of state-of-the-art classical baselines. As illustrative cases, on four 50-band splits selected from Indian Pines, the quantum model achieved a 78.0±6.2% accuracy for a binary classification task compared to 72.0±5.0% for the standard radial basis function kernel. For a four-class classification task, the quantum kernel reached 83.3±3.1% accuracy, outperforming several state-of-the-art baselines. On five 75-band splits selected from the methane detection dataset, the quantum approach yielded 58.5±5.0% accuracy versus 55.1±2.5% for the classical counterpart. This study provides a foundation for future exploration of quantum machine learning in high-dimensional Earth observation tasks.
Neural quantum kernels (NQKs) construct quantum kernels by pretraining a quantum neural network (QNN) and subsequently reusing the trained circuit as a task-adapted embedding. Extending this framework to qudits, with local unitaries in SU(d), provides a natural route to richer data embeddings through the increased local degrees of freedom and a direct interface for multiclass classification via intrinsically multi-level quantum systems. In this work, focusing on qutrits (d=3), we extend NQKs to the qudit setting and perform a systematic study of key design choices, including the number of encoded features, the number of qutrits, the kernel construction (1-to-n and n-to-n), and the parameterization of SU(3) unitaries. Across binary and three-class tasks on four benchmark datasets, qutrit NQKs improve over the corresponding QNN baselines in nearly all settings considered and can benefit from scaling both the feature budget and the system size, although the magnitude of these gains may saturate, is dataset-dependent, and depends on the chosen parameterization. In particular, an ablation over SU(3) parameterizations shows that the unitary representation can substantially impact both optimization behaviour and classifier performance. These findings highlight the potential of qudit-based quantum models not only as a straightforward generalization of qubit-based architectures, but also as a promising means to better exploit complex data structures in quantum machine learning.
Kernel methods are a cornerstone of classical machine learning. The idea of using quantum computers to compute kernels has recently attracted attention. Quantum embedding kernels (QEKs), constructed by embedding data into the Hilbert space of a quantum computer, are a particular quantum kernel technique that is particularly suitable for noisy intermediate-scale quantum devices. Unfortunately, kernel methods face three major problems: Constructing the kernel matrix has quadratic computational complexity in the number of training samples, choosing the right kernel function is nontrivial, and the effects of noise are unknown. In this work, we addressed the latter two. In particular, we introduced the notion of trainable QEKs, based on the idea of classical model optimization methods. To train the parameters of the QEK, we proposed the use of kernel-target alignment. We verified the feasibility of this method, and showed that for our experimental setup we could reduce the training error significantly. Furthermore, we investigated the effects of device and finite sampling noise, and we evaluated various mitigation techniques numerically on classical hardware. We took the best performing strategy and evaluated it on data from a real quantum processing unit. We found that using this mitigation strategy demonstrated an increased kernel matrix quality.
We present a systematic design for large-scale quantum kernel classification, demonstrated through a quantum support vector classifier (QSVC) for particle-track classification using centroid-based CLAS12 drift-chamber features. Each event is encoded into a six-qubit state via a fully entangled ZZFeatureMap, whose fidelities define a quantum kernel within a standard SVM framework. By decoupling state preparation from kernel construction and distributing evaluation across a multi-node MPI-based HPC allocation, the approach scales to 1.0x10^5 training and 4.0x10^5 test events with an exactly constructed kernel matrix, to our knowledge more than an order of magnitude larger than prior high-energy-physics quantum-kernel studies.
Benchmarked against linear, polynomial, RBF, and sigmoid SVM kernels and extremely randomized trees (ERT), the ideal QSVC achieves the highest recall (99.99%) among all models. Under a calibrated hardware noise model (FakeMumbaiV2, 500 training / 2,000 test events), AUC falls from 0.9985 to 0.9671 and peak significance improvement falls from 17.5 to ~3.5, yet recall remains at 99.51% -- indicating this signal-retention advantage is attenuated but not eliminated by circuit-level decoherence.
Geometric analysis of the quantum embedding shows near-orthogonal inter-class states with coherent intra-class neighborhoods under ideal simulation; under noise this structure compresses toward the maximally mixed state while preserving its relative ordering.
These results demonstrate a scalable, reproducible workflow for quantum kernel experimentation at HEP-relevant scale, quantifying the practical cost of realistic hardware noise on quantum-enhanced classification.