The power of quantum computing and quantum machine learning relies on harnessing uniquely quantum phenomena as computational resources. While superposition, coherence and entanglement have been central to this effort, the role of particle exchange statistics remains largely unexplored. Here, we introduce a quantum kernel framework that unifies bosonic, fermionic, and anyonic (fractional) exchange statistics within a single learning paradigm. We study this family of kernels from three perspectives. At the representation level, Haar-averaged effective-dimension analysis shows that fractional exchange phases access feature-space directions inaccessible to the purely symmetric or antisymmetric limits. At the level of kernel geometry, the corresponding Gram matrices show greater separation from the distinguishable-particle baseline and reduced label-dependent model complexity. Finally, on learning benchmarks, anyonic kernels consistently outperform their bosonic and fermionic counterparts, with stronger target alignment and more favorable class geometry. Together, these findings show that exchange statistics reshape the structure and geometry of quantum feature space, leading to enhanced learning performance. Our work identifies particle exchange statistics as an overlooked computational ingredient for quantum machine learning and provides the first systematic comparison of quantum learning models across exchange phases.
The power of quantum computing and quantum machine learning relies on harnessing uniquely quantum phenomena as computational resources. While superposition, coherence and entanglement have been central to this effort, the role of particle exchange statistics remains largely unexplored. Here, we introduce a quantum kernel framework that unifies bosonic, fermionic, and anyonic (fractional) exchange statistics within a single learning paradigm. We study this family of kernels from three perspectives. At the representation level, Haar-averaged effective-dimension analysis shows that fractional exchange phases access feature-space directions inaccessible to the purely symmetric or antisymmetric limits. At the level of kernel geometry, the corresponding Gram matrices show greater separation from the distinguishable-particle baseline and reduced label-dependent model complexity. Finally, on learning benchmarks, anyonic kernels consistently outperform their bosonic and fermionic counterparts, with stronger target alignment and more favorable class geometry. Together, these findings show that exchange statistics reshape the structure and geometry of quantum feature space, leading to enhanced learning performance. Our work identifies particle exchange statistics as an overlooked computational ingredient for quantum machine learning and provides the first systematic comparison of quantum learning models across exchange phases.
Abstract Quantum machine learning, an emerging field at the intersection of quantum computing and classical machine learning, has shown great promise in enhancing computational capabilities beyond classical bounds. A key element in this area of research is the utilization of Quantum Kernel Estimators, traditionally grounded in the symmetries of SU(2) groups associated with qubits. This study extends the conceptual framework of Quantum Kernel Estimators to incorporate a broader spectrum of symmetry groups. By harnessing the various structures of Lie groups, we develop novel quantum-inspired feature maps that offer more flexible and potentially powerful ways to encode and compress classical data into quantum states. We present a comprehensive theoretical introduction for this approach, followed by a methodology that integrates the developed feature maps into kernel-based quantum classifiers. Our results, derived from a series of computational experiments across various datasets, demonstrate the efficacy of this approach in comparison to traditional quantum and classical machine learning models. The findings not only underline the versatility of Lie-group theory in enhancing quantum machine learning algorithms but also open new avenues for exploring complex symmetries in quantum information processing. This research bridges a gap between the study of symmetries and machine learning, paving the way for more sophisticated quantum algorithms capable of tackling complex, high-dimensional data in ways previously unattainable.
Quantum-enhanced machine learning is a rapidly evolving field that aims to leverage the unique properties of quantum mechanics to enhance classical machine learning. However, the practical applicability of these methods remains an open question, particularly beyond the context of specifically crafted toy problems, and given the current limitations of quantum hardware. This study focuses on quantum kernel methods in the context of classification tasks. In particular, it examines the performance of quantum kernel estimation and quantum kernel training (QKT) in connection with two quantum feature mappings, namely, ZZFeatureMap and CovariantFeatureMap. Remarkably, these feature maps have been proposed in the literature under the conjecture of possible near-term quantum advantage and have shown promising performance in ad hoc datasets. This study aims to evaluate their versatility and generalization capabilities in a more general benchmark, encompassing both artificial and established reference datasets. Classical machine learning methods, specifically support vector machines and logistic regression, are also incorporated as baseline comparisons. Experimental results indicate that quantum methods exhibit varying performance across different datasets. Despite outperforming classical methods in ad hoc datasets, mixed results are obtained for the general case among standard classical benchmarks. The experimental data call into question a general added value of applying QKT optimization, for which the additional computational cost does not necessarily translate into improved classification performance. Instead, it is suggested that a careful choice of the quantum feature map in connection with proper hyperparameterization may prove more effective.
Quantum kernel methods have been proposed as a promising approach for leveraging near-term quantum computers for supervised learning, yet rigorous benchmarks against strong classical baselines remain scarce. We present a comprehensive empirical study of quantum kernel support vector machines (QSVMs) across nine binary classification datasets, four quantum feature maps, three classical kernels, and multiple noise models, totalling 970 experiments with strict nested cross-validation.
Our analysis spans four phases: (i) statistical significance testing, revealing that none of 29 pairwise quantum-classical comparisons reach significance at α=0.05; (ii) learning curve analysis over six training fractions, showing steeper quantum slopes on six of eight datasets that nonetheless fail to close the gap to the best classical baseline; (iii) hardware validation on IBM ibm_fez (Heron r2), demonstrating kernel fidelity r≥0.976 across six experiments; and (iv) seed sensitivity analysis confirming reproducibility (mean CV 1.4%).
A Kruskal-Wallis factorial analysis reveals that dataset choice dominates performance variance (ε2=0.73), while kernel type accounts for only 9%. Spectral analysis offers a mechanistic explanation: current quantum feature maps produce eigenspectra that are either too flat or too concentrated, missing the intermediate profile of the best classical kernel, the radial basis function (RBF). Quantum kernel training (QKT) via kernel-target alignment yields the single competitive result -- balanced accuracy 0.968 on breast cancer -- but with ~2,000x computational overhead.
Our findings provide actionable guidelines for quantum kernel research. The complete benchmark suite is publicly available to facilitate reproduction and extension.
This thesis explores the integration of quantum computing into Machine Learning (ML), aiming to evaluate the effectiveness and limitations of quantum-enhanced models compared to classical approaches. As quantum technologies continue to develop, they offer the potential for solving complex computational problems more efficiently, particularly in fields requiring high-dimensional data processing. A literature review is conducted to contextualize current advancements in Quantum Machine Learning, highlighting theoretical benefits and existing practical limitations. This work investigates whether quantum methods, specifically the Quantum Support Vector Classifier (QSVC), can provide measurable improvements over its classical counterpart. The QSVC, implemented using IBM’s Qiskit ML library, replaces traditional kernel functions with quantum kernels computed via quantum circuits and feature maps, embedding classical data into a Hilbert space. The experimental portion of this thesis compares classical and quantum models on two distinct datasets: one from the healthcare domain and another from particle physics. Various parameters are tested in a constrained grid search due to the high computational demands of quantum circuits. Results indicate that while quantum models are significantly more resource-intensive, they can achieve comparable or even improved performance on data that has more complex relations between their variables. However, scalability remains a major challenge. This work concludes that although QSVC does not yet consistently outperform classical models, it offers advantages in specific contexts and lays the groundwork for identifying future use cases where quantum computing may offer a practical advantage in ML.
Abstract Quantum Machine Learning (QML) is an emerging field at the intersection of quantum computing and artificial intelligence, offering high potential for extracting complex nonlinear patterns from high-dimensional data. However, many quantum kernel-based methods suffer from high computational costs, the requirement for numerous quantum circuit executions, and the limitations of current Noisy Intermediate-Scale Quantum (NISQ) hardware. These challenges, particularly when dealing with large datasets, represent a major barrier to the widespread adoption of these methods in practical applications. In this paper, a hybrid quantum machine learning framework based on Nyström approximation is proposed to effectively reduce the computational complexity of quantum kernels and enhance their scalability. In the proposed framework, classical data is first mapped to the quantum Hilbert space via parameterized quantum circuits, and the quantum kernel is defined based on the overlap of quantum states. Then, utilizing the Nyström approximation technique, the full kernel calculation is restricted to a representative subset of data, and the final learning process is conducted in the classical space. This approach reduces computational complexity from O(N2) to O(Nm), where N is the number of samples and m is the size of the selected subset. Analytical results and simulations on the Breast Cancer Wisconsin dataset demonstrate that the proposed framework reduces computational costs by over 60% while maintaining the geometric structure of the quantum feature space, with a classification accuracy loss of less than 3%. These results suggest that the proposed method can serve as a practical, scalable, and noise-resilient solution for applying quantum machine learning to real-world data-driven problems.
The integration of quantum computing into classical machine learning architectures has emerged as a promising approach to enhance model efficiency and computational capacity. In this work, we introduce the Quantum Kernel-Based Long Short-Term Memory (QK-LSTM) network, which utilizes quantum kernel functions within the classical LSTM framework to capture complex, non-linear patterns in sequential data. By embedding input data into a high-dimensional quantum feature space, the QK-LSTM model reduces the reliance on large parameter sets, achieving effective compression while maintaining accuracy in sequence modeling tasks. This quantum-enhanced architecture demonstrates efficient convergence, robust loss minimization, and model compactness, making it suitable for deployment in edge computing environments and resource-limited quantum devices (especially in the NISQ era). Benchmark comparisons reveal that QK-LSTM achieves performance on par with classical LSTM models, yet with fewer parameters, underscoring its potential to advance quantum machine learning applications in natural language processing and other domains requiring efficient temporal data processing.